Index

_

_base_ordering() (in module sympy.combinatorics.util) _check_cycles_alt_sym() (in module sympy.combinatorics.util) _cmp_perm_lists() (in module sympy.combinatorics.testutil) _distribute_gens_by_base() (in module sympy.combinatorics.util) _handle_precomputed_bsgs() (in module sympy.combinatorics.util) _LorentzContainer (class in sympy.physics.hep.gamma_matrices) _naive_list_centralizer() (in module sympy.combinatorics.testutil) _orbits_transversals_from_bsgs() (in module sympy.combinatorics.util)

_print() (sympy.printing.printer.Printer method) _remove_gens() (in module sympy.combinatorics.util) _strip() (in module sympy.combinatorics.util) _strong_gens_from_distr() (in module sympy.combinatorics.util) _TensorManager (class in sympy.tensor.tensor) _verify_bsgs() (in module sympy.combinatorics.testutil) _verify_centralizer() (in module sympy.combinatorics.testutil) _verify_normal_closure() (in module sympy.combinatorics.testutil)

A

A (sympy.physics.gaussopt.RayTransferMatrix attribute) a (sympy.physics.quantum.shor.CMod attribute) a1pt_theory() (sympy.physics.vector.point.Point method) a2idx() (in module sympy.matrices.matrices) a2pt_theory() (sympy.physics.vector.point.Point method) AbelianGroup() (in module sympy.combinatorics.named_groups) above() (sympy.printing.pretty.stringpict.stringPict method) Abs (class in sympy.functions.elementary.complexes) abs() (sympy.polys.domains.domain.Domain method) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) acc() (sympy.physics.vector.point.Point method) accepted_latex_functions (in module sympy.printing.latex) acos (class in sympy.functions.elementary.trigonometric) acos() (in module mpmath) acosh (class in sympy.functions.elementary.hyperbolic) acosh() (in module mpmath) acot (class in sympy.functions.elementary.trigonometric) acot() (in module mpmath) acoth (class in sympy.functions.elementary.hyperbolic) acoth() (in module mpmath) acsc() (in module mpmath) acsch() (in module mpmath) Add (class in sympy.core.add) add() (sympy.assumptions.assume.AssumptionsContext method) Add() (sympy.assumptions.handlers.calculus.AskBoundedHandler static method) (sympy.assumptions.handlers.calculus.AskInfinitesimalHandler static method) (sympy.assumptions.handlers.order.AskNegativeHandler static method) (sympy.assumptions.handlers.sets.AskAntiHermitianHandler static method) (sympy.assumptions.handlers.sets.AskHermitianHandler static method) (sympy.assumptions.handlers.sets.AskImaginaryHandler static method) (sympy.assumptions.handlers.sets.AskIntegerHandler static method) (sympy.assumptions.handlers.sets.AskRationalHandler static method) (sympy.assumptions.handlers.sets.AskRealHandler static method) add() (sympy.matrices.matrices.MatrixBase method) (sympy.matrices.sparse.SparseMatrix method) (sympy.polys.domains.domain.Domain method) (sympy.polys.polyclasses.DMF method) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) add_ground() (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) add_paren() (in module sympy.galgebra.precedence) adjoint() (sympy.matrices.immutable.ImmutableMatrix method) (sympy.matrices.matrices.MatrixBase method) adjugate() (sympy.matrices.matrices.MatrixBase method) agm() (in module mpmath) airyai (class in sympy.functions.special.bessel) airyai() (in module mpmath) airyaiprime (class in sympy.functions.special.bessel) airyaizero() (in module mpmath) AiryBase (class in sympy.functions.special.bessel) airybi (class in sympy.functions.special.bessel) airybi() (in module mpmath) airybiprime (class in sympy.functions.special.bessel) airybizero() (in module mpmath) algebraic_field() (sympy.polys.domains.AlgebraicField method) (sympy.polys.domains.IntegerRing method) (sympy.polys.domains.RationalField method) (sympy.polys.domains.domain.Domain method) AlgebraicField (class in sympy.polys.domains) AlgebraicNumber (class in sympy.polys.numberfields) all_coeffs() (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) all_monoms() (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) all_roots() (sympy.polys.polytools.Poly method) all_terms() (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) allhints (in module sympy.solvers.ode) almosteq() (in module mpmath) (sympy.polys.domains.RealField method) (sympy.polys.domains.domain.Domain method) alphabet_of_cipher() (in module sympy.crypto.crypto) alternating() (sympy.combinatorics.generators static method) AlternatingGroup() (in module sympy.combinatorics.named_groups) altitudes (sympy.geometry.polygon.Triangle attribute) altzeta() (in module mpmath) an (sympy.functions.special.hyper.meijerg attribute) And (class in sympy.logic.boolalg) Anderson (class in mpmath.calculus.optimization) ANewton (class in mpmath.calculus.optimization) ang_acc_in() (sympy.physics.vector.frame.ReferenceFrame method) ang_vel_in() (sympy.physics.vector.frame.ReferenceFrame method) angerj() (in module mpmath) angle (sympy.physics.gaussopt.GeometricRay attribute) angle_between() (sympy.geometry.line.LinearEntity method) angles (sympy.geometry.polygon.Polygon attribute) (sympy.geometry.polygon.RegularPolygon attribute) angular_momentum() (in module sympy.physics.mechanics.functions) (sympy.physics.mechanics.particle.Particle method) (sympy.physics.mechanics.rigidbody.RigidBody method) AnnihilateBoson (class in sympy.physics.secondquant) AnnihilateFermion (class in sympy.physics.secondquant) annotated() (in module sympy.printing.pretty.pretty_symbology) ANP (class in sympy.polys.polyclasses) AntiCommutator (class in sympy.physics.quantum.anticommutator) AntiSymmetricTensor (class in sympy.physics.secondquant) any() (in module sympy.parsing.sympy_tokenize) aother (sympy.functions.special.hyper.meijerg attribute) ap (sympy.functions.special.hyper.hyper attribute) (sympy.functions.special.hyper.meijerg attribute) apart() (in module sympy.polys.partfrac) (sympy.core.expr.Expr method) apart_list() (in module sympy.polys.partfrac) apery (mpmath.mp attribute) apoapsis (sympy.geometry.ellipse.Ellipse attribute) apothem (sympy.geometry.polygon.RegularPolygon attribute) appellf1() (in module mpmath) appellf2() (in module mpmath) appellf3() (in module mpmath) appellf4() (in module mpmath) append() (sympy.plotting.plot.Plot method) AppliedPredicate (class in sympy.assumptions.assume) apply() (sympy.printing.pretty.stringpict.prettyForm static method) (sympy.simplify.epathtools.EPath method) apply_grover() (in module sympy.physics.quantum.grover) apply_operator() (sympy.physics.secondquant.AnnihilateBoson method) (sympy.physics.secondquant.AnnihilateFermion method) (sympy.physics.secondquant.CreateBoson method) (sympy.physics.secondquant.CreateFermion method) apply_operators() (in module sympy.physics.secondquant) applyfunc() (sympy.matrices.sparse.SparseMatrix method) (sympy.tensor.tensor.TensAdd method) (sympy.tensor.tensor.TensMul method) approximation() (sympy.core.numbers.NumberSymbol method) arange() (in module mpmath) arbitrary_metric() (in module sympy.galgebra.ga)

arbitrary_metric_conformal() (in module sympy.galgebra.ga) arbitrary_point() (sympy.geometry.curve.Curve method) (sympy.geometry.ellipse.Ellipse method) (sympy.geometry.line.LinearEntity method) (sympy.geometry.polygon.Polygon method) Arcsin() (in module sympy.stats) are_similar() (in module sympy.geometry.util) area (sympy.geometry.ellipse.Ellipse attribute) (sympy.geometry.polygon.Polygon attribute) (sympy.geometry.polygon.RegularPolygon attribute) arg (class in sympy.functions.elementary.complexes) (sympy.assumptions.assume.AppliedPredicate attribute) arg() (in module mpmath) args (sympy.core.basic.Basic attribute) (sympy.geometry.polygon.RegularPolygon attribute) (sympy.polys.polytools.Poly attribute) (sympy.tensor.indexed.IndexedBase attribute) args_cnc() (sympy.core.expr.Expr method) Argument (class in sympy.utilities.codegen) argument (sympy.functions.special.bessel.BesselBase attribute) (sympy.functions.special.hyper.hyper attribute) (sympy.functions.special.hyper.meijerg attribute) array_form (sympy.combinatorics.permutations.Permutation attribute) (sympy.combinatorics.polyhedron.Polyhedron attribute) ArrowStringDescription (class in sympy.categories.diagram_drawing) as_base_exp() (sympy.core.function.Function method) (sympy.core.power.Pow method) (sympy.functions.elementary.exponential.log method) as_coeff_add() (sympy.core.add.Add method) as_coeff_Add() (sympy.core.add.Add method) (sympy.core.expr.Expr method) as_coeff_add() (sympy.core.expr.Expr method) as_coeff_Add() (sympy.core.numbers.Number method) as_coeff_exponent() (sympy.core.expr.Expr method) as_coeff_Mul() (sympy.core.expr.Expr method) as_coeff_mul() (sympy.core.expr.Expr method) as_coeff_Mul() (sympy.core.mul.Mul method) (sympy.core.numbers.Number method) as_coefficient() (sympy.core.expr.Expr method) as_coefficients_dict() (sympy.core.add.Add method) (sympy.core.expr.Expr method) as_content_primitive() (sympy.core.add.Add method) (sympy.core.basic.Basic method) (sympy.core.expr.Expr method) (sympy.core.mul.Mul method) (sympy.core.numbers.Rational method) (sympy.core.power.Pow method) as_dict() (sympy.combinatorics.partitions.IntegerPartition method) (sympy.polys.polytools.Poly method) as_explicit() (sympy.matrices.expressions.MatrixExpr method) as_expr() (sympy.core.expr.Expr method) (sympy.polys.numberfields.AlgebraicNumber method) (sympy.polys.polytools.Poly method) as_ferrers() (sympy.combinatorics.partitions.IntegerPartition method) as_immutable() (sympy.matrices.sparse.SparseMatrix method) as_independent() (sympy.core.expr.Expr method) as_int() (in module sympy.core.compatibility) as_leading_term() (sympy.core.expr.Expr method) as_list() (sympy.polys.polytools.Poly method) as_mutable() (sympy.matrices.expressions.MatrixExpr method) (sympy.matrices.immutable.ImmutableMatrix method) (sympy.matrices.sparse.SparseMatrix method) as_numer_denom() (sympy.core.expr.Expr method) as_ordered_factors() (sympy.core.expr.Expr method) (sympy.core.mul.Mul method) as_ordered_terms() (sympy.core.expr.Expr method) as_poly() (sympy.core.basic.Basic method) (sympy.polys.numberfields.AlgebraicNumber method) as_powers_dict() (sympy.core.expr.Expr method) as_real_imag() (sympy.core.add.Add method) (sympy.core.expr.Expr method) (sympy.functions.elementary.complexes.re method) (sympy.functions.elementary.exponential.exp method) (sympy.functions.elementary.exponential.log method) (sympy.functions.elementary.hyperbolic.sinh method) as_relational() (sympy.core.sets.FiniteSet method) (sympy.core.sets.Intersection method) (sympy.core.sets.Interval method) (sympy.core.sets.Union method) as_sum() (sympy.integrals.Integral method) as_terms() (sympy.core.expr.Expr method) as_two_terms() (sympy.core.add.Add method) (sympy.core.mul.Mul method) ascents() (sympy.combinatorics.permutations.Permutation method) asec() (in module mpmath) asech() (in module mpmath) asin (class in sympy.functions.elementary.trigonometric) asin() (in module mpmath) asinh (class in sympy.functions.elementary.hyperbolic) asinh() (in module mpmath) ask() (in module sympy.assumptions.ask) ask_full_inference() (in module sympy.assumptions.ask) AskAlgebraicHandler (class in sympy.assumptions.handlers.sets) AskAntiHermitianHandler (class in sympy.assumptions.handlers.sets) AskBoundedHandler (class in sympy.assumptions.handlers.calculus) AskComplexHandler (class in sympy.assumptions.handlers.sets) AskExtendedRealHandler (class in sympy.assumptions.handlers.sets) AskHermitianHandler (class in sympy.assumptions.handlers.sets) AskImaginaryHandler (class in sympy.assumptions.handlers.sets) AskInfinitesimalHandler (class in sympy.assumptions.handlers.calculus) AskIntegerHandler (class in sympy.assumptions.handlers.sets) AskNegativeHandler (class in sympy.assumptions.handlers.order) AskNonZeroHandler (class in sympy.assumptions.handlers.order) AskOddHandler (class in sympy.assumptions.handlers.ntheory) AskPositiveHandler (class in sympy.assumptions.handlers.order) AskPrimeHandler (class in sympy.assumptions.handlers.ntheory) AskRationalHandler (class in sympy.assumptions.handlers.sets) AskRealHandler (class in sympy.assumptions.handlers.sets) assemble_partfrac_list() (in module sympy.polys.partfrac) AssignmentError assoc_laguerre (class in sympy.functions.special.polynomials) assoc_legendre (class in sympy.functions.special.polynomials) assoc_recurrence_memo() (in module sympy.utilities.memoization) assuming() (in module sympy.assumptions.assume) assumptions0 (sympy.core.basic.Basic attribute) AssumptionsContext (class in sympy.assumptions.assume) atan (class in sympy.functions.elementary.trigonometric) atan() (in module mpmath) atan2 (class in sympy.functions.elementary.trigonometric) atan2() (in module mpmath) atanh (class in sympy.functions.elementary.hyperbolic) atanh() (in module mpmath) Atom (class in sympy.core.basic) AtomicExpr (class in sympy.core.expr) atoms() (sympy.combinatorics.permutations.Permutation method) (sympy.core.basic.Basic method) (sympy.matrices.matrices.MatrixBase method) atoms_table (in module sympy.printing.pretty.pretty_symbology) auto_number() (in module sympy.parsing.sympy_parser) auto_symbol() (in module sympy.parsing.sympy_parser) autoprec() (in module mpmath) autowrap() (in module sympy.utilities.autowrap)

B

B (in module sympy.physics.secondquant) (sympy.physics.gaussopt.RayTransferMatrix attribute) backlunds() (in module mpmath) barnesg() (in module mpmath) base (sympy.combinatorics.perm_groups.PermutationGroup attribute) (sympy.functions.elementary.exponential.exp attribute) (sympy.tensor.indexed.Indexed attribute) base_oneform() (sympy.diffgeom.CoordSystem method) base_oneforms() (sympy.diffgeom.CoordSystem method) base_solution_linear() (in module sympy.solvers.diophantine) base_vector() (sympy.diffgeom.CoordSystem method) base_vectors() (sympy.diffgeom.CoordSystem method) BaseCovarDerivativeOp (class in sympy.diffgeom) BasePolynomialError (class in sympy.polys.polyerrors) BaseScalarField (class in sympy.diffgeom) BaseSeries (class in sympy.plotting.plot) baseswap() (sympy.combinatorics.perm_groups.PermutationGroup method) BaseVectorField (class in sympy.diffgeom) Basic (class in sympy.core.basic) basic_dot() (sympy.galgebra.vector.Vector static method) basic_orbits (sympy.combinatorics.perm_groups.PermutationGroup attribute) basic_stabilizers (sympy.combinatorics.perm_groups.PermutationGroup attribute) basic_transversals (sympy.combinatorics.perm_groups.PermutationGroup attribute) Basis() (in module sympy.galgebra.ga) basis() (sympy.polys.agca.modules.FreeModule method) BBra (in module sympy.physics.secondquant) Bd (in module sympy.physics.secondquant) BeamParameter (class in sympy.physics.gaussopt) bei() (in module mpmath) bell (class in sympy.functions.combinatorial.numbers) bell() (in module mpmath) below() (sympy.printing.pretty.stringpict.stringPict method) Benini() (in module sympy.stats) ber() (in module mpmath) berkowitz() (sympy.matrices.matrices.MatrixBase method) berkowitz_charpoly() (sympy.matrices.matrices.MatrixBase method) berkowitz_det() (sympy.matrices.matrices.MatrixBase method) berkowitz_eigenvals() (sympy.matrices.matrices.MatrixBase method) berkowitz_minors() (sympy.matrices.matrices.MatrixBase method) bernfrac() (in module mpmath) bernoulli (class in sympy.functions.combinatorial.numbers) bernoulli() (in module mpmath) Bernoulli() (in module sympy.stats) bernpoly() (in module mpmath) BesselBase (class in sympy.functions.special.bessel) besseli (class in sympy.functions.special.bessel) besseli() (in module mpmath) besselj (class in sympy.functions.special.bessel) besselj() (in module mpmath) besseljzero() (in module mpmath)

besselk (class in sympy.functions.special.bessel) besselk() (in module mpmath) besselsimp() (in module sympy.simplify.simplify) bessely (class in sympy.functions.special.bessel) bessely() (in module mpmath) besselyzero() (in module mpmath) beta() (in module mpmath) (in module sympy.functions.special.gamma_functions) Beta() (in module sympy.stats) betainc() (in module mpmath) BetaPrime() (in module sympy.stats) bifid5_square() (in module sympy.crypto.crypto) bifid6_square() (in module sympy.crypto.crypto) bifid7_square() (in module sympy.crypto.crypto) bihyper() (in module mpmath) bilinear_function() (in module sympy.galgebra.ncutil) bilinear_product() (in module sympy.galgebra.ncutil) bin_to_gray() (sympy.combinatorics.graycode static method) binary_function() (in module sympy.utilities.autowrap) binary_partitions() (in module sympy.utilities.iterables) binomial (class in sympy.functions.combinatorial.factorials) binomial() (in module mpmath) Binomial() (in module sympy.stats) binomial_coefficients() (in module sympy.ntheory.multinomial) binomial_coefficients_list() (in module sympy.ntheory.multinomial) Bisection (class in mpmath.calculus.optimization) bisectors() (sympy.geometry.polygon.Triangle method) bitlist_from_subset() (sympy.combinatorics.subsets.Subset class method) BKet (in module sympy.physics.secondquant) block_collapse() (in module sympy.matrices.expressions.blockmatrix) BlockDiagMatrix (class in sympy.matrices.expressions.blockmatrix) BlockMatrix (class in sympy.matrices.expressions.blockmatrix) bm (sympy.functions.special.hyper.meijerg attribute) bool_map() (in module sympy.logic.boolalg) BooleanFalse (class in sympy.logic.boolalg) BooleanTrue (class in sympy.logic.boolalg) BosonicBasis (class in sympy.physics.secondquant) bother (sympy.functions.special.hyper.meijerg attribute) boundary (sympy.core.sets.Set attribute) bq (sympy.functions.special.hyper.hyper attribute) (sympy.functions.special.hyper.meijerg attribute) Bra (class in sympy.physics.quantum.state) bra (sympy.physics.quantum.operator.OuterProduct attribute) (sympy.physics.secondquant.InnerProduct attribute) BraBase (class in sympy.physics.quantum.state) bracelets() (in module sympy.utilities.iterables) bsgs_direct_product() (in module sympy.combinatorics.tensor_can) bspline_basis() (in module sympy.functions.special.bsplines) bspline_basis_set() (in module sympy.functions.special.bsplines) build_expression_tree() (in module sympy.series.gruntz)

C

C (in module sympy.core.basic) (sympy.matrices.immutable.ImmutableMatrix attribute) (sympy.matrices.matrices.MatrixBase attribute) (sympy.physics.gaussopt.RayTransferMatrix attribute) cacheit() (in module sympy.core.cache) calc_nodes() (mpmath.calculus.quadrature.GaussLegendre method) (mpmath.calculus.quadrature.QuadratureRule method) (mpmath.calculus.quadrature.TanhSinh method) calculate_series() (in module sympy.series.gruntz) cancel() (in module sympy.polys.polytools) (sympy.core.expr.Expr method) (sympy.polys.polyclasses.DMF method) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) canon_args() (sympy.tensor.tensor.TIDS method) canon_bp() (in module sympy.tensor.tensor) (sympy.tensor.tensor.TensAdd method) (sympy.tensor.tensor.TensMul method) canonical_variables (sympy.core.basic.Basic attribute) canonicalize() (in module sympy.combinatorics.tensor_can) capture() (in module sympy.utilities.iterables) cardinality (sympy.combinatorics.permutations.Permutation attribute) (sympy.combinatorics.subsets.Subset attribute) casoratian() (in module sympy.matrices.dense) Catalan (class in sympy.core.numbers) catalan (class in sympy.functions.combinatorial.numbers) (mpmath.mp attribute) Category (class in sympy.categories) Cauchy() (in module sympy.stats) cbrt() (in module mpmath) ccode() (in module sympy.printing.ccode) CCodeGen (class in sympy.utilities.codegen) CCodePrinter (class in sympy.printing.ccode) cdf() (sympy.statistics.distributions.Normal method) (sympy.statistics.distributions.PDF method) (sympy.statistics.distributions.Uniform method) ceil() (in module mpmath) ceiling (class in sympy.functions.elementary.integers) center (sympy.geometry.ellipse.Ellipse attribute) (sympy.geometry.polygon.RegularPolygon attribute) center() (sympy.combinatorics.perm_groups.PermutationGroup method) central_inertia (sympy.physics.mechanics.rigidbody.RigidBody attribute) centralizer() (sympy.combinatorics.perm_groups.PermutationGroup method) centroid (sympy.geometry.polygon.Polygon attribute) (sympy.geometry.polygon.RegularPolygon attribute) centroid() (in module sympy.geometry.util) CG (class in sympy.physics.quantum.cg) cg_simp() (in module sympy.physics.quantum.cg) CGate (class in sympy.physics.quantum.gate) CGateS (class in sympy.physics.quantum.gate) characteristic() (sympy.polys.domains.domain.Domain method) (sympy.polys.domains.FiniteField method) charpoly() (sympy.matrices.matrices.MatrixBase method) chebyfit() (in module mpmath) chebyshevt (class in sympy.functions.special.polynomials) chebyshevt_poly() (in module sympy.polys.orthopolys) chebyshevt_root (class in sympy.functions.special.polynomials) chebyshevu (class in sympy.functions.special.polynomials) chebyshevu_poly() (in module sympy.polys.orthopolys) chebyshevu_root (class in sympy.functions.special.polynomials) chebyt() (in module mpmath) chebyu() (in module mpmath) check_assumptions() (in module sympy.solvers.solvers) check_output() (sympy.utilities.runtests.SymPyOutputChecker method) checkinfsol() (in module sympy.solvers.ode) checkodesol() (in module sympy.solvers.ode) checkpdesol() (in module sympy.solvers.pde) checksol() (in module sympy.solvers.solvers) Chi (class in sympy.functions.special.error_functions) chi() (in module mpmath) Chi() (in module sympy.stats) ChiNoncentral() (in module sympy.stats) ChiSquared() (in module sympy.stats) cholesky() (in module mpmath) (sympy.matrices.matrices.MatrixBase method) (sympy.matrices.sparse.SparseMatrix method) cholesky_solve() (sympy.matrices.matrices.MatrixBase method) chop() (in module mpmath) Ci (class in sympy.functions.special.error_functions) ci() (in module mpmath) Circle (class in sympy.geometry.ellipse) circumcenter (sympy.geometry.polygon.RegularPolygon attribute) (sympy.geometry.polygon.Triangle attribute) circumcircle (sympy.geometry.polygon.RegularPolygon attribute) (sympy.geometry.polygon.Triangle attribute) circumference (sympy.geometry.ellipse.Circle attribute) (sympy.geometry.ellipse.Ellipse attribute) circumradius (sympy.geometry.polygon.RegularPolygon attribute) (sympy.geometry.polygon.Triangle attribute) CL (sympy.matrices.sparse.SparseMatrix attribute) class_key() (sympy.core.add.Add class method) (sympy.core.basic.Basic class method) classify_diop() (in module sympy.solvers.diophantine) classify_ode() (in module sympy.solvers.ode) classify_pde() (in module sympy.solvers.pde) classof() (in module sympy.matrices.matrices) clcos() (in module mpmath) clear() (mpmath.calculus.quadrature.QuadratureRule method) (sympy.tensor.tensor._TensorManager method) clear_denoms() (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) clebsch_gordan() (in module sympy.physics.wigner) clsin() (in module mpmath) CMod (class in sympy.physics.quantum.shor) CNOT (in module sympy.physics.quantum.gate) CNotGate (class in sympy.physics.quantum.gate) CodeGen (class in sympy.utilities.codegen) codegen() (in module sympy.utilities.codegen) CodePrinter (class in sympy.printing.codeprinter) CodeWrapper (class in sympy.utilities.autowrap) codomain (sympy.categories.CompositeMorphism attribute) (sympy.categories.Morphism attribute) coef_function() (in module sympy.galgebra.ncutil) coeff() (sympy.core.expr.Expr method) coeff_monomial() (sympy.polys.polytools.Poly method) coefficients (sympy.geometry.line.LinearEntity attribute) coeffs() (sympy.polys.numberfields.AlgebraicNumber method) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) CoercionFailed (class in sympy.polys.polyerrors) cofactor() (sympy.matrices.matrices.MatrixBase method) cofactorMatrix() (sympy.matrices.matrices.MatrixBase method) cofactors() (in module sympy.polys.polytools) (sympy.core.numbers.Number method) (sympy.polys.domains.domain.Domain method) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) cohen_alt() (in module mpmath) Coin() (in module sympy.stats) col() (sympy.matrices.sparse.SparseMatrix method) col_del() (sympy.matrices.dense.MutableDenseMatrix method) (sympy.matrices.sparse.MutableSparseMatrix method) col_insert() (sympy.matrices.matrices.MatrixBase method) col_join() (sympy.matrices.matrices.MatrixBase method) (sympy.matrices.sparse.MutableSparseMatrix method) col_list() (sympy.matrices.sparse.SparseMatrix method) col_op() (sympy.matrices.dense.MutableDenseMatrix method) (sympy.matrices.sparse.MutableSparseMatrix method) col_swap() (sympy.matrices.dense.MutableDenseMatrix method) (sympy.matrices.sparse.MutableSparseMatrix method) collect() (in module sympy.simplify.simplify) (sympy.core.expr.Expr method) collect_const() (in module sympy.simplify.simplify) collect_sqrt() (in module sympy.simplify.simplify) combsimp() (in module sympy.simplify.simplify) (sympy.core.expr.Expr method) comm_i2symbol() (sympy.tensor.tensor._TensorManager method) comm_symbols2i() (sympy.tensor.tensor._TensorManager method) common_prefix() (in module sympy.utilities.iterables) common_suffix() (in module sympy.utilities.iterables)

commutative_diagrams (sympy.categories.Category attribute) Commutator (class in sympy.diffgeom) (class in sympy.physics.quantum.commutator) (class in sympy.physics.secondquant) commutator() (sympy.combinatorics.perm_groups.PermutationGroup method) (sympy.combinatorics.permutations.Permutation method) commutes_with() (sympy.combinatorics.permutations.Permutation method) (sympy.tensor.tensor.TensorHead method) comp() (in module sympy.utilities.randtest) compare() (in module sympy.series.gruntz) (sympy.core.basic.Basic method) compare_pretty() (sympy.core.basic.Basic static method) complement (sympy.core.sets.Set attribute) ComplexInfinity (class in sympy.core.numbers) ComplexSpace (class in sympy.physics.quantum.hilbert) components (sympy.categories.CompositeMorphism attribute) compose() (in module sympy.polys.polytools) (sympy.categories.Morphism method) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) CompositeDomain (class in sympy.polys.domains.compositedomain) CompositeMorphism (class in sympy.categories) ComputationFailed (class in sympy.polys.polyerrors) compute_known_facts() (in module sympy.assumptions.ask) compute_leading_term() (sympy.core.expr.Expr method) conclusions (sympy.categories.Diagram attribute) cond (sympy.functions.elementary.piecewise.ExprCondPair attribute) condition_number() (sympy.matrices.matrices.MatrixBase method) ConditionalDomain (class in sympy.stats.rv) confidence() (sympy.statistics.distributions.Normal method) (sympy.statistics.distributions.Uniform method) conj() (in module mpmath) conjugate (class in sympy.functions.elementary.complexes) (sympy.combinatorics.partitions.IntegerPartition attribute) conjugate_gauss_beams() (in module sympy.physics.gaussopt) connect_to() (sympy.diffgeom.CoordSystem method) conserve_mpmath_dps() (in module sympy.utilities.decorator) constant_renumber() (in module sympy.solvers.ode) constantsimp() (in module sympy.solvers.ode) construct_domain() (in module sympy.polys.constructor) contains() (sympy.combinatorics.perm_groups.PermutationGroup method) (sympy.core.sets.Set method) (sympy.geometry.line.Line method) (sympy.geometry.line.LinearEntity method) (sympy.geometry.line.Ray method) (sympy.geometry.line.Segment method) (sympy.polys.agca.ideals.Ideal method) (sympy.polys.agca.modules.Module method) (sympy.polys.polytools.GroebnerBasis method) (sympy.series.order.Order method) contains_interval() (in module sympy.galgebra.precedence) content() (in module sympy.polys.polytools) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) continued_fraction() (in module sympy.physics.quantum.shor) ContinuousDomain (class in sympy.stats.crv) ContinuousProbability (class in sympy.statistics.distributions) ContinuousPSpace (class in sympy.stats.crv) ContinuousRV() (in module sympy.stats) contract_metric() (sympy.tensor.tensor.TensAdd method) (sympy.tensor.tensor.TensMul method) contraction() (in module sympy.physics.secondquant) controls (sympy.physics.quantum.gate.CGate attribute) (sympy.physics.quantum.gate.CNotGate attribute) convergence_statement (sympy.functions.special.hyper.hyper attribute) convert() (sympy.polys.agca.modules.FreeModule method) (sympy.polys.agca.modules.Module method) (sympy.polys.agca.modules.QuotientModule method) (sympy.polys.agca.modules.SubModule method) (sympy.polys.domains.domain.Domain method) (sympy.polys.polyclasses.DMP method) convert_from() (sympy.polys.domains.domain.Domain method) convert_to_native_paths() (in module sympy.utilities.runtests) convert_xor() (in module sympy.parsing.sympy_parser) convex_hull() (in module sympy.geometry.util) coord_function() (sympy.diffgeom.CoordSystem method) coord_functions() (sympy.diffgeom.CoordSystem method) coord_tuple_transform_to() (sympy.diffgeom.CoordSystem method) CoordinateSym (class in sympy.physics.vector.frame) coords() (sympy.diffgeom.Point method) CoordSystem (class in sympy.diffgeom) copyin_list() (sympy.matrices.dense.MutableDenseMatrix method) copyin_matrix() (sympy.matrices.dense.MutableDenseMatrix method) cornacchia() (in module sympy.solvers.diophantine) corners (sympy.combinatorics.polyhedron.Polyhedron attribute) correct_signature_from_indices() (sympy.tensor.tensor.VTIDS method) cos (class in sympy.functions.elementary.trigonometric) cos() (in module mpmath) coset_factor() (sympy.combinatorics.perm_groups.PermutationGroup method) coset_rank() (sympy.combinatorics.perm_groups.PermutationGroup method) coset_unrank() (sympy.combinatorics.perm_groups.PermutationGroup method) cosh (class in sympy.functions.elementary.hyperbolic) cosh() (in module mpmath) cosine_transform() (in module sympy.integrals.transforms) cosm() (in module mpmath) cospi() (in module mpmath) cot (class in sympy.functions.elementary.trigonometric) cot() (in module mpmath) coth (class in sympy.functions.elementary.hyperbolic) coth() (in module mpmath) could_extract_minus_sign() (sympy.core.expr.Expr method) coulombc() (in module mpmath) coulombf() (in module mpmath) coulombg() (in module mpmath) count() (sympy.core.basic.Basic method) count_complex_roots() (sympy.polys.polyclasses.DMP method) count_ops() (in module sympy.core.function) (sympy.core.basic.Basic method) (sympy.core.expr.Expr method) count_partitions() (sympy.utilities.enumerative.MultisetPartitionTraverser method) count_real_roots() (sympy.polys.polyclasses.DMP method) count_roots() (in module sympy.polys.polytools) (sympy.polys.polytools.Poly method) couple() (in module sympy.physics.quantum.spin) CovarDerivativeOp (class in sympy.diffgeom) cplot() (in module mpmath) CreateBoson (class in sympy.physics.secondquant) CreateCGate() (in module sympy.physics.quantum.circuitplot) CreateFermion (class in sympy.physics.secondquant) cross() (in module sympy.physics.vector.functions) (sympy.matrices.matrices.MatrixBase method) (sympy.physics.vector.dyadic.Dyadic method) (sympy.physics.vector.vector.Vector method) crt() (in module sympy.ntheory.modular) crt1() (in module sympy.ntheory.modular) crt2() (in module sympy.ntheory.modular) csc() (in module mpmath) csch() (in module mpmath) cse() (in module sympy.simplify.cse_main) current (sympy.combinatorics.graycode.GrayCode attribute) Curve (class in sympy.geometry.curve) CurvedMirror (class in sympy.physics.gaussopt) CurvedRefraction (class in sympy.physics.gaussopt) Cycle (class in sympy.combinatorics.permutations) cycle_length() (in module sympy.ntheory.generate) cycle_list() (in module sympy.crypto.crypto) cycle_structure (sympy.combinatorics.permutations.Permutation attribute) cycles (sympy.combinatorics.permutations.Permutation attribute) cyclic() (sympy.combinatorics.generators static method) cyclic_form (sympy.combinatorics.permutations.Permutation attribute) (sympy.combinatorics.polyhedron.Polyhedron attribute) CyclicGroup() (in module sympy.combinatorics.named_groups) cyclotomic() (in module mpmath) cyclotomic_poly() (in module sympy.polys.specialpolys) CythonCodeWrapper (class in sympy.utilities.autowrap)

D

D (sympy.matrices.matrices.MatrixBase attribute) (sympy.physics.gaussopt.RayTransferMatrix attribute) D() (sympy.physics.quantum.spin.Rotation class method) d() (sympy.physics.quantum.spin.Rotation class method) Dagger (class in sympy.physics.quantum.dagger) (class in sympy.physics.secondquant) Dagum() (in module sympy.stats) DataType (class in sympy.utilities.codegen) dcm() (sympy.physics.vector.frame.ReferenceFrame method) DD() (in module sympy.galgebra.ga) debug() (in module sympy.utilities.misc) debug_decorator() (in module sympy.utilities.misc) decipher_bifid5() (in module sympy.crypto.crypto) decipher_bifid6() (in module sympy.crypto.crypto) decipher_elgamal() (in module sympy.crypto.crypto) decipher_hill() (in module sympy.crypto.crypto) decipher_kid_rsa() (in module sympy.crypto.crypto) decipher_rsa() (in module sympy.crypto.crypto) decipher_vigenere() (in module sympy.crypto.crypto) decode_morse() (in module sympy.crypto.crypto) decompose() (in module sympy.polys.polytools) (sympy.physics.quantum.gate.CGate method) (sympy.physics.quantum.gate.SwapGate method) (sympy.physics.quantum.qft.IQFT method) (sympy.physics.quantum.qft.QFT method) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) define_precedence() (in module sympy.galgebra.precedence) deflate() (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) degree (mpmath.mp attribute) (sympy.combinatorics.perm_groups.PermutationGroup attribute) degree() (in module sympy.polys.polytools) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) degree_list() (in module sympy.polys.polytools) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) degrees() (in module mpmath) delta (sympy.functions.special.hyper.meijerg attribute) deltaintegrate() (sympy.integrals static method) denom() (sympy.polys.domains.AlgebraicField method) (sympy.polys.domains.ExpressionDomain method) (sympy.polys.domains.FractionField method) (sympy.polys.domains.domain.Domain method) (sympy.polys.domains.ring.Ring method) (sympy.polys.polyclasses.DMF method) density() (in module sympy.stats) depth() (sympy.polys.agca.ideals.Ideal method) Derivative (class in sympy.core.function) derived_series() (sympy.combinatorics.perm_groups.PermutationGroup method) derived_subgroup() (sympy.combinatorics.perm_groups.PermutationGroup method) descent() (in module sympy.solvers.diophantine) descents() (sympy.combinatorics.permutations.Permutation method) det() (sympy.matrices.matrices.MatrixBase method) det_bareis() (sympy.matrices.matrices.MatrixBase method) det_LU_decomposition() (sympy.matrices.matrices.MatrixBase method) diag() (in module sympy.matrices.dense) diagonal_solve() (sympy.matrices.matrices.MatrixBase method) diagonalize() (sympy.matrices.matrices.MatrixBase method) diagpq() (in module sympy.galgebra.ga) Diagram (class in sympy.categories) DiagramGrid (class in sympy.categories.diagram_drawing) Dict (class in sympy.core.containers) dict_merge() (in module sympy.utilities.iterables) Die() (in module sympy.stats) DiePSpace (class in sympy.stats.frv_types) diff() (in module mpmath) (in module sympy.core.function) (sympy.matrices.matrices.MatrixBase method) (sympy.physics.vector.vector.Vector method) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) Differential (class in sympy.diffgeom) DifferentialOperator (class in sympy.physics.quantum.operator) differint() (in module mpmath) diffs() (in module mpmath) diffs_exp() (in module mpmath) diffs_prod() (in module mpmath) digamma() (in module mpmath) (in module sympy.functions.special.gamma_functions) digit_2txt (in module sympy.printing.pretty.pretty_symbology) dihedral() (sympy.combinatorics.generators static method) DihedralGroup() (in module sympy.combinatorics.named_groups) dimension (sympy.physics.quantum.hilbert.HilbertSpace attribute) diop_bf_DN() (in module sympy.solvers.diophantine) diop_DN() (in module sympy.solvers.diophantine) diop_general_pythagorean() (in module sympy.solvers.diophantine) diop_general_sum_of_squares() (in module sympy.solvers.diophantine) diop_linear() (in module sympy.solvers.diophantine) diop_quadratic() (in module sympy.solvers.diophantine) diop_solve() (in module sympy.solvers.diophantine) diop_ternary_quadratic() (in module sympy.solvers.diophantine) diop_ternary_quadratic_normal() (in module sympy.solvers.diophantine) diophantine() (in module sympy.solvers.diophantine) DiracDelta (class in sympy.functions.special.delta_functions) DirectProduct() (in module sympy.combinatorics.group_constructs) dirichlet() (in module mpmath) dirichlet_eta (class in sympy.functions.special.zeta_functions) DiscreteUniform() (in module sympy.stats) discriminant() (in module sympy.polys.polytools) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) dispersion() (in module sympy.polys.dispersion), [1] (sympy.polys.polytools.Poly method) dispersionset() (in module sympy.polys.dispersion), [1] (sympy.polys.polytools.Poly method) distance() (sympy.geometry.line.Line method) (sympy.geometry.line.Ray method) (sympy.geometry.line.Segment method) (sympy.geometry.point.Point method) (sympy.geometry.polygon.Polygon method) div() (in module sympy.polys.polytools) (sympy.polys.domains.domain.Domain method) (sympy.polys.domains.field.Field method) (sympy.polys.domains.ring.Ring method) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) divergence (sympy.physics.gaussopt.BeamParameter attribute) divisible() (in module sympy.solvers.diophantine) divisor_count() (in module sympy.ntheory.factor_) divisors() (in module sympy.ntheory.factor_) DMF (class in sympy.polys.polyclasses) DMP (class in sympy.polys.polyclasses) dmp_abs() (in module sympy.polys.densearith) dmp_add() (in module sympy.polys.densearith) dmp_add_ground() (in module sympy.polys.densearith) dmp_add_mul() (in module sympy.polys.densearith) dmp_add_term() (in module sympy.polys.densearith) dmp_apply_pairs() (in module sympy.polys.densebasic) dmp_cancel() (in module sympy.polys.euclidtools) dmp_clear_denoms() (in module sympy.polys.densetools) dmp_compose() (in module sympy.polys.densetools) dmp_content() (in module sympy.polys.euclidtools) dmp_convert() (in module sympy.polys.densebasic) dmp_copy() (in module sympy.polys.densebasic) dmp_deflate() (in module sympy.polys.densebasic) dmp_degree() (in module sympy.polys.densebasic) dmp_degree_in() (in module sympy.polys.densebasic) dmp_degree_list() (in module sympy.polys.densebasic) dmp_diff() (in module sympy.polys.densetools) dmp_diff_eval_in() (in module sympy.polys.densetools) dmp_diff_in() (in module sympy.polys.densetools) dmp_discriminant() (in module sympy.polys.euclidtools) dmp_div() (in module sympy.polys.densearith) dmp_eject() (in module sympy.polys.densebasic) dmp_euclidean_prs() (in module sympy.polys.euclidtools) dmp_eval() (in module sympy.polys.densetools) dmp_eval_in() (in module sympy.polys.densetools) dmp_eval_tail() (in module sympy.polys.densetools) dmp_exclude() (in module sympy.polys.densebasic) dmp_expand() (in module sympy.polys.densearith) dmp_exquo() (in module sympy.polys.densearith) dmp_exquo_ground() (in module sympy.polys.densearith) dmp_ext_factor() (in module sympy.polys.factortools) dmp_factor_list() (in module sympy.polys.factortools) dmp_factor_list_include() (in module sympy.polys.factortools) dmp_ff_div() (in module sympy.polys.densearith) dmp_ff_prs_gcd() (in module sympy.polys.euclidtools) dmp_from_dict() (in module sympy.polys.densebasic) dmp_from_sympy() (in module sympy.polys.densebasic) dmp_gcd() (in module sympy.polys.euclidtools) dmp_gcdex() (in module sympy.polys.euclidtools) dmp_ground() (in module sympy.polys.densebasic) dmp_ground_content() (in module sympy.polys.densetools) dmp_ground_extract() (in module sympy.polys.densetools) dmp_ground_LC() (in module sympy.polys.densebasic) dmp_ground_monic() (in module sympy.polys.densetools) dmp_ground_nth() (in module sympy.polys.densebasic) dmp_ground_p() (in module sympy.polys.densebasic) dmp_ground_primitive() (in module sympy.polys.densetools) dmp_ground_TC() (in module sympy.polys.densebasic)

dmp_ground_trunc() (in module sympy.polys.densetools) dmp_grounds() (in module sympy.polys.densebasic) dmp_half_gcdex() (in module sympy.polys.euclidtools) dmp_include() (in module sympy.polys.densebasic) dmp_inflate() (in module sympy.polys.densebasic) dmp_inject() (in module sympy.polys.densebasic) dmp_inner_gcd() (in module sympy.polys.euclidtools) dmp_inner_subresultants() (in module sympy.polys.euclidtools) dmp_integrate() (in module sympy.polys.densetools) dmp_integrate_in() (in module sympy.polys.densetools) dmp_invert() (in module sympy.polys.euclidtools) dmp_irreducible_p() (in module sympy.polys.factortools) dmp_l1_norm() (in module sympy.polys.densearith) dmp_LC() (in module sympy.polys.densebasic) dmp_lcm() (in module sympy.polys.euclidtools) dmp_lift() (in module sympy.polys.densetools) dmp_list_terms() (in module sympy.polys.densebasic) dmp_max_norm() (in module sympy.polys.densearith) dmp_mul() (in module sympy.polys.densearith) dmp_mul_ground() (in module sympy.polys.densearith) dmp_mul_term() (in module sympy.polys.densearith) dmp_multi_deflate() (in module sympy.polys.densebasic) dmp_neg() (in module sympy.polys.densearith) dmp_negative_p() (in module sympy.polys.densebasic) dmp_nest() (in module sympy.polys.densebasic) dmp_normal() (in module sympy.polys.densebasic) dmp_nth() (in module sympy.polys.densebasic) dmp_one() (in module sympy.polys.densebasic) dmp_one_p() (in module sympy.polys.densebasic) dmp_pdiv() (in module sympy.polys.densearith) dmp_permute() (in module sympy.polys.densebasic) dmp_pexquo() (in module sympy.polys.densearith) dmp_positive_p() (in module sympy.polys.densebasic) dmp_pow() (in module sympy.polys.densearith) dmp_pquo() (in module sympy.polys.densearith) dmp_prem() (in module sympy.polys.densearith) dmp_primitive() (in module sympy.polys.euclidtools) dmp_primitive_prs() (in module sympy.polys.euclidtools) dmp_prs_resultant() (in module sympy.polys.euclidtools) dmp_qq_collins_resultant() (in module sympy.polys.euclidtools) dmp_qq_heu_gcd() (in module sympy.polys.euclidtools) dmp_quo() (in module sympy.polys.densearith) dmp_quo_ground() (in module sympy.polys.densearith) dmp_raise() (in module sympy.polys.densebasic) dmp_rem() (in module sympy.polys.densearith) dmp_resultant() (in module sympy.polys.euclidtools) dmp_revert() (in module sympy.polys.densetools) dmp_rr_div() (in module sympy.polys.densearith) dmp_rr_prs_gcd() (in module sympy.polys.euclidtools) dmp_slice() (in module sympy.polys.densebasic) dmp_sqr() (in module sympy.polys.densearith) dmp_strip() (in module sympy.polys.densebasic) dmp_sub() (in module sympy.polys.densearith) dmp_sub_ground() (in module sympy.polys.densearith) dmp_sub_mul() (in module sympy.polys.densearith) dmp_sub_term() (in module sympy.polys.densearith) dmp_subresultants() (in module sympy.polys.euclidtools) dmp_swap() (in module sympy.polys.densebasic) dmp_TC() (in module sympy.polys.densebasic) dmp_terms_gcd() (in module sympy.polys.densebasic) dmp_to_dict() (in module sympy.polys.densebasic) dmp_to_tuple() (in module sympy.polys.densebasic) dmp_trial_division() (in module sympy.polys.factortools) dmp_true_LT() (in module sympy.polys.densebasic) dmp_trunc() (in module sympy.polys.densetools) dmp_validate() (in module sympy.polys.densebasic) dmp_zero() (in module sympy.polys.densebasic) dmp_zero_p() (in module sympy.polys.densebasic) dmp_zeros() (in module sympy.polys.densebasic) dmp_zz_collins_resultant() (in module sympy.polys.euclidtools) dmp_zz_diophantine() (in module sympy.polys.factortools) dmp_zz_factor() (in module sympy.polys.factortools) dmp_zz_heu_gcd() (in module sympy.polys.euclidtools) dmp_zz_mignotte_bound() (in module sympy.polys.factortools) dmp_zz_modular_resultant() (in module sympy.polys.euclidtools) dmp_zz_wang() (in module sympy.polys.factortools) dmp_zz_wang_hensel_lifting() (in module sympy.polys.factortools) dmp_zz_wang_lead_coeffs() (in module sympy.polys.factortools) dmp_zz_wang_non_divisors() (in module sympy.polys.factortools) dmp_zz_wang_test_points() (in module sympy.polys.factortools) doctest() (in module sympy.utilities.runtests) doctest_depends_on() (in module sympy.utilities.decorator) doit() (sympy.core.basic.Basic method) (sympy.functions.elementary.piecewise.Piecewise method) (sympy.integrals.Integral method) (sympy.physics.quantum.anticommutator.AntiCommutator method) (sympy.physics.quantum.commutator.Commutator method) (sympy.physics.secondquant.AntiSymmetricTensor method) (sympy.physics.secondquant.Commutator method) (sympy.physics.secondquant.NO method) (sympy.physics.vector.dyadic.Dyadic method) (sympy.physics.vector.vector.Vector method) (sympy.series.limits.Limit method) doit_numerically() (sympy.core.function.Derivative method) Domain (class in sympy.polys.domains.domain) domain (sympy.categories.CompositeMorphism attribute) (sympy.categories.Morphism attribute) (sympy.polys.polytools.Poly attribute) DomainError (class in sympy.polys.polyerrors) doprint() (sympy.printing.ccode.CCodePrinter method) (sympy.printing.fcode.FCodePrinter method) (sympy.printing.mathml.MathMLPrinter method) (sympy.printing.printer.Printer method) dot() (in module sympy.physics.vector.functions) (sympy.geometry.point.Point method) (sympy.matrices.matrices.MatrixBase method) (sympy.physics.vector.dyadic.Dyadic method) (sympy.physics.vector.vector.Vector method) dotprint() (in module sympy.printing.dot) double_coset_can_rep() (in module sympy.combinatorics.tensor_can) draw() (sympy.categories.diagram_drawing.XypicDiagramDrawer method) dsolve() (in module sympy.solvers.ode) dt() (sympy.physics.vector.dyadic.Dyadic method) (sympy.physics.vector.vector.Vector method) dtype (sympy.polys.agca.modules.FreeModule attribute) (sympy.polys.agca.modules.QuotientModule attribute) (sympy.polys.domains.AlgebraicField attribute) (sympy.polys.domains.ExpressionDomain attribute) dual (sympy.physics.quantum.state.StateBase attribute) dual() (sympy.matrices.matrices.MatrixBase method) dual_class() (sympy.physics.quantum.state.StateBase class method) Dummy (class in sympy.core.symbol) dummy_eq() (sympy.core.basic.Basic method) DummyWrapper (class in sympy.utilities.autowrap) dump_c() (sympy.utilities.codegen.CCodeGen method) dump_code() (sympy.utilities.codegen.CodeGen method) dump_f95() (sympy.utilities.codegen.FCodeGen method) dump_h() (sympy.utilities.codegen.CCodeGen method) (sympy.utilities.codegen.FCodeGen method) dump_pyx() (sympy.utilities.autowrap.CythonCodeWrapper method) dup_content() (in module sympy.polys.densetools) dup_cyclotomic_p() (in module sympy.polys.factortools) dup_decompose() (in module sympy.polys.densetools) dup_extract() (in module sympy.polys.densetools) dup_gf_factor() (in module sympy.polys.factortools) dup_lshift() (in module sympy.polys.densearith) dup_mirror() (in module sympy.polys.densetools) dup_monic() (in module sympy.polys.densetools) dup_primitive() (in module sympy.polys.densetools) dup_random() (in module sympy.polys.densebasic) dup_real_imag() (in module sympy.polys.densetools) dup_reverse() (in module sympy.polys.densebasic) dup_rshift() (in module sympy.polys.densearith) dup_scale() (in module sympy.polys.densetools) dup_shift() (in module sympy.polys.densetools) dup_sign_variations() (in module sympy.polys.densetools) dup_transform() (in module sympy.polys.densetools) dup_zz_cyclotomic_factor() (in module sympy.polys.factortools) dup_zz_cyclotomic_poly() (in module sympy.polys.factortools) dup_zz_factor() (in module sympy.polys.factortools) dup_zz_factor_sqf() (in module sympy.polys.factortools) dup_zz_hensel_lift() (in module sympy.polys.factortools) dup_zz_hensel_step() (in module sympy.polys.factortools) dup_zz_irreducible_p() (in module sympy.polys.factortools) dup_zz_zassenhaus() (in module sympy.polys.factortools) Dyadic (class in sympy.physics.vector.dyadic) dynamicsymbols() (in module sympy.physics.vector)

E

e (mpmath.mp attribute) E() (in module sympy.stats) e1() (in module mpmath) E1() (in module sympy.functions.special.error_functions) E_n() (in module sympy.physics.qho_1d) E_nl() (in module sympy.physics.hydrogen) (in module sympy.physics.sho) E_nl_dirac() (in module sympy.physics.hydrogen) EC() (sympy.polys.polytools.Poly method) eccentricity (sympy.geometry.ellipse.Ellipse attribute) edges (sympy.combinatorics.polyhedron.Polyhedron attribute) edges() (sympy.combinatorics.prufer.Prufer static method) Ei (class in sympy.functions.special.error_functions) ei() (in module mpmath) eigenvals() (sympy.matrices.matrices.MatrixBase method) eigenvects() (sympy.matrices.matrices.MatrixBase method) Eijk() (in module sympy.functions.special.tensor_functions) eject() (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) elgamal_private_key() (in module sympy.crypto.crypto) elgamal_public_key() (in module sympy.crypto.crypto) ellipe() (in module mpmath) ellipf() (in module mpmath) ellipfun() (in module mpmath) ellipk() (in module mpmath) ellippi() (in module mpmath) elliprc() (in module mpmath) elliprd() (in module mpmath) elliprf() (in module mpmath) elliprg() (in module mpmath) elliprj() (in module mpmath) Ellipse (class in sympy.geometry.ellipse) elliptic_e (class in sympy.functions.special.elliptic_integrals) elliptic_f (class in sympy.functions.special.elliptic_integrals) elliptic_k (class in sympy.functions.special.elliptic_integrals) elliptic_pi (class in sympy.functions.special.elliptic_integrals) EM() (sympy.polys.polytools.Poly method) emptyPrinter() (sympy.printing.repr.ReprPrinter method) EmptySet (class in sympy.core.sets) encipher_affine() (in module sympy.crypto.crypto) encipher_bifid5() (in module sympy.crypto.crypto) encipher_bifid6() (in module sympy.crypto.crypto) encipher_bifid7() (in module sympy.crypto.crypto) encipher_elgamal() (in module sympy.crypto.crypto) encipher_hill() (in module sympy.crypto.crypto) encipher_kid_rsa() (in module sympy.crypto.crypto) encipher_rsa() (in module sympy.crypto.crypto) encipher_shift() (in module sympy.crypto.crypto) encipher_substitution() (in module sympy.crypto.crypto) encipher_vigenere() (in module sympy.crypto.crypto) encloses() (sympy.geometry.entity.GeometryEntity method) encloses_point() (sympy.geometry.ellipse.Ellipse method) (sympy.geometry.polygon.Polygon method) (sympy.geometry.polygon.RegularPolygon method) encode_morse() (in module sympy.crypto.crypto) end (sympy.core.sets.Interval attribute) enhance_print (class in sympy.galgebra.printing) enum_all() (sympy.utilities.enumerative.MultisetPartitionTraverser method) enum_large() (sympy.utilities.enumerative.MultisetPartitionTraverser method) enum_range() (sympy.utilities.enumerative.MultisetPartitionTraverser method) enum_small() (sympy.utilities.enumerative.MultisetPartitionTraverser method) enumerate_states() (in module sympy.physics.quantum.represent) EPath (class in sympy.simplify.epathtools) epath() (in module sympy.simplify.epathtools) Eq (in module sympy.core.relational) Equality (class in sympy.core.relational) equals() (sympy.core.expr.Expr method) (sympy.matrices.expressions.MatrixExpr method) (sympy.matrices.immutable.ImmutableMatrix method) equation() (sympy.geometry.ellipse.Circle method) (sympy.geometry.ellipse.Ellipse method) (sympy.geometry.line.Line method) Equivalent (class in sympy.logic.boolalg) equivalent() (in module sympy.solvers.diophantine) erf (class in sympy.functions.special.error_functions) erf() (in module mpmath) erf2 (class in sympy.functions.special.error_functions)

erf2inv (class in sympy.functions.special.error_functions) erfc (class in sympy.functions.special.error_functions) erfc() (in module mpmath) erfcinv (class in sympy.functions.special.error_functions) erfi (class in sympy.functions.special.error_functions) erfi() (in module mpmath) erfinv (class in sympy.functions.special.error_functions) erfinv() (in module mpmath) Erlang() (in module sympy.stats) estimate_error() (mpmath.calculus.quadrature.QuadratureRule method) ET() (sympy.polys.polytools.Poly method) eta (sympy.functions.special.hyper.hyper attribute) euler (class in sympy.functions.combinatorial.numbers) (mpmath.mp attribute) euler_maclaurin() (sympy.concrete.summations.Sum method) EulerGamma (class in sympy.core.numbers) eulernum() (in module mpmath) eulerpoly() (in module mpmath) eval() (sympy.assumptions.assume.Predicate method) (sympy.functions.special.tensor_functions.KroneckerDelta class method) (sympy.physics.secondquant.Commutator class method) (sympy.physics.secondquant.Dagger class method) (sympy.physics.secondquant.KroneckerDelta class method) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) eval_controls() (sympy.physics.quantum.gate.CGate method) eval_expr() (in module sympy.parsing.sympy_parser) eval_levicivita() (in module sympy.functions.special.tensor_functions) evalf() (sympy.geometry.point.Point method) (sympy.matrices.matrices.MatrixBase method) (sympy.polys.domains.domain.Domain method) evaluate_deltas() (in module sympy.physics.secondquant) evaluate_pauli_product() (in module sympy.physics.paulialgebra) EvaluationFailed (class in sympy.polys.polyerrors) ExactQuotientFailed (class in sympy.polys.polyerrors) exclude() (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) exp (class in sympy.functions.elementary.exponential) exp() (in module mpmath) (sympy.matrices.matrices.MatrixBase method) Exp1 (class in sympy.core.numbers) expand() (in module sympy.core.function) (sympy.core.expr.Expr method) (sympy.matrices.matrices.MatrixBase method) expand_complex() (in module sympy.core.function) expand_func() (in module sympy.core.function) expand_log() (in module sympy.core.function) expand_mul() (in module sympy.core.function) expand_multinomial() (in module sympy.core.function) expand_power_base() (in module sympy.core.function) expand_power_exp() (in module sympy.core.function) expand_trig() (in module sympy.core.function) expint (class in sympy.functions.special.error_functions) expint() (in module mpmath) expj() (in module mpmath) expjpi() (in module mpmath) expm() (in module mpmath) expm1() (in module mpmath) Exponential() (in module sympy.stats) Expr (class in sympy.core.expr) expr (sympy.core.function.Lambda attribute) (sympy.core.function.Subs attribute) (sympy.functions.elementary.piecewise.ExprCondPair attribute) (sympy.physics.quantum.operator.DifferentialOperator attribute) (sympy.physics.quantum.state.Wavefunction attribute) ExprCondPair (class in sympy.functions.elementary.piecewise) express() (in module sympy.physics.vector.functions) (sympy.physics.vector.dyadic.Dyadic method) (sympy.physics.vector.vector.Vector method) ExpressionDomain (class in sympy.polys.domains) ExpressionDomain.Expression (class in sympy.polys.domains) exquo() (in module sympy.polys.polytools) (sympy.polys.domains.domain.Domain method) (sympy.polys.domains.field.Field method) (sympy.polys.domains.ring.Ring method) (sympy.polys.polyclasses.DMF method) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) exquo_ground() (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) extend() (sympy.ntheory.generate.Sieve method) (sympy.plotting.plot.Plot method) extend_to_no() (sympy.ntheory.generate.Sieve method) extended_euclid() (in module sympy.solvers.diophantine) exterior_angle (sympy.geometry.polygon.RegularPolygon attribute) extract() (sympy.matrices.matrices.MatrixBase method) (sympy.matrices.sparse.SparseMatrix method) extract_additively() (sympy.core.expr.Expr method) extract_branch_factor() (sympy.core.expr.Expr method) extract_leading_order() (sympy.core.add.Add method) extract_multiplicatively() (sympy.core.expr.Expr method) extract_type_tens() (sympy.physics.hep.gamma_matrices.GammaMatrixHead static method) extradps() (in module mpmath) ExtraneousFactors (class in sympy.polys.polyerrors) extraprec() (in module mpmath) eye() (in module sympy.matrices.dense) (sympy.matrices.sparse.SparseMatrix class method)

F

F (in module sympy.physics.secondquant) F2PyCodeWrapper (class in sympy.utilities.autowrap) fabs() (in module mpmath) fac2() (in module mpmath) faces (sympy.combinatorics.polyhedron.Polyhedron attribute) factor() (in module sympy.polys.polytools) (sympy.core.expr.Expr method) factor_list() (in module sympy.polys.polytools) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) factor_list_include() (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) factor_terms() (in module sympy.core.exprtools) factorial (class in sympy.functions.combinatorial.factorials) factorial() (in module mpmath) (sympy.polys.domains.FractionField method) (sympy.polys.domains.PolynomialRing method) factorial2 (class in sympy.functions.combinatorial.factorials) factorial_notation() (in module sympy.parsing.sympy_parser) factoring_visitor() (in module sympy.utilities.enumerative) factorint() (in module sympy.ntheory.factor_) factors() (sympy.core.numbers.Rational method) fadd() (in module mpmath) FallingFactorial (class in sympy.functions.combinatorial.factorials) FBra (in module sympy.physics.secondquant) fcode() (in module sympy.printing.fcode) FCodeGen (class in sympy.utilities.codegen) FCodePrinter (class in sympy.printing.fcode) fct_sym_array() (in module sympy.galgebra.stringarrays) Fd (in module sympy.physics.secondquant) fdiff() (sympy.core.function.Function method) (sympy.functions.elementary.complexes.Abs method) (sympy.functions.elementary.exponential.LambertW method) (sympy.functions.elementary.exponential.exp method) (sympy.functions.elementary.exponential.log method) (sympy.functions.elementary.hyperbolic.sinh method) FDistribution() (in module sympy.stats) fdiv() (in module mpmath) fdot() (in module mpmath) ff() (in module mpmath) fglm() (sympy.polys.polytools.GroebnerBasis method) fibonacci (class in sympy.functions.combinatorial.numbers) fibonacci() (in module mpmath) Field (class in sympy.polys.domains.field) field_isomorphism() (in module sympy.polys.numberfields) fill() (sympy.matrices.dense.MutableDenseMatrix method) (sympy.matrices.sparse.MutableSparseMatrix method) find() (sympy.core.basic.Basic method) find_DN() (in module sympy.solvers.diophantine) find_executable() (in module sympy.galgebra.printing) (in module sympy.utilities.misc) find_unit() (in module sympy.physics.units) findpoly() (in module mpmath) findroot() (in module mpmath) FiniteDomain (class in sympy.stats.frv) FiniteField (class in sympy.polys.domains) FinitePSpace (class in sympy.stats.frv) FiniteRV() (in module sympy.stats) FiniteSet (class in sympy.core.sets) FisherZ() (in module sympy.stats) fit() (sympy.statistics.distributions.Normal static method) (sympy.statistics.distributions.Uniform static method) FixedBosonicBasis (class in sympy.physics.secondquant) FKet (in module sympy.physics.secondquant) FlagError (class in sympy.polys.polyerrors) FlatMirror (class in sympy.physics.gaussopt) FlatRefraction (class in sympy.physics.gaussopt) flatten() (in module sympy.galgebra.vector) (in module sympy.utilities.iterables) (sympy.categories.CompositeMorphism method) (sympy.core.add.Add class method) (sympy.core.mul.Mul class method) Float (class in sympy.core.numbers) floor (class in sympy.functions.elementary.integers) floor() (in module mpmath) fmod() (in module mpmath) fmul() (in module mpmath) fneg() (in module mpmath) foci (sympy.geometry.ellipse.Ellipse attribute) FockSpace (class in sympy.physics.quantum.hilbert) FockState (class in sympy.physics.secondquant) FockStateBosonBra (class in sympy.physics.secondquant) FockStateBosonKet (class in sympy.physics.secondquant) FockStateBra (class in sympy.physics.secondquant)

FockStateKet (class in sympy.physics.secondquant) focus_distance (sympy.geometry.ellipse.Ellipse attribute) forcing (sympy.physics.mechanics.lagrange.LagrangesMethod attribute) forcing_full (sympy.physics.mechanics.lagrange.LagrangesMethod attribute) form_lagranges_equations() (sympy.physics.mechanics.lagrange.LagrangesMethod method) fourier() (in module mpmath) fourier_transform() (in module sympy.integrals.transforms) fourierval() (in module mpmath) fprod() (in module mpmath) frac (in module sympy.printing.pretty.pretty_symbology) frac() (in module mpmath) frac_field() (sympy.polys.domains.domain.Domain method) frac_unify() (sympy.polys.polyclasses.DMF method) fraction() (in module mpmath) (in module sympy.simplify.simplify) FractionField (class in sympy.polys.domains) Frechet() (in module sympy.stats) free_dum_from_indices() (sympy.tensor.tensor.TIDS static method) free_module() (sympy.polys.domains.ring.Ring method) free_symbols (sympy.concrete.products.Product attribute) (sympy.core.basic.Basic attribute) (sympy.functions.elementary.piecewise.ExprCondPair attribute) (sympy.geometry.curve.Curve attribute) (sympy.integrals.Integral attribute) (sympy.physics.quantum.operator.DifferentialOperator attribute) (sympy.polys.polytools.Poly attribute) (sympy.polys.polytools.PurePoly attribute) free_symbols_in_domain (sympy.polys.polytools.Poly attribute) FreeModule (class in sympy.polys.agca.modules) FreeSpace (class in sympy.physics.gaussopt) fresnelc (class in sympy.functions.special.error_functions) fresnelc() (in module mpmath) FresnelIntegral (class in sympy.functions.special.error_functions) fresnels (class in sympy.functions.special.error_functions) fresnels() (in module mpmath) frexp() (in module mpmath) from_AlgebraicField() (sympy.polys.domains.domain.Domain method) (sympy.polys.domains.FractionField method) (sympy.polys.domains.IntegerRing method) (sympy.polys.domains.PolynomialRing method) (sympy.polys.domains.RationalField method) from_ComplexField() (sympy.polys.domains.domain.Domain method) from_components_and_indices() (sympy.tensor.tensor.TIDS static method) from_dict() (sympy.polys.polyclasses.DMP class method) (sympy.polys.polytools.Poly class method) from_expr() (sympy.polys.polytools.Poly class method) from_ExpressionDomain() (sympy.polys.domains.domain.Domain method) (sympy.polys.domains.ExpressionDomain method) from_FF_gmpy() (sympy.polys.domains.domain.Domain method) (sympy.polys.domains.FiniteField method) from_FF_python() (sympy.polys.domains.domain.Domain method) (sympy.polys.domains.FiniteField method) from_FractionField() (sympy.polys.domains.domain.Domain method) (sympy.polys.domains.ExpressionDomain method) (sympy.polys.domains.FractionField method) (sympy.polys.domains.PolynomialRing method) from_GlobalPolynomialRing() (sympy.polys.domains.domain.Domain method) from_inversion_vector() (sympy.combinatorics.permutations.Permutation class method) from_list() (sympy.polys.polyclasses.DMP class method) (sympy.polys.polytools.Poly class method) from_poly() (sympy.polys.polytools.Poly class method) from_PolynomialRing() (sympy.polys.domains.domain.Domain method) (sympy.polys.domains.ExpressionDomain method) (sympy.polys.domains.FractionField method) (sympy.polys.domains.PolynomialRing method) from_QQ_gmpy() (sympy.polys.domains.AlgebraicField method) (sympy.polys.domains.ExpressionDomain method) (sympy.polys.domains.FiniteField method) (sympy.polys.domains.FractionField method) (sympy.polys.domains.PolynomialRing method) (sympy.polys.domains.domain.Domain method) from_QQ_python() (sympy.polys.domains.AlgebraicField method) (sympy.polys.domains.ExpressionDomain method) (sympy.polys.domains.FiniteField method) (sympy.polys.domains.FractionField method) (sympy.polys.domains.PolynomialRing method) (sympy.polys.domains.domain.Domain method) from_RealField() (sympy.polys.domains.AlgebraicField method) (sympy.polys.domains.ExpressionDomain method) (sympy.polys.domains.FiniteField method) (sympy.polys.domains.FractionField method) (sympy.polys.domains.PolynomialRing method) (sympy.polys.domains.domain.Domain method) from_rgs() (sympy.combinatorics.partitions.Partition class method) from_sequence() (sympy.combinatorics.permutations.Permutation class method) from_sympy() (sympy.polys.domains.AlgebraicField method) (sympy.polys.domains.ExpressionDomain method) (sympy.polys.domains.FiniteField method) (sympy.polys.domains.FractionField method) (sympy.polys.domains.PolynomialRing method) (sympy.polys.domains.RealField method) (sympy.polys.domains.domain.Domain method) from_sympy_list() (sympy.polys.polyclasses.DMP class method) from_TIDS_list() (sympy.tensor.tensor.TensAdd static method) from_ZZ_gmpy() (sympy.polys.domains.AlgebraicField method) (sympy.polys.domains.ExpressionDomain method) (sympy.polys.domains.FiniteField method) (sympy.polys.domains.FractionField method) (sympy.polys.domains.PolynomialRing method) (sympy.polys.domains.domain.Domain method) from_ZZ_python() (sympy.polys.domains.AlgebraicField method) (sympy.polys.domains.ExpressionDomain method) (sympy.polys.domains.FiniteField method) (sympy.polys.domains.FractionField method) (sympy.polys.domains.PolynomialRing method) (sympy.polys.domains.domain.Domain method) fromiter() (sympy.core.basic.Basic class method) fsub() (in module mpmath) fsum() (in module mpmath) full_cyclic_form (sympy.combinatorics.permutations.Permutation attribute) fun_eval() (sympy.tensor.tensor.TensAdd method) (sympy.tensor.tensor.TensMul method) func (sympy.core.basic.Basic attribute) func_field_modgcd (class in sympy.polys.modulargcd) Function (class in sympy.core.function) function (sympy.physics.quantum.operator.DifferentialOperator attribute) function_exponentiation() (in module sympy.parsing.sympy_parser) FunctionClass (class in sympy.core.function) FunctionMatrix (class in sympy.matrices.expressions) functions (sympy.geometry.curve.Curve attribute)

G

G() (in module sympy.printing.pretty.pretty_symbology) g() (in module sympy.printing.pretty.pretty_symbology) GA_LatexPrinter (class in sympy.galgebra.printing) GA_Printer (class in sympy.galgebra.printing) GAeval() (in module sympy.galgebra.precedence) gamma (class in sympy.functions.special.gamma_functions) gamma() (in module mpmath) Gamma() (in module sympy.stats) gamma_trace() (sympy.physics.hep.gamma_matrices.GammaMatrixHead method) gammainc() (in module mpmath) GammaInverse() (in module sympy.stats) GammaMatrixHead (class in sympy.physics.hep.gamma_matrices) gammaprod() (in module mpmath) Gate (class in sympy.physics.quantum.gate) gate (sympy.physics.quantum.gate.CGate attribute) (sympy.physics.quantum.gate.CNotGate attribute) gate_simp() (in module sympy.physics.quantum.gate) gate_sort() (in module sympy.physics.quantum.gate) gaunt() (in module sympy.physics.wigner) gauss_chebyshev_t() (in module sympy.integrals.quadrature) gauss_chebyshev_u() (in module sympy.integrals.quadrature) gauss_gen_laguerre() (in module sympy.integrals.quadrature) gauss_hermite() (in module sympy.integrals.quadrature) gauss_jacobi() (in module sympy.integrals.quadrature) gauss_laguerre() (in module sympy.integrals.quadrature) gauss_legendre() (in module sympy.integrals.quadrature) gaussian_conj() (in module sympy.physics.gaussopt) gaussian_reduce() (in module sympy.solvers.diophantine) GaussLegendre (class in mpmath.calculus.quadrature) gcd() (in module sympy.polys.polytools) (sympy.core.numbers.Number method) (sympy.polys.domains.PolynomialRing method) (sympy.polys.domains.RealField method) (sympy.polys.domains.domain.Domain method) (sympy.polys.domains.field.Field method) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) gcd_list() (in module sympy.polys.polytools) gcd_terms() (in module sympy.core.exprtools) gcdex() (in module sympy.polys.polytools) (sympy.polys.domains.PolynomialRing method) (sympy.polys.domains.domain.Domain method) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) Ge (in module sympy.core.relational) gegenbauer (class in sympy.functions.special.polynomials) gegenbauer() (in module mpmath) gegenbauer_poly() (in module sympy.polys.orthopolys) gen (sympy.polys.polytools.Poly attribute) generate() (sympy.combinatorics.perm_groups.PermutationGroup method) generate_bell() (in module sympy.utilities.iterables) generate_derangements() (in module sympy.utilities.iterables) generate_dimino() (sympy.combinatorics.perm_groups.PermutationGroup method) generate_gray() (sympy.combinatorics.graycode.GrayCode method) generate_involutions() (in module sympy.utilities.iterables) generate_oriented_forest() (in module sympy.utilities.iterables) generate_schreier_sims() (sympy.combinatorics.perm_groups.PermutationGroup method) generate_tokens() (in module sympy.parsing.sympy_tokenize) generators (sympy.combinatorics.perm_groups.PermutationGroup attribute) GeneratorsError (class in sympy.polys.polyerrors) GeneratorsNeeded (class in sympy.polys.polyerrors) Geometric() (in module sympy.stats) geometric_conj_ab() (in module sympy.physics.gaussopt) geometric_conj_af() (in module sympy.physics.gaussopt) geometric_conj_bf() (in module sympy.physics.gaussopt) GeometricRay (class in sympy.physics.gaussopt) GeometryEntity (class in sympy.geometry.entity) get() (sympy.core.containers.Dict method) get_adjacency_distance() (sympy.combinatorics.permutations.Permutation method) get_adjacency_matrix() (sympy.combinatorics.permutations.Permutation method) get_basis() (in module sympy.physics.quantum.represent) get_class() (in module sympy.utilities.source) get_comm() (sympy.tensor.tensor._TensorManager method) get_components_with_free_indices() (sympy.tensor.tensor.TIDS method) get_contraction_structure() (in module sympy.tensor.index_methods) get_default_datatype() (in module sympy.utilities.codegen) get_diag_blocks() (sympy.matrices.matrices.MatrixBase method) get_domain() (sympy.polys.polytools.Poly method) get_exact() (sympy.polys.domains.domain.Domain method) (sympy.polys.domains.RealField method) get_field() (sympy.polys.domains.domain.Domain method) (sympy.polys.domains.ExpressionDomain method) (sympy.polys.domains.FiniteField method) (sympy.polys.domains.IntegerRing method) (sympy.polys.domains.PolynomialRing method) (sympy.polys.domains.field.Field method) get_indices() (in module sympy.tensor.index_methods) (sympy.tensor.tensor.TensMul method) get_interface() (sympy.utilities.codegen.FCodeGen method) get_mass() (sympy.physics.mechanics.particle.Particle method) get_matrix() (sympy.tensor.tensor.TensExpr method) get_mod_func() (in module sympy.utilities.source) get_modulus() (sympy.polys.polytools.Poly method) get_motion_params() (in module sympy.physics.vector.functions) get_nodes() (mpmath.calculus.quadrature.QuadratureRule method) get_period() (sympy.functions.special.hyper.meijerg method) get_permuted() (sympy.physics.secondquant.PermutationOperator method) get_point() (sympy.physics.mechanics.particle.Particle method) get_positional_distance() (sympy.combinatorics.permutations.Permutation method) get_precedence_distance() (sympy.combinatorics.permutations.Permutation method) get_precedence_matrix() (sympy.combinatorics.permutations.Permutation method) Get_Program() (in module sympy.galgebra.printing) get_prototype() (sympy.utilities.codegen.CCodeGen method) get_resource() (in module sympy.utilities.pkgdata) get_ring() (sympy.polys.domains.AlgebraicField method) (sympy.polys.domains.ExpressionDomain method) (sympy.polys.domains.FractionField method) (sympy.polys.domains.RealField method) (sympy.polys.domains.domain.Domain method) (sympy.polys.domains.field.Field method) (sympy.polys.domains.ring.Ring method) get_segments() (sympy.plotting.plot.LineOver1DRangeSeries method) (sympy.plotting.plot.Parametric2DLineSeries method) get_subNO() (sympy.physics.secondquant.NO method) get_subset_from_bitstring() (sympy.combinatorics.graycode static method) get_symmetric_group_sgs() (in module sympy.combinatorics.tensor_can) get_sympy_dir() (in module sympy.utilities.runtests) get_target_matrix() (sympy.physics.quantum.gate.Gate method) (sympy.physics.quantum.gate.UGate method)

getn() (sympy.core.expr.Expr method) getO() (sympy.core.expr.Expr method) gf_add() (in module sympy.polys.galoistools) gf_add_ground() (in module sympy.polys.galoistools) gf_add_mul() (in module sympy.polys.galoistools) gf_berlekamp() (in module sympy.polys.galoistools) gf_cofactors() (in module sympy.polys.galoistools) gf_compose() (in module sympy.polys.galoistools) gf_compose_mod() (in module sympy.polys.galoistools) gf_crt() (in module sympy.polys.galoistools) gf_crt1() (in module sympy.polys.galoistools) gf_crt2() (in module sympy.polys.galoistools) gf_csolve() (in module sympy.polys.galoistools) gf_degree() (in module sympy.polys.galoistools) gf_diff() (in module sympy.polys.galoistools) gf_div() (in module sympy.polys.galoistools) gf_eval() (in module sympy.polys.galoistools) gf_expand() (in module sympy.polys.galoistools) gf_exquo() (in module sympy.polys.galoistools) gf_factor() (in module sympy.polys.galoistools) gf_factor_sqf() (in module sympy.polys.galoistools) gf_from_dict() (in module sympy.polys.galoistools) gf_from_int_poly() (in module sympy.polys.galoistools) gf_gcd() (in module sympy.polys.galoistools) gf_gcdex() (in module sympy.polys.galoistools) gf_int() (in module sympy.polys.galoistools) gf_irreducible() (in module sympy.polys.galoistools) gf_irreducible_p() (in module sympy.polys.galoistools) gf_LC() (in module sympy.polys.galoistools) gf_lcm() (in module sympy.polys.galoistools) gf_lshift() (in module sympy.polys.galoistools) gf_monic() (in module sympy.polys.galoistools) gf_mul() (in module sympy.polys.galoistools) gf_mul_ground() (in module sympy.polys.galoistools) gf_multi_eval() (in module sympy.polys.galoistools) gf_neg() (in module sympy.polys.galoistools) gf_normal() (in module sympy.polys.galoistools) gf_pow() (in module sympy.polys.galoistools) gf_pow_mod() (in module sympy.polys.galoistools) gf_Qbasis() (in module sympy.polys.galoistools) gf_Qmatrix() (in module sympy.polys.galoistools) gf_quo() (in module sympy.polys.galoistools) gf_quo_ground() (in module sympy.polys.galoistools) gf_random() (in module sympy.polys.galoistools) gf_rem() (in module sympy.polys.galoistools) gf_rshift() (in module sympy.polys.galoistools) gf_shoup() (in module sympy.polys.galoistools) gf_sqf_list() (in module sympy.polys.galoistools) gf_sqf_p() (in module sympy.polys.galoistools) gf_sqf_part() (in module sympy.polys.galoistools) gf_sqr() (in module sympy.polys.galoistools) gf_strip() (in module sympy.polys.galoistools) gf_sub() (in module sympy.polys.galoistools) gf_sub_ground() (in module sympy.polys.galoistools) gf_sub_mul() (in module sympy.polys.galoistools) gf_TC() (in module sympy.polys.galoistools) gf_to_dict() (in module sympy.polys.galoistools) gf_to_int_poly() (in module sympy.polys.galoistools) gf_trace_map() (in module sympy.polys.galoistools) gf_trunc() (in module sympy.polys.galoistools) gf_value() (in module sympy.polys.galoistools) gf_zassenhaus() (in module sympy.polys.galoistools) gff() (in module sympy.polys.polytools) gff_list() (in module sympy.polys.polytools) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) given() (in module sympy.stats) glaisher (mpmath.mp attribute) GMPYFiniteField (class in sympy.polys.domains) GMPYIntegerRing (class in sympy.polys.domains) GMPYRationalField (class in sympy.polys.domains) GoldenRatio (class in sympy.core.numbers) gosper_normal() (in module sympy.concrete.gosper) gosper_sum() (in module sympy.concrete.gosper) gosper_term() (in module sympy.concrete.gosper) gouy (sympy.physics.gaussopt.BeamParameter attribute) Grad() (in module sympy.galgebra.ga) GradedLexOrder (class in sympy.polys.orderings) grampoint() (in module mpmath) GramSchmidt() (in module sympy.matrices.dense) gray_to_bin() (sympy.combinatorics.graycode static method) GrayCode (class in sympy.combinatorics.graycode) graycode_subsets() (sympy.combinatorics.graycode static method) GreaterThan (class in sympy.core.relational) greek_letters (in module sympy.printing.pretty.pretty_symbology) groebner() (in module sympy.polys.groebnertools) (in module sympy.polys.polytools) GroebnerBasis (class in sympy.polys.polytools) ground_roots() (in module sympy.polys.polytools) (sympy.polys.polytools.Poly method) group() (in module sympy.parsing.sympy_tokenize) (in module sympy.utilities.iterables) grover_iteration() (in module sympy.physics.quantum.grover) gruntz() (in module sympy.series.gruntz) Gt (in module sympy.core.relational) guess_degree() (mpmath.calculus.quadrature.QuadratureRule method)

H

H (in module sympy.physics.quantum.gate) (sympy.matrices.matrices.MatrixBase attribute) HadamardGate (class in sympy.physics.quantum.gate) Half (class in sympy.core.numbers) half_gcdex() (in module sympy.polys.polytools) (sympy.polys.domains.domain.Domain method) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) half_per() (sympy.polys.polyclasses.DMF method) Halley (class in mpmath.calculus.optimization) hankel1 (class in sympy.functions.special.bessel) hankel1() (in module mpmath) hankel2 (class in sympy.functions.special.bessel) hankel2() (in module mpmath) hankel_transform() (in module sympy.integrals.transforms) harmonic (class in sympy.functions.combinatorial.numbers) harmonic() (in module mpmath) has() (sympy.core.basic.Basic method) (sympy.matrices.matrices.MatrixBase method) (sympy.matrices.sparse.SparseMatrix method) has_dups() (in module sympy.utilities.iterables) has_only_gens() (sympy.polys.polytools.Poly method) has_q_annihilators (sympy.physics.secondquant.NO attribute) has_q_creators (sympy.physics.secondquant.NO attribute) has_variety() (in module sympy.utilities.iterables) Heaviside (class in sympy.functions.special.delta_functions) height (sympy.categories.diagram_drawing.DiagramGrid attribute) (sympy.physics.gaussopt.GeometricRay attribute) height() (sympy.polys.agca.ideals.Ideal method) (sympy.printing.pretty.stringpict.stringPict method) hermite (class in sympy.functions.special.polynomials) hermite() (in module mpmath) hermite_poly() (in module sympy.polys.orthopolys) HermitianOperator (class in sympy.physics.quantum.operator) hessian() (in module sympy.matrices.dense) heurisch() (sympy.integrals static method) heurisch_wrapper() (sympy.integrals static method) HeuristicGCDFailed (class in sympy.polys.polyerrors) HilbertSpace (class in sympy.physics.quantum.hilbert)

hobj() (in module sympy.printing.pretty.pretty_symbology) holzer() (in module sympy.solvers.diophantine) hom() (sympy.categories.Diagram method) homogeneous_order() (in module sympy.solvers.ode) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) homogenize() (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) homomorphism() (in module sympy.polys.agca.homomorphisms) HomomorphismFailed (class in sympy.polys.polyerrors) horner() (in module sympy.polys.polyfuncs) hradius (sympy.geometry.ellipse.Ellipse attribute) hstack() (sympy.matrices.matrices.MatrixBase class method) hyp0f1() (in module mpmath) hyp1f1() (in module mpmath) hyp1f2() (in module mpmath) hyp2f0() (in module mpmath) hyp2f1() (in module mpmath) hyp2f2() (in module mpmath) hyp2f3() (in module mpmath) hyp3f2() (in module mpmath) hyper (class in sympy.functions.special.hyper) hyper() (in module mpmath) hyper2d() (in module mpmath) HyperbolicFunction (class in sympy.functions.elementary.hyperbolic) hypercomb() (in module mpmath) hyperexpand() (in module sympy.simplify.hyperexpand) hyperfac() (in module mpmath) Hypergeometric() (in module sympy.stats) hypersimilar() (in module sympy.simplify.simplify) hypersimp() (in module sympy.simplify.simplify) hyperu() (in module mpmath) hypot() (in module mpmath)

I

ibin() (in module sympy.utilities.iterables) Ideal (class in sympy.polys.agca.ideals) ideal() (sympy.polys.domains.ring.Ring method) identify() (in module mpmath) Identity (class in sympy.matrices.expressions) identity_hom() (sympy.polys.agca.modules.FreeModule method) (sympy.polys.agca.modules.Module method) (sympy.polys.agca.modules.QuotientModule method) (sympy.polys.agca.modules.SubModule method) IdentityFunction (class in sympy.functions.elementary.miscellaneous) IdentityGate (class in sympy.physics.quantum.gate) IdentityMorphism (class in sympy.categories) Idx (class in sympy.tensor.indexed) igcd() (in module sympy.core.numbers) ilcm() (in module sympy.core.numbers) Illinois (class in mpmath.calculus.optimization) im() (in module mpmath) image() (sympy.polys.agca.homomorphisms.ModuleHomomorphism method) ImageSet (class in sympy.sets.fancysets) ImaginaryUnit (class in sympy.core.numbers) ImmutableMatrix (class in sympy.matrices.immutable) ImmutableSparseMatrix (class in sympy.matrices.immutable) implemented_function() (in module sympy.utilities.lambdify) implicit_application() (in module sympy.parsing.sympy_parser) implicit_multiplication() (in module sympy.parsing.sympy_parser) implicit_multiplication_application() (in module sympy.parsing.sympy_parser) ImplicitSeries (class in sympy.plotting.plot_implicit) Implies (class in sympy.logic.boolalg) in_terms_of_generators() (sympy.polys.agca.modules.SubModule method) incenter (sympy.geometry.polygon.Triangle attribute) incircle (sympy.geometry.polygon.RegularPolygon attribute) (sympy.geometry.polygon.Triangle attribute) inclusion_hom() (sympy.polys.agca.modules.SubModule method) indent_code() (sympy.printing.ccode.CCodePrinter method) (sympy.printing.fcode.FCodePrinter method) index() (sympy.combinatorics.permutations.Permutation method) (sympy.core.containers.Tuple method) (sympy.physics.secondquant.FixedBosonicBasis method) (sympy.physics.secondquant.VarBosonicBasis method) Indexed (class in sympy.tensor.indexed) IndexedBase (class in sympy.tensor.indexed) indices (sympy.tensor.indexed.Indexed attribute) indices_contain_equal_information (sympy.functions.special.tensor_functions.KroneckerDelta attribute) (sympy.physics.secondquant.KroneckerDelta attribute) inertia() (in module sympy.physics.mechanics.functions) inertia_of_point_mass() (in module sympy.physics.mechanics.functions) inf (sympy.core.sets.Set attribute) infinitesimals() (in module sympy.solvers.ode) Infinity (class in sympy.core.numbers) init_printing() (in module sympy.physics.vector.printing) inject() (sympy.polys.domains.compositedomain.CompositeDomain method) (sympy.polys.domains.domain.Domain method) (sympy.polys.domains.simpledomain.SimpleDomain method) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) InnerProduct (class in sympy.physics.quantum.innerproduct) (class in sympy.physics.secondquant) inradius (sympy.geometry.polygon.RegularPolygon attribute) (sympy.geometry.polygon.Triangle attribute) intcurve_diffequ() (in module sympy.diffgeom) intcurve_series() (in module sympy.diffgeom) Integer (class in sympy.core.numbers) integer_nthroot() (in module sympy.core.power) IntegerPartition (class in sympy.combinatorics.partitions) IntegerRing (class in sympy.polys.domains) Integers (class in sympy.sets.fancysets) Integral (class in sympy.integrals) Integral.is_commutative (in module sympy.integrals.transforms) integral_steps() (sympy.integrals.manualintegrate static method) integrand() (sympy.functions.special.hyper.meijerg method) integrate() (sympy.core.expr.Expr method) (sympy.integrals static method) (sympy.matrices.matrices.MatrixBase method) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) integrate_result() (in module sympy.physics.quantum.represent) interactive_traversal() (in module sympy.utilities.iterables) interior_angle (sympy.geometry.polygon.RegularPolygon attribute) interpolate() (in module sympy.polys.polyfuncs) interpolating_poly() (in module sympy.polys.specialpolys) intersect() (sympy.core.sets.Set method) (sympy.polys.agca.ideals.Ideal method) (sympy.polys.agca.modules.SubModule method) Intersection (class in sympy.core.sets) intersection() (in module sympy.geometry.util) (sympy.geometry.ellipse.Circle method) (sympy.geometry.ellipse.Ellipse method) (sympy.geometry.entity.GeometryEntity method) (sympy.geometry.line.LinearEntity method) (sympy.geometry.point.Point method) (sympy.geometry.polygon.Polygon method) Interval (class in sympy.core.sets) intervals() (in module sympy.polys.polytools) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) IntQubit (class in sympy.physics.quantum.qubit) IntQubitBra (class in sympy.physics.quantum.qubit) inv_mod() (sympy.matrices.matrices.MatrixBase method) Inverse (class in sympy.matrices.expressions) inverse() (sympy.functions.elementary.exponential.log method) (sympy.functions.elementary.hyperbolic.acosh method) (sympy.functions.elementary.hyperbolic.acoth method) (sympy.functions.elementary.hyperbolic.asinh method) (sympy.functions.elementary.hyperbolic.atanh method) (sympy.functions.elementary.hyperbolic.coth method) (sympy.functions.elementary.hyperbolic.sinh method) (sympy.functions.elementary.hyperbolic.tanh method) (sympy.functions.elementary.trigonometric.acos method) (sympy.functions.elementary.trigonometric.acot method) (sympy.functions.elementary.trigonometric.asin method) (sympy.functions.elementary.trigonometric.atan method) (sympy.functions.elementary.trigonometric.cot method) (sympy.functions.elementary.trigonometric.tan method) inverse_ADJ() (sympy.matrices.matrices.MatrixBase method) inverse_cosine_transform() (in module sympy.integrals.transforms) inverse_fourier_transform() (in module sympy.integrals.transforms) inverse_GE() (sympy.matrices.matrices.MatrixBase method) inverse_hankel_transform() (in module sympy.integrals.transforms) inverse_laplace_transform() (in module sympy.integrals.transforms) inverse_LU() (sympy.matrices.matrices.MatrixBase method) inverse_mellin_transform() (in module sympy.integrals.transforms) inverse_sine_transform() (in module sympy.integrals.transforms) inversion_vector() (sympy.combinatorics.permutations.Permutation method) inversions() (sympy.combinatorics.permutations.Permutation method) invert() (in module sympy.polys.polytools) (sympy.core.expr.Expr method) (sympy.polys.domains.domain.Domain method) (sympy.polys.domains.ring.Ring method) (sympy.polys.polyclasses.DMF method) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) IQFT (class in sympy.physics.quantum.qft) is_abelian (sympy.combinatorics.perm_groups.PermutationGroup attribute) is_above_fermi (sympy.functions.special.tensor_functions.KroneckerDelta attribute) (sympy.physics.secondquant.KroneckerDelta attribute) is_algebraic_expr() (sympy.core.expr.Expr method) is_aliased (sympy.polys.numberfields.AlgebraicNumber attribute) is_alt_sym() (sympy.combinatorics.perm_groups.PermutationGroup method) is_anti_symmetric() (sympy.matrices.matrices.MatrixBase method) is_below_fermi (sympy.functions.special.tensor_functions.KroneckerDelta attribute) (sympy.physics.secondquant.KroneckerDelta attribute) is_cnf() (in module sympy.logic.boolalg) is_collinear() (sympy.geometry.point.Point method) is_commutative (sympy.core.function.Function attribute) (sympy.physics.quantum.state.Wavefunction attribute) is_comparable (sympy.core.basic.Basic attribute) is_concurrent() (sympy.geometry.line.LinearEntity method) is_concyclic() (sympy.geometry.point.Point method) is_constant() (sympy.core.expr.Expr method) is_convex() (sympy.geometry.polygon.Polygon method) is_cyclotomic (sympy.polys.polyclasses.DMP attribute) (sympy.polys.polytools.Poly attribute) is_diagonal() (sympy.matrices.matrices.MatrixBase method) is_diagonalizable() (sympy.matrices.matrices.MatrixBase method)

is_dnf() (in module sympy.logic.boolalg) is_Empty (sympy.combinatorics.permutations.Permutation attribute) is_equilateral() (sympy.geometry.polygon.Triangle method) is_even (sympy.combinatorics.permutations.Permutation attribute) is_full_module() (sympy.polys.agca.modules.SubModule method) (sympy.polys.agca.modules.SubQuotientModule method) is_groebner() (in module sympy.polys.groebnertools) is_ground (sympy.polys.polyclasses.ANP attribute) (sympy.polys.polyclasses.DMP attribute) (sympy.polys.polytools.Poly attribute) is_group() (sympy.combinatorics.perm_groups.PermutationGroup method) is_homogeneous (sympy.polys.polyclasses.DMP attribute) (sympy.polys.polytools.Poly attribute) is_Identity (sympy.combinatorics.permutations.Permutation attribute) is_identity (sympy.core.function.Lambda attribute) is_injective() (sympy.polys.agca.homomorphisms.ModuleHomomorphism method) is_irreducible (sympy.polys.polyclasses.DMP attribute) (sympy.polys.polytools.Poly attribute) is_isomorphism() (sympy.polys.agca.homomorphisms.ModuleHomomorphism method) is_isosceles() (sympy.geometry.polygon.Triangle method) is_left_unbounded (sympy.core.sets.Interval attribute) is_linear (sympy.polys.polyclasses.DMP attribute) (sympy.polys.polytools.Poly attribute) is_lower (sympy.matrices.matrices.MatrixBase attribute) is_lower_hessenberg (sympy.matrices.matrices.MatrixBase attribute) is_maximal() (sympy.polys.agca.ideals.Ideal method) is_minimal() (in module sympy.polys.groebnertools) is_monic (sympy.polys.polyclasses.DMP attribute) (sympy.polys.polytools.Poly attribute) is_monomial (sympy.polys.polyclasses.DMP attribute) (sympy.polys.polytools.Poly attribute) is_multivariate (sympy.polys.polytools.Poly attribute) is_negative() (sympy.polys.domains.AlgebraicField method) (sympy.polys.domains.ExpressionDomain method) (sympy.polys.domains.FractionField method) (sympy.polys.domains.PolynomialRing method) (sympy.polys.domains.domain.Domain method) is_nilpotent (sympy.combinatorics.perm_groups.PermutationGroup attribute) is_nilpotent() (sympy.matrices.matrices.MatrixBase method) is_nonnegative() (sympy.polys.domains.AlgebraicField method) (sympy.polys.domains.ExpressionDomain method) (sympy.polys.domains.FractionField method) (sympy.polys.domains.PolynomialRing method) (sympy.polys.domains.domain.Domain method) is_nonpositive() (sympy.polys.domains.AlgebraicField method) (sympy.polys.domains.ExpressionDomain method) (sympy.polys.domains.FractionField method) (sympy.polys.domains.PolynomialRing method) (sympy.polys.domains.domain.Domain method) is_normal() (sympy.combinatorics.perm_groups.PermutationGroup method) is_normalized (sympy.physics.quantum.state.Wavefunction attribute) is_nthpow_residue() (in module sympy.ntheory.residue_ntheory) is_number (sympy.concrete.products.Product attribute) (sympy.concrete.summations.Sum attribute) (sympy.core.basic.Basic attribute) (sympy.core.expr.Expr attribute) (sympy.integrals.Integral attribute) is_odd (sympy.combinatorics.permutations.Permutation attribute) is_one (sympy.polys.polyclasses.ANP attribute) (sympy.polys.polyclasses.DMF attribute) (sympy.polys.polyclasses.DMP attribute) (sympy.polys.polytools.Poly attribute) is_one() (sympy.polys.domains.domain.Domain method) is_only_above_fermi (sympy.functions.special.tensor_functions.KroneckerDelta attribute) (sympy.physics.secondquant.KroneckerDelta attribute) is_only_below_fermi (sympy.functions.special.tensor_functions.KroneckerDelta attribute) (sympy.physics.secondquant.KroneckerDelta attribute) is_only_q_annihilator (sympy.physics.secondquant.AnnihilateFermion attribute) (sympy.physics.secondquant.CreateFermion attribute) is_only_q_creator (sympy.physics.secondquant.AnnihilateFermion attribute) (sympy.physics.secondquant.CreateFermion attribute) is_parallel() (sympy.geometry.line.LinearEntity method) is_perpendicular() (sympy.geometry.line.LinearEntity method) is_polynomial() (sympy.core.expr.Expr method) is_positive() (sympy.polys.domains.AlgebraicField method) (sympy.polys.domains.ExpressionDomain method) (sympy.polys.domains.FractionField method) (sympy.polys.domains.PolynomialRing method) (sympy.polys.domains.domain.Domain method) is_primary() (sympy.polys.agca.ideals.Ideal method) is_prime() (sympy.polys.agca.ideals.Ideal method) is_primitive (sympy.polys.polyclasses.DMP attribute) (sympy.polys.polytools.Poly attribute) is_primitive() (sympy.combinatorics.perm_groups.PermutationGroup method) is_primitive_root() (in module sympy.ntheory.residue_ntheory) is_principal() (sympy.polys.agca.ideals.Ideal method) is_q_annihilator (sympy.physics.secondquant.AnnihilateFermion attribute) (sympy.physics.secondquant.CreateFermion attribute) is_q_creator (sympy.physics.secondquant.AnnihilateFermion attribute) (sympy.physics.secondquant.CreateFermion attribute) is_quad_residue() (in module sympy.ntheory.residue_ntheory) is_quadratic (sympy.polys.polyclasses.DMP attribute) (sympy.polys.polytools.Poly attribute) is_radical() (sympy.polys.agca.ideals.Ideal method) is_rational_function() (sympy.core.expr.Expr method) is_reduced() (in module sympy.polys.groebnertools) is_right() (sympy.geometry.polygon.Triangle method) is_right_unbounded (sympy.core.sets.Interval attribute) is_scalene() (sympy.geometry.polygon.Triangle method) is_sequence() (in module sympy.core.compatibility) is_similar() (sympy.geometry.entity.GeometryEntity method) (sympy.geometry.line.LinearEntity method) (sympy.geometry.polygon.Triangle method) is_simple() (sympy.functions.special.delta_functions.DiracDelta method) is_Singleton (sympy.combinatorics.permutations.Permutation attribute) is_solvable (sympy.combinatorics.perm_groups.PermutationGroup attribute) is_sqf (sympy.polys.polyclasses.DMP attribute) (sympy.polys.polytools.Poly attribute) is_square (sympy.matrices.matrices.MatrixBase attribute) is_subdiagram() (sympy.categories.Diagram method) is_subgroup() (sympy.combinatorics.perm_groups.PermutationGroup method) is_submodule() (sympy.polys.agca.modules.FreeModule method) (sympy.polys.agca.modules.Module method) (sympy.polys.agca.modules.QuotientModule method) (sympy.polys.agca.modules.SubModule method) is_surjective() (sympy.polys.agca.homomorphisms.ModuleHomomorphism method) is_symbolic() (sympy.matrices.matrices.MatrixBase method) is_symmetric() (sympy.matrices.matrices.MatrixBase method) (sympy.matrices.sparse.SparseMatrix method) is_tangent() (sympy.geometry.ellipse.Ellipse method) is_transitive() (sympy.combinatorics.perm_groups.PermutationGroup method) is_trivial (sympy.combinatorics.perm_groups.PermutationGroup attribute) is_univariate (sympy.polys.polytools.Poly attribute) is_upper (sympy.matrices.matrices.MatrixBase attribute) is_upper_hessenberg (sympy.matrices.matrices.MatrixBase attribute) is_whole_ring() (sympy.polys.agca.ideals.Ideal method) is_zero (sympy.concrete.products.Product attribute) (sympy.concrete.summations.Sum attribute) (sympy.integrals.Integral attribute) (sympy.matrices.immutable.ImmutableMatrix attribute) (sympy.matrices.matrices.MatrixBase attribute) (sympy.polys.polyclasses.ANP attribute) (sympy.polys.polyclasses.DMF attribute) (sympy.polys.polyclasses.DMP attribute) (sympy.polys.polytools.Poly attribute) is_zero() (sympy.polys.agca.homomorphisms.ModuleHomomorphism method) (sympy.polys.agca.ideals.Ideal method) (sympy.polys.agca.modules.FreeModule method) (sympy.polys.agca.modules.Module method) (sympy.polys.agca.modules.QuotientModule method) (sympy.polys.agca.modules.SubModule method) (sympy.polys.domains.domain.Domain method) is_zero_dimensional (sympy.polys.polytools.GroebnerBasis attribute) is_zero_dimensional() (in module sympy.polys.polytools) isfinite() (in module mpmath) isinf() (in module mpmath) isint() (in module mpmath) isnan() (in module mpmath) isnormal() (in module mpmath) isolate() (in module sympy.polys.numberfields) IsomorphismFailed (class in sympy.polys.polyerrors) isprime() (in module sympy.ntheory.primetest) ITE (class in sympy.logic.boolalg) items() (sympy.core.containers.Dict method) iter_basic_args() (sympy.core.basic.Basic method) iter_q_annihilators() (sympy.physics.secondquant.NO method) iter_q_creators() (sympy.physics.secondquant.NO method) iterable() (in module sympy.core.compatibility) iterate_binary() (sympy.combinatorics.subsets.Subset method) iterate_graycode() (sympy.combinatorics.subsets.Subset method) itermonomials() (in module sympy.polys.monomials)

J

j0() (in module mpmath) j1() (in module mpmath) jacobi (class in sympy.functions.special.polynomials) jacobi() (in module mpmath) jacobi_normalized() (in module sympy.functions.special.polynomials) jacobi_poly() (in module sympy.polys.orthopolys) jacobi_symbol() (in module sympy.ntheory.residue_ntheory) jacobian() (sympy.diffgeom.CoordSystem method) (sympy.matrices.matrices.MatrixBase method) jn (class in sympy.functions.special.bessel) jn_zeros() (in module sympy.functions.special.bessel) jordan_cell() (in module sympy.matrices.dense) jordan_cells() (sympy.matrices.matrices.MatrixBase method) jordan_form() (sympy.matrices.matrices.MatrixBase method) josephus() (sympy.combinatorics.permutations.Permutation class method)

jtheta() (in module mpmath) JxBra (class in sympy.physics.quantum.spin) JxBraCoupled (class in sympy.physics.quantum.spin) JxKet (class in sympy.physics.quantum.spin) JxKetCoupled (class in sympy.physics.quantum.spin) JyBra (class in sympy.physics.quantum.spin) JyBraCoupled (class in sympy.physics.quantum.spin) JyKet (class in sympy.physics.quantum.spin) JyKetCoupled (class in sympy.physics.quantum.spin) JzBra (class in sympy.physics.quantum.spin) JzBraCoupled (class in sympy.physics.quantum.spin) JzKet (class in sympy.physics.quantum.spin) JzKetCoupled (class in sympy.physics.quantum.spin)

K

kanes_equations() (sympy.physics.mechanics.kane.KanesMethod method) KanesMethod (class in sympy.physics.mechanics.kane) kbins() (in module sympy.utilities.iterables) kei() (in module mpmath) ker() (in module mpmath) kernel() (sympy.polys.agca.homomorphisms.ModuleHomomorphism method) Ket (class in sympy.physics.quantum.state) ket (sympy.physics.quantum.operator.OuterProduct attribute) (sympy.physics.secondquant.InnerProduct attribute) KetBase (class in sympy.physics.quantum.state) key2bounds() (sympy.matrices.matrices.MatrixBase method) key2ij() (sympy.matrices.matrices.MatrixBase method) keys() (sympy.core.containers.Dict method) kfrom() (in module mpmath)

khinchin (mpmath.mp attribute) kid_rsa_private_key() (in module sympy.crypto.crypto) kid_rsa_public_key() (in module sympy.crypto.crypto) killable_index (sympy.functions.special.tensor_functions.KroneckerDelta attribute) (sympy.physics.secondquant.KroneckerDelta attribute) kindiffdict() (sympy.physics.mechanics.kane.KanesMethod method) kinematic_equations() (in module sympy.physics.vector.functions) kinetic_energy() (in module sympy.physics.mechanics.functions) (sympy.physics.mechanics.particle.Particle method) (sympy.physics.mechanics.rigidbody.RigidBody method) kleinj() (in module mpmath) known_functions (in module sympy.printing.ccode) KroneckerDelta (class in sympy.functions.special.tensor_functions) (class in sympy.physics.secondquant) ksubsets() (sympy.combinatorics.subsets static method) Kumaraswamy() (in module sympy.stats)

L

l1_norm() (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) L2 (class in sympy.physics.quantum.hilbert) label (sympy.physics.quantum.state.TimeDepState attribute) (sympy.tensor.indexed.Idx attribute) (sympy.tensor.indexed.IndexedBase attribute) labeller() (in module sympy.physics.quantum.circuitplot) LagrangesMethod (class in sympy.physics.mechanics.lagrange) Lagrangian() (in module sympy.physics.mechanics.functions) laguerre (class in sympy.functions.special.polynomials) laguerre() (in module mpmath) laguerre_poly() (in module sympy.polys.orthopolys) Lambda (class in sympy.core.function) LambdaPrinter (class in sympy.printing.lambdarepr) lambdarepr() (in module sympy.printing.lambdarepr) lambdastr() (in module sympy.utilities.lambdify) lambdify() (in module sympy.utilities.lambdify) LambertW (class in sympy.functions.elementary.exponential) lambertw() (in module mpmath) Laplace() (in module sympy.stats) laplace_transform() (in module sympy.integrals.transforms) latex() (in module sympy.galgebra.printing) (in module sympy.printing.latex) LatexPrinter (class in sympy.printing.latex) LC() (in module sympy.polys.polytools) (sympy.polys.polyclasses.ANP method) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) lcm() (in module sympy.polys.polytools) (sympy.core.numbers.Number method) (sympy.polys.domains.PolynomialRing method) (sympy.polys.domains.RealField method) (sympy.polys.domains.domain.Domain method) (sympy.polys.domains.field.Field method) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) lcm_list() (in module sympy.polys.polytools) ldescent() (in module sympy.solvers.diophantine) ldexp() (in module mpmath) LDLdecomposition() (sympy.matrices.matrices.MatrixBase method) (sympy.matrices.sparse.SparseMatrix method) LDLsolve() (sympy.matrices.matrices.MatrixBase method) Le (in module sympy.core.relational) leadterm() (sympy.core.expr.Expr method) left (sympy.core.sets.Interval attribute) left() (sympy.printing.pretty.stringpict.stringPict method) left_open (sympy.core.sets.Interval attribute) leftslash() (sympy.printing.pretty.stringpict.stringPict method) legendre (class in sympy.functions.special.polynomials) legendre() (in module mpmath) legendre_poly() (in module sympy.polys.orthopolys) legendre_symbol() (in module sympy.ntheory.residue_ntheory) legenp() (in module mpmath) legenq() (in module mpmath) length (sympy.geometry.line.LinearEntity attribute) (sympy.geometry.line.Segment attribute) (sympy.geometry.point.Point attribute) (sympy.geometry.polygon.RegularPolygon attribute) length() (sympy.combinatorics.permutations.Permutation method) (sympy.polys.polytools.Poly method) lerchphi (class in sympy.functions.special.zeta_functions) lerchphi() (in module mpmath) LessThan (class in sympy.core.relational) LeviCivita (class in sympy.functions.special.tensor_functions) levin() (in module mpmath) LexOrder (class in sympy.polys.orderings) lfsr_autocorrelation() (in module sympy.crypto.crypto) lfsr_connection_polynomial() (in module sympy.crypto.crypto) lfsr_sequence() (in module sympy.crypto.crypto) Li (class in sympy.functions.special.error_functions) li (class in sympy.functions.special.error_functions) li() (in module mpmath) lie_heuristic_abaco1_product() (in module sympy.solvers.ode) lie_heuristic_abaco1_simple() (in module sympy.solvers.ode) lie_heuristic_abaco2_similar() (in module sympy.solvers.ode) lie_heuristic_abaco2_unique_general() (in module sympy.solvers.ode)

lie_heuristic_abaco2_unique_unknown() (in module sympy.solvers.ode) lie_heuristic_bivariate() (in module sympy.solvers.ode) lie_heuristic_chi() (in module sympy.solvers.ode) lie_heuristic_function_sum() (in module sympy.solvers.ode) lie_heuristic_linear() (in module sympy.solvers.ode) LieDerivative (class in sympy.diffgeom) lift() (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) Limit (class in sympy.series.limits) limit() (in module mpmath) (in module sympy.series.limits) (sympy.core.expr.Expr method) (sympy.matrices.matrices.MatrixBase method) limit_denominator() (sympy.core.numbers.Rational method) limitinf() (in module sympy.series.gruntz) limits (sympy.geometry.curve.Curve attribute) (sympy.physics.quantum.state.Wavefunction attribute) Line (class in sympy.geometry.line) Line2DBaseSeries (class in sympy.plotting.plot) Line3DBaseSeries (class in sympy.plotting.plot) line_integrate() (sympy.integrals static method) linear_derivation() (in module sympy.galgebra.ncutil) linear_expand() (in module sympy.galgebra.ncutil) linear_function() (in module sympy.galgebra.ncutil) linear_momentum() (in module sympy.physics.mechanics.functions) (sympy.physics.mechanics.particle.Particle method) (sympy.physics.mechanics.rigidbody.RigidBody method) linear_projection() (in module sympy.galgebra.ncutil) LinearEntity (class in sympy.geometry.line) linearize() (sympy.physics.mechanics.kane.KanesMethod method) LineOver1DRangeSeries (class in sympy.plotting.plot) linspace() (in module mpmath) list() (sympy.combinatorics.permutations.Cycle method) (sympy.combinatorics.permutations.Permutation method) list2numpy() (in module sympy.matrices.dense) list_visitor() (in module sympy.utilities.enumerative) liupc() (sympy.matrices.sparse.SparseMatrix method) LM() (in module sympy.polys.polytools) (sympy.polys.polytools.Poly method) ln() (in module mpmath) locatenew() (sympy.physics.vector.point.Point method) log (class in sympy.functions.elementary.exponential) log() (in module mpmath) (sympy.polys.domains.IntegerRing method) (sympy.polys.domains.domain.Domain method) log10() (in module mpmath) logcombine() (in module sympy.simplify.simplify) loggamma (class in sympy.functions.special.gamma_functions) loggamma() (in module mpmath) Logistic() (in module sympy.stats) logm() (in module mpmath) LogNormal() (in module sympy.stats) lommels1() (in module mpmath) lommels2() (in module mpmath) lower (sympy.physics.secondquant.AntiSymmetricTensor attribute) (sympy.tensor.indexed.Idx attribute) lower_central_series() (sympy.combinatorics.perm_groups.PermutationGroup method) lower_triangular_solve() (sympy.matrices.matrices.MatrixBase method) lowergamma (class in sympy.functions.special.gamma_functions) lseries() (sympy.core.expr.Expr method) Lt (in module sympy.core.relational) LT() (in module sympy.polys.polytools) (sympy.polys.polytools.Poly method) ltrim() (sympy.polys.polytools.Poly method) lucas (class in sympy.functions.combinatorial.numbers) LUdecomposition() (sympy.matrices.matrices.MatrixBase method) LUdecomposition_Simple() (sympy.matrices.matrices.MatrixBase method) LUdecompositionFF() (sympy.matrices.matrices.MatrixBase method) LUsolve() (sympy.matrices.matrices.MatrixBase method)

M

mag() (in module mpmath) magnitude() (sympy.physics.vector.vector.Vector method) major (sympy.geometry.ellipse.Ellipse attribute) make_perm() (sympy.combinatorics.perm_groups.PermutationGroup method) make_prime() (in module sympy.solvers.diophantine) mangoldt() (in module mpmath) Manifold (class in sympy.diffgeom) (class in sympy.galgebra.manifold) Manifold() (in module sympy.galgebra.ga) manualintegrate() (sympy.integrals static method) map() (sympy.polys.domains.domain.Domain method) mass (sympy.physics.mechanics.particle.Particle attribute) mass_matrix (sympy.physics.mechanics.lagrange.LagrangesMethod attribute) mass_matrix_full (sympy.physics.mechanics.lagrange.LagrangesMethod attribute) MatAdd (class in sympy.matrices.expressions) match() (sympy.core.basic.Basic method) matches() (sympy.core.basic.Basic method) mathematica() (in module sympy.parsing.mathematica) mathml() (in module sympy.printing.mathml) mathml_tag() (sympy.printing.mathml.MathMLPrinter method) MathMLPrinter (class in sympy.printing.mathml) MatMul (class in sympy.matrices.expressions) MatPow (class in sympy.matrices.expressions) matrix2numpy() (in module sympy.matrices.dense) matrix_fglm() (in module sympy.polys.fglmtools) matrix_multiply_elementwise() (in module sympy.matrices.dense) matrix_rep() (in module sympy.physics.secondquant) matrix_to_density() (in module sympy.physics.quantum.qubit) matrix_to_qubit() (in module sympy.physics.quantum.qubit) MatrixBase (class in sympy.matrices.matrices) MatrixError (class in sympy.matrices.matrices) MatrixExpr (class in sympy.matrices.expressions) MatrixSymbol (class in sympy.matrices.expressions) Max (class in sympy.functions.elementary.miscellaneous) max() (sympy.combinatorics.permutations.Permutation method) max_div (sympy.combinatorics.perm_groups.PermutationGroup attribute) max_norm() (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) maxcalls() (in module mpmath) Maxwell() (in module sympy.stats) maybe() (in module sympy.parsing.sympy_tokenize) MDNewton (class in mpmath.calculus.optimization) measure (sympy.core.sets.Set attribute) measure_all() (in module sympy.physics.quantum.qubit) measure_all_oneshot() (in module sympy.physics.quantum.qubit) measure_partial() (in module sympy.physics.quantum.qubit) measure_partial_oneshot() (in module sympy.physics.quantum.qubit) medial (sympy.geometry.polygon.Triangle attribute) medians (sympy.geometry.polygon.Triangle attribute) meets() (sympy.series.gruntz.SubsSet method) meijerg (class in sympy.functions.special.hyper) meijerg() (in module mpmath) mellin_transform() (in module sympy.integrals.transforms) memoize() (in module mpmath) merge_solution() (in module sympy.solvers.diophantine) mertens (mpmath.mp attribute) metric_to_Christoffel_1st() (in module sympy.diffgeom) metric_to_Christoffel_2nd() (in module sympy.diffgeom) metric_to_Ricci_components() (in module sympy.diffgeom) metric_to_Riemann_components() (in module sympy.diffgeom) mfrom() (in module mpmath) mgamma() (in module sympy.physics.matrices) midpoint (sympy.geometry.line.Segment attribute) midpoint() (sympy.geometry.point.Point method)

Min (class in sympy.functions.elementary.miscellaneous) min() (sympy.combinatorics.permutations.Permutation method) min_qubits (sympy.physics.quantum.gate.CGate attribute) (sympy.physics.quantum.gate.CNotGate attribute) (sympy.physics.quantum.gate.Gate attribute) minimal_block() (sympy.combinatorics.perm_groups.PermutationGroup method) minimal_polynomial() (in module sympy.polys.numberfields) minlex() (in module sympy.utilities.iterables) minor (sympy.geometry.ellipse.Ellipse attribute) minorEntry() (sympy.matrices.matrices.MatrixBase method) minorMatrix() (sympy.matrices.matrices.MatrixBase method) minpoly() (in module sympy.polys.numberfields) MNewton (class in mpmath.calculus.optimization) mnorm() (in module mpmath) Mod (class in sympy.core.mod) modgcd_bivariate (class in sympy.polys.modulargcd) modgcd_multivariate (class in sympy.polys.modulargcd) modgcd_univariate (class in sympy.polys.modulargcd) Module (class in sympy.polys.agca.modules) module_quotient() (sympy.polys.agca.modules.SubModule method) ModuleHomomorphism (class in sympy.polys.agca.homomorphisms) momentum (sympy.physics.quantum.cartesian.PxBra attribute) (sympy.physics.quantum.cartesian.PxKet attribute) monic() (in module sympy.polys.polytools) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) monitor() (in module mpmath) Monomial (class in sympy.polys.monomials) monomial_count() (in module sympy.polys.monomials) monoms() (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) Morphism (class in sympy.categories) morphisms (sympy.categories.diagram_drawing.DiagramGrid attribute) mpmath.functions.elliptic (module) mpmathify() (in module mpmath) mr() (in module sympy.ntheory.primetest) mrv() (in module sympy.series.gruntz) mrv_leadterm() (in module sympy.series.gruntz) mrv_max1() (in module sympy.series.gruntz) mrv_max3() (in module sympy.series.gruntz) msigma() (in module sympy.physics.matrices) Mul (class in sympy.core.mul) Mul() (sympy.assumptions.handlers.calculus.AskBoundedHandler static method) (sympy.assumptions.handlers.calculus.AskInfinitesimalHandler static method) (sympy.assumptions.handlers.sets.AskAntiHermitianHandler static method) (sympy.assumptions.handlers.sets.AskHermitianHandler static method) (sympy.assumptions.handlers.sets.AskImaginaryHandler static method) (sympy.assumptions.handlers.sets.AskIntegerHandler static method) (sympy.assumptions.handlers.sets.AskRationalHandler static method) (sympy.assumptions.handlers.sets.AskRealHandler static method) mul() (sympy.polys.domains.domain.Domain method) (sympy.polys.polyclasses.DMF method) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) (sympy.tensor.tensor.TIDS static method) (sympy.tensor.tensor.VTIDS static method) mul_ground() (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) mul_inv() (sympy.combinatorics.permutations.Permutation method) Muller (class in mpmath.calculus.optimization) MultiFactorial (class in sympy.functions.combinatorial.factorials) multilinear_derivation() (in module sympy.galgebra.ncutil) multilinear_function() (in module sympy.galgebra.ncutil) multilinear_product() (in module sympy.galgebra.ncutil) multinomial_coefficients() (in module sympy.ntheory.multinomial) multinomial_coefficients_iterator() (in module sympy.ntheory.multinomial) multiplicity() (in module sympy.ntheory.factor_) multiply() (sympy.matrices.matrices.MatrixBase method) (sympy.matrices.sparse.SparseMatrix method) multiply_elementwise() (sympy.matrices.matrices.MatrixBase method) multiply_ideal() (sympy.polys.agca.modules.FreeModule method) (sympy.polys.agca.modules.Module method) (sympy.polys.agca.modules.SubModule method) multiset() (in module sympy.utilities.iterables) multiset_combinations() (in module sympy.utilities.iterables) multiset_partitions() (in module sympy.utilities.iterables) multiset_partitions_taocp() (in module sympy.utilities.enumerative) multiset_permutations() (in module sympy.utilities.iterables) MultisetPartitionTraverser (class in sympy.utilities.enumerative) MultivariatePolynomialError (class in sympy.polys.polyerrors) MutableDenseMatrix (class in sympy.matrices.dense) MutableSparseMatrix (class in sympy.matrices.sparse) Mx (class in sympy.physics.quantum.circuitplot) Mz (class in sympy.physics.quantum.circuitplot)

N

N (class in sympy.core.evalf) n (sympy.combinatorics.graycode.GrayCode attribute) N (sympy.physics.quantum.shor.CMod attribute) n() (sympy.geometry.point.Point method) (sympy.matrices.matrices.MatrixBase method) (sympy.polys.domains.domain.Domain method) n_order() (in module sympy.ntheory.residue_ntheory) Nakagami() (in module sympy.stats) name (sympy.categories.Category attribute) (sympy.categories.NamedMorphism attribute) NamedMorphism (class in sympy.categories) NaN (class in sympy.core.numbers) Nand (class in sympy.logic.boolalg) nargs (sympy.core.function.FunctionClass attribute) native_coeffs() (sympy.polys.numberfields.AlgebraicNumber method) Naturals (class in sympy.sets.fancysets) Naturals0 (class in sympy.sets.fancysets) ncdf() (in module mpmath) Ne (in module sympy.core.relational) necklaces() (in module sympy.utilities.iterables) neg() (sympy.polys.domains.domain.Domain method) (sympy.polys.polyclasses.DMF method) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) NegativeInfinity (class in sympy.core.numbers) NegativeOne (class in sympy.core.numbers) new() (sympy.polys.polytools.Poly class method) Newton (class in mpmath.calculus.optimization) next() (sympy.combinatorics.graycode.GrayCode method) (sympy.combinatorics.prufer.Prufer method) (sympy.printing.pretty.stringpict.stringPict static method) next_binary() (sympy.combinatorics.subsets.Subset method) next_gray() (sympy.combinatorics.subsets.Subset method) next_lex() (sympy.combinatorics.partitions.IntegerPartition method) (sympy.combinatorics.permutations.Permutation method) next_lexicographic() (sympy.combinatorics.subsets.Subset method) next_nonlex() (sympy.combinatorics.permutations.Permutation method) next_trotterjohnson() (sympy.combinatorics.permutations.Permutation method) nextprime() (in module sympy.ntheory.generate) nfloat() (in module sympy.core.function) nint() (in module mpmath) nint_distance() (in module mpmath) nnz() (sympy.matrices.sparse.SparseMatrix method) NO (class in sympy.physics.secondquant) no_attrs_in_subclass (in module sympy.utilities.decorator) nodes (sympy.combinatorics.prufer.Prufer attribute) non_scalar_projection() (in module sympy.galgebra.ncutil)

NonSquareMatrixError (class in sympy.matrices.matrices) Nor (class in sympy.logic.boolalg) norm (sympy.physics.quantum.state.Wavefunction attribute) norm() (in module mpmath) (sympy.matrices.matrices.MatrixBase method) Normal (class in sympy.statistics.distributions) Normal() (in module sympy.stats) normal_closure() (sympy.combinatorics.perm_groups.PermutationGroup method) normal_lines() (sympy.geometry.ellipse.Ellipse method) normalize() (sympy.physics.quantum.state.Wavefunction method) (sympy.physics.vector.vector.Vector method) (sympy.statistics.distributions.PDF method) normalized() (in module sympy.physics.quantum.gate) (sympy.matrices.matrices.MatrixBase method) NormalPSpace (class in sympy.stats.crv_types) Not (class in sympy.logic.boolalg) NotAlgebraic (class in sympy.polys.polyerrors) NotInvertible (class in sympy.polys.polyerrors) NotReversible (class in sympy.polys.polyerrors) npartitions() (in module sympy.ntheory.partitions_) npdf() (in module mpmath) nprint() (in module mpmath) nprod() (in module mpmath) nqubits (sympy.physics.quantum.gate.CGate attribute) (sympy.physics.quantum.gate.Gate attribute) nroots() (in module sympy.polys.polytools) (sympy.polys.polytools.Poly method) nseries() (sympy.core.expr.Expr method) nsimplify() (in module sympy.simplify.simplify) (sympy.core.expr.Expr method) nsolve() (in module sympy.solvers.solvers) nstr() (in module mpmath) nsum() (in module mpmath) nth() (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) nth_power_roots_poly() (in module sympy.polys.polytools) (sympy.polys.polytools.Poly method) nthroot() (in module sympy.simplify.simplify) nthroot_mod() (in module sympy.ntheory.residue_ntheory) nu (sympy.functions.special.hyper.meijerg attribute) nullspace() (sympy.matrices.matrices.MatrixBase method) Number (class in sympy.core.numbers) numbered_symbols() (in module sympy.utilities.iterables) NumberSymbol (class in sympy.core.numbers) numer() (sympy.polys.domains.AlgebraicField method) (sympy.polys.domains.ExpressionDomain method) (sympy.polys.domains.FractionField method) (sympy.polys.domains.domain.Domain method) (sympy.polys.domains.ring.Ring method) (sympy.polys.polyclasses.DMF method) nzeros() (in module mpmath)

O

Object (class in sympy.categories) objects (sympy.categories.Category attribute) (sympy.categories.Diagram attribute) ode_1st_exact() (in module sympy.solvers.ode) ode_1st_homogeneous_coeff_best() (in module sympy.solvers.ode) ode_1st_homogeneous_coeff_subs_dep_div_indep() (in module sympy.solvers.ode) ode_1st_homogeneous_coeff_subs_indep_div_dep() (in module sympy.solvers.ode) ode_1st_linear() (in module sympy.solvers.ode) ode_1st_power_series() (in module sympy.solvers.ode) ode_2nd_power_series_ordinary() (in module sympy.solvers.ode) ode_2nd_power_series_regular() (in module sympy.solvers.ode) ode_almost_linear() (in module sympy.solvers.ode) ode_Bernoulli() (in module sympy.solvers.ode) ode_lie_group() (in module sympy.solvers.ode) ode_linear_coefficients() (in module sympy.solvers.ode) ode_Liouville() (in module sympy.solvers.ode) ode_nth_linear_constant_coeff_homogeneous() (in module sympy.solvers.ode) ode_nth_linear_constant_coeff_undetermined_coefficients() (in module sympy.solvers.ode) ode_nth_linear_constant_coeff_variation_of_parameters() (in module sympy.solvers.ode) ode_order() (in module sympy.solvers.deutils) ode_Riccati_special_minus2() (in module sympy.solvers.ode) ode_separable() (in module sympy.solvers.ode) ode_separable_reduced() (in module sympy.solvers.ode) ode_sol_simplicity() (in module sympy.solvers.ode) odefun() (in module mpmath) odesimp() (in module sympy.solvers.ode) of_type() (sympy.polys.domains.domain.Domain method) old_frac_field() (sympy.polys.domains.domain.Domain method)

old_poly_ring() (sympy.polys.domains.domain.Domain method) One (class in sympy.core.numbers) one (sympy.polys.polytools.Poly attribute) OneQubitGate (class in sympy.physics.quantum.gate) ones() (in module sympy.matrices.dense) OperationNotSupported (class in sympy.polys.polyerrors) Operator (class in sympy.physics.quantum.operator) operators (sympy.physics.quantum.state.StateBase attribute) operators_to_state() (in module sympy.physics.quantum.operatorset) oprint() (in module sympy.galgebra.debug) opt_cse() (in module sympy.simplify.cse_main) OptionError (class in sympy.polys.polyerrors) Or (class in sympy.logic.boolalg) OracleGate (class in sympy.physics.quantum.grover) orbit() (sympy.combinatorics.perm_groups.PermutationGroup method) orbit_rep() (sympy.combinatorics.perm_groups.PermutationGroup method) orbit_transversal() (sympy.combinatorics.perm_groups.PermutationGroup method) orbits() (sympy.combinatorics.perm_groups.PermutationGroup method) Order (class in sympy.series.order) order (sympy.functions.special.bessel.BesselBase attribute) order() (sympy.combinatorics.perm_groups.PermutationGroup method) (sympy.combinatorics.permutations.Permutation method) orient() (sympy.physics.vector.frame.ReferenceFrame method) orientnew() (sympy.physics.vector.frame.ReferenceFrame method) orthocenter (sympy.geometry.polygon.Triangle attribute) ostr() (in module sympy.galgebra.debug) outer() (in module sympy.physics.vector.functions) (sympy.physics.vector.vector.Vector method) OuterProduct (class in sympy.physics.quantum.operator)

P

P() (in module sympy.stats) p1 (sympy.geometry.line.LinearEntity attribute) p2 (sympy.geometry.line.LinearEntity attribute) pade() (in module mpmath) pairwise_prime() (in module sympy.solvers.diophantine) parallel_line() (sympy.geometry.line.LinearEntity method) parallel_poly_from_expr() (in module sympy.polys.polytools) parameter (sympy.geometry.curve.Curve attribute) Parametric2DLineSeries (class in sympy.plotting.plot) Parametric3DLineSeries (class in sympy.plotting.plot) ParametricSurfaceSeries (class in sympy.plotting.plot) parametrize_ternary_quadratic() (in module sympy.solvers.diophantine) parens() (sympy.printing.pretty.stringpict.stringPict method) Pareto() (in module sympy.stats) parity() (sympy.combinatorics.permutations.Permutation method) parse_data() (sympy.tensor.tensor.VTIDS static method) parse_expr() (in module sympy.parsing.sympy_parser) parse_line() (in module sympy.galgebra.precedence) parse_maxima() (in module sympy.parsing.maxima) parse_paren() (in module sympy.galgebra.precedence) partial_velocity() (in module sympy.physics.vector.functions) Particle (class in sympy.physics.mechanics.particle) Partition (class in sympy.combinatorics.partitions) partition (sympy.combinatorics.partitions.Partition attribute) partition() (in module sympy.solvers.diophantine) partitions() (in module sympy.utilities.iterables) pat_matrix() (in module sympy.physics.matrices) Patch (class in sympy.diffgeom) pcfd() (in module mpmath) pcfu() (in module mpmath) pcfv() (in module mpmath) pcfw() (in module mpmath) pde_1st_linear_constant_coeff() (in module sympy.solvers.pde) pde_1st_linear_constant_coeff_homogeneous() (in module sympy.solvers.pde) pde_1st_linear_variable_coeff() (in module sympy.solvers.pde) pde_separate() (in module sympy.solvers.pde) pde_separate_add() (in module sympy.solvers.pde) pde_separate_mul() (in module sympy.solvers.pde) PDF (class in sympy.statistics.distributions) pdf() (sympy.statistics.distributions.Normal method) (sympy.statistics.distributions.Uniform method) pdiv() (in module sympy.polys.polytools) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) pdsolve() (in module sympy.solvers.pde) Pegasus (class in mpmath.calculus.optimization) per() (sympy.polys.polyclasses.DMF method) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) perfect_power() (in module sympy.ntheory.factor_) periapsis (sympy.geometry.ellipse.Ellipse attribute) perimeter (sympy.geometry.polygon.Polygon attribute) period_find() (in module sympy.physics.quantum.shor) perm2tensor() (sympy.tensor.tensor.TensMul method) (sympy.tensor.tensor.TIDS method) Permutation (class in sympy.combinatorics.permutations) PermutationGroup (class in sympy.combinatorics.perm_groups) PermutationOperator (class in sympy.physics.secondquant) permute() (sympy.polys.polyclasses.DMP method) permuteBkwd() (sympy.matrices.matrices.MatrixBase method) permuteFwd() (sympy.matrices.matrices.MatrixBase method) perpendicular_bisector() (sympy.geometry.line.Segment method) perpendicular_line() (sympy.geometry.line.LinearEntity method) perpendicular_segment() (sympy.geometry.line.LinearEntity method) pexquo() (in module sympy.polys.polytools) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) pgroup (sympy.combinatorics.polyhedron.Polyhedron attribute) Phase (in module sympy.physics.quantum.gate) PhaseGate (class in sympy.physics.quantum.gate) phi (mpmath.mp attribute) Pi (class in sympy.core.numbers) pi (mpmath.mp attribute) PIABBra (class in sympy.physics.quantum.piab) PIABHamiltonian (class in sympy.physics.quantum.piab) PIABKet (class in sympy.physics.quantum.piab) Piecewise (class in sympy.functions.elementary.piecewise) piecewise_fold() (in module sympy.functions.elementary.piecewise) pinv() (sympy.matrices.matrices.MatrixBase method) pinv_solve() (sympy.matrices.matrices.MatrixBase method) Plot (class in sympy.plotting.plot) plot() (in module mpmath) (in module sympy.plotting.plot) plot3d() (in module sympy.plotting.plot) plot3d_parametric_line() (in module sympy.plotting.plot) plot3d_parametric_surface() (in module sympy.plotting.plot) plot_gate() (sympy.physics.quantum.gate.CGate method) plot_implicit() (in module sympy.plotting.plot_implicit) plot_interval() (sympy.geometry.curve.Curve method) (sympy.geometry.ellipse.Ellipse method) (sympy.geometry.line.Line method) (sympy.geometry.line.Ray method) (sympy.geometry.line.Segment method) (sympy.geometry.polygon.Polygon method) plot_parametric() (in module sympy.plotting.plot) Point (class in sympy.diffgeom) (class in sympy.geometry.point) (class in sympy.physics.vector.point) point (sympy.core.function.Subs attribute) (sympy.physics.mechanics.particle.Particle attribute) point() (sympy.diffgeom.CoordSystem method) point_to_coords() (sympy.diffgeom.CoordSystem method) points (sympy.geometry.line.LinearEntity attribute) pointwise_stabilizer() (sympy.combinatorics.perm_groups.PermutationGroup method) Poisson() (in module sympy.stats) polar() (in module mpmath) PoleError (class in sympy.core.function) PolificationFailed (class in sympy.polys.polyerrors) pollard_pm1() (in module sympy.ntheory.factor_) pollard_rho() (in module sympy.ntheory.factor_) Poly (class in sympy.polys.polytools) poly() (in module sympy.polys.polytools) poly_from_expr() (in module sympy.polys.polytools) poly_ring() (sympy.polys.domains.domain.Domain method) poly_unify() (sympy.polys.polyclasses.DMF method) polyexp() (in module mpmath) polygamma (class in sympy.functions.special.gamma_functions) Polygon (class in sympy.geometry.polygon) Polyhedron (class in sympy.combinatorics.polyhedron) polylog (class in sympy.functions.special.zeta_functions) polylog() (in module mpmath) PolynomialError (class in sympy.polys.polyerrors) PolynomialRing (class in sympy.polys.domains) polyroots() (in module mpmath) polyval() (in module mpmath)

pos() (sympy.polys.domains.domain.Domain method) pos_from() (sympy.physics.vector.point.Point method) POSform() (in module sympy.logic.boolalg) posify() (in module sympy.simplify.simplify) position (sympy.physics.quantum.cartesian.XBra attribute) (sympy.physics.quantum.cartesian.XKet attribute) position_x (sympy.physics.quantum.cartesian.PositionState3D attribute) position_y (sympy.physics.quantum.cartesian.PositionState3D attribute) position_z (sympy.physics.quantum.cartesian.PositionState3D attribute) PositionBra3D (class in sympy.physics.quantum.cartesian) PositionKet3D (class in sympy.physics.quantum.cartesian) PositionState3D (class in sympy.physics.quantum.cartesian) postfixes() (in module sympy.utilities.iterables) postorder_traversal() (in module sympy.utilities.iterables) potential_energy (sympy.physics.mechanics.particle.Particle attribute) (sympy.physics.mechanics.rigidbody.RigidBody attribute) potential_energy() (in module sympy.physics.mechanics.functions) Pow (class in sympy.core.power) Pow() (sympy.assumptions.handlers.calculus.AskBoundedHandler static method) (sympy.assumptions.handlers.calculus.AskInfinitesimalHandler static method) (sympy.assumptions.handlers.ntheory.AskPrimeHandler static method) (sympy.assumptions.handlers.order.AskNegativeHandler static method) (sympy.assumptions.handlers.sets.AskAntiHermitianHandler static method) (sympy.assumptions.handlers.sets.AskHermitianHandler static method) (sympy.assumptions.handlers.sets.AskImaginaryHandler static method) (sympy.assumptions.handlers.sets.AskIntegerHandler static method) (sympy.assumptions.handlers.sets.AskRationalHandler static method) (sympy.assumptions.handlers.sets.AskRealHandler static method) pow() (sympy.polys.domains.domain.Domain method) (sympy.polys.polyclasses.ANP method) (sympy.polys.polyclasses.DMF method) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) powdenest() (in module sympy.simplify.simplify) power() (in module mpmath) powm() (in module mpmath) powm1() (in module mpmath) powsimp() (in module sympy.simplify.simplify) (sympy.core.expr.Expr method) pprint_nodes() (in module sympy.printing.tree) PQa() (in module sympy.solvers.diophantine) pquo() (in module sympy.polys.polytools) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) PRECEDENCE (in module sympy.printing.precedence) precedence() (in module sympy.printing.precedence) PRECEDENCE_FUNCTIONS (in module sympy.printing.precedence) PRECEDENCE_VALUES (in module sympy.printing.precedence) PrecisionExhausted (class in sympy.core.evalf) Predicate (class in sympy.assumptions.assume) preferred_index (sympy.functions.special.tensor_functions.KroneckerDelta attribute) (sympy.physics.secondquant.KroneckerDelta attribute) prefixes() (in module sympy.utilities.iterables) prem() (in module sympy.polys.polytools) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) premises (sympy.categories.Diagram attribute) pretty() (in module sympy.printing.pretty.pretty) pretty_atom() (in module sympy.printing.pretty.pretty_symbology) pretty_print() (in module sympy.printing.pretty.pretty) pretty_symbol() (in module sympy.printing.pretty.pretty_symbology) pretty_try_use_unicode() (in module sympy.printing.pretty.pretty_symbology) pretty_use_unicode() (in module sympy.printing.pretty.pretty_symbology) prettyForm (class in sympy.printing.pretty.stringpict) PrettyPrinter (class in sympy.printing.pretty.pretty) prev() (sympy.combinatorics.prufer.Prufer method) prev_binary() (sympy.combinatorics.subsets.Subset method) prev_gray() (sympy.combinatorics.subsets.Subset method) prev_lex() (sympy.combinatorics.partitions.IntegerPartition method) prev_lexicographic() (sympy.combinatorics.subsets.Subset method) preview() (in module sympy.printing.preview) preview_diagram() (in module sympy.categories.diagram_drawing) prevprime() (in module sympy.ntheory.generate) prime() (in module sympy.ntheory.generate) prime_as_sum_of_two_squares() (in module sympy.solvers.diophantine) primefactors() (in module sympy.ntheory.factor_) primepi() (in module mpmath) (in module sympy.ntheory.generate) primepi2() (in module mpmath) primerange() (in module sympy.ntheory.generate) (sympy.ntheory.generate.Sieve method) primezeta() (in module mpmath) primitive() (in module sympy.polys.polytools) (sympy.core.add.Add method) (sympy.core.expr.Expr method) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) primitive_element() (in module sympy.polys.numberfields) primitive_root() (in module sympy.ntheory.residue_ntheory) primorial() (in module sympy.ntheory.generate) print_ccode() (in module sympy.printing.ccode) print_fcode() (in module sympy.printing.fcode) Print_Function() (in module sympy.galgebra.printing) print_gtk() (in module sympy.printing.gtk) print_latex() (in module sympy.galgebra.printing) (in module sympy.printing.latex) print_mathml() (in module sympy.printing.mathml) print_node() (in module sympy.printing.tree) print_nonzero() (sympy.matrices.matrices.MatrixBase method) print_product_table() (in module sympy.galgebra.debug) print_sub_table() (in module sympy.galgebra.debug) print_tree() (in module sympy.printing.tree) Printer (class in sympy.printing.printer) printmethod (sympy.printing.ccode.CCodePrinter attribute) (sympy.printing.codeprinter.CodePrinter attribute) (sympy.printing.fcode.FCodePrinter attribute) (sympy.printing.lambdarepr.LambdaPrinter attribute) (sympy.printing.latex.LatexPrinter attribute) (sympy.printing.mathml.MathMLPrinter attribute) (sympy.printing.pretty.pretty.PrettyPrinter attribute) (sympy.printing.printer.Printer attribute) (sympy.printing.repr.ReprPrinter attribute) (sympy.printing.str.StrPrinter attribute) printtoken() (in module sympy.parsing.sympy_tokenize) prob() (sympy.physics.quantum.state.Wavefunction method) probability() (sympy.statistics.distributions.ContinuousProbability method) prod() (in module sympy.core.mul) Product (class in sympy.concrete.products) product() (in module sympy.concrete.products) (sympy.polys.agca.ideals.Ideal method) product_derivation() (in module sympy.galgebra.ncutil) ProductDomain (class in sympy.stats.rv) ProductPSpace (class in sympy.stats.rv) ProductSet (class in sympy.core.sets) Proj() (in module sympy.galgebra.ga) project() (sympy.matrices.matrices.MatrixBase method) projection() (sympy.geometry.line.LinearEntity method) Prufer (class in sympy.combinatorics.prufer) prufer_rank() (sympy.combinatorics.prufer.Prufer method) prufer_repr (sympy.combinatorics.prufer.Prufer attribute) psi() (in module mpmath) psi_n() (in module sympy.physics.qho_1d) pslq() (in module mpmath) PSpace (class in sympy.stats.rv) pspace() (in module sympy.stats.rv) public() (in module sympy.utilities.decorator) PurePoly (class in sympy.polys.polytools) PxBra (class in sympy.physics.quantum.cartesian) PxKet (class in sympy.physics.quantum.cartesian) PxOp (class in sympy.physics.quantum.cartesian) PyTestReporter (class in sympy.utilities.runtests) Python Enhancement Proposals PEP 335, [1], [2], [3] PythonFiniteField (class in sympy.polys.domains) PythonIntegerRing (class in sympy.polys.domains) PythonRationalField (class in sympy.polys.domains)

Q

Q (class in sympy.assumptions.ask) q (sympy.physics.gaussopt.BeamParameter attribute) qapply() (in module sympy.physics.quantum.qapply) qbarfrom() (in module mpmath) qfac() (in module mpmath) qfrom() (in module mpmath) QFT (class in sympy.physics.quantum.qft) qgamma() (in module mpmath) qhyper() (in module mpmath) qp() (in module mpmath) QRdecomposition() (sympy.matrices.matrices.MatrixBase method) QRsolve() (sympy.matrices.matrices.MatrixBase method) quad() (in module mpmath) quadosc() (in module mpmath) quadratic_residues() (in module sympy.ntheory.residue_ntheory)

QuadraticU() (in module sympy.stats) QuadratureRule (class in mpmath.calculus.quadrature) Qubit (class in sympy.physics.quantum.qubit) qubit_to_matrix() (in module sympy.physics.quantum.qubit) QubitBra (class in sympy.physics.quantum.qubit) quo() (in module sympy.polys.polytools) (sympy.polys.domains.domain.Domain method) (sympy.polys.domains.field.Field method) (sympy.polys.domains.ring.Ring method) (sympy.polys.polyclasses.DMF method) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) quo_ground() (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) quotient() (sympy.polys.agca.ideals.Ideal method) quotient_codomain() (sympy.polys.agca.homomorphisms.ModuleHomomorphism method) quotient_domain() (sympy.polys.agca.homomorphisms.ModuleHomomorphism method) quotient_hom() (sympy.polys.agca.modules.QuotientModule method) (sympy.polys.agca.modules.SubQuotientModule method) quotient_module() (sympy.polys.agca.modules.FreeModule method) (sympy.polys.agca.modules.Module method) (sympy.polys.agca.modules.SubModule method) quotient_ring() (sympy.polys.domains.ring.Ring method) QuotientModule (class in sympy.polys.agca.modules)

R

R_nl() (in module sympy.physics.hydrogen) (in module sympy.physics.sho) racah() (in module sympy.physics.wigner) rad_rationalize() (in module sympy.simplify.simplify) radians() (in module mpmath) radical() (sympy.polys.agca.ideals.Ideal method) radius (sympy.geometry.ellipse.Circle attribute) (sympy.geometry.polygon.RegularPolygon attribute) (sympy.physics.gaussopt.BeamParameter attribute) radius_of_convergence (sympy.functions.special.hyper.hyper attribute) radsimp() (in module sympy.simplify.simplify) (sympy.core.expr.Expr method) RaisedCosine() (in module sympy.stats) raises() (in module sympy.utilities.pytest) rand() (in module mpmath) randMatrix() (in module sympy.matrices.dense) random() (sympy.combinatorics.perm_groups.PermutationGroup method) (sympy.combinatorics.permutations.Permutation class method) (sympy.statistics.distributions.ContinuousProbability method) random_bitstring() (sympy.combinatorics.graycode static method) random_circuit() (in module sympy.physics.quantum.gate) random_complex_number() (in module sympy.utilities.randtest) random_integer_partition() (in module sympy.combinatorics.partitions) random_point() (sympy.geometry.ellipse.Ellipse method) (sympy.geometry.line.LinearEntity method) random_poly() (in module sympy.polys.specialpolys) random_pr() (sympy.combinatorics.perm_groups.PermutationGroup method) random_stab() (sympy.combinatorics.perm_groups.PermutationGroup method) random_symbols() (in module sympy.stats.rv) RandomDomain (class in sympy.stats.rv) RandomSymbol (class in sympy.stats.rv) randprime() (in module sympy.ntheory.generate) ranges (sympy.tensor.indexed.Indexed attribute) rank (sympy.combinatorics.graycode.GrayCode attribute) (sympy.combinatorics.partitions.Partition attribute) (sympy.combinatorics.prufer.Prufer attribute) (sympy.tensor.indexed.Indexed attribute) rank() (sympy.combinatorics.permutations.Permutation method) (sympy.matrices.matrices.MatrixBase method) rank_binary (sympy.combinatorics.subsets.Subset attribute) rank_gray (sympy.combinatorics.subsets.Subset attribute) rank_lexicographic (sympy.combinatorics.subsets.Subset attribute) rank_nonlex() (sympy.combinatorics.permutations.Permutation method) rank_trotterjohnson() (sympy.combinatorics.permutations.Permutation method) rat_clear_denoms() (sympy.polys.polytools.Poly method) ratint() (sympy.integrals static method) Rational (class in sympy.core.numbers) RationalField (class in sympy.polys.domains) rationalize() (in module sympy.parsing.sympy_parser) ratsimp() (in module sympy.simplify.simplify) (sympy.core.expr.Expr method) rawlines() (in module sympy.utilities.misc) Ray (class in sympy.geometry.line) Rayleigh() (in module sympy.stats) rayleigh2waist() (in module sympy.physics.gaussopt) RayTransferMatrix (class in sympy.physics.gaussopt) rcall() (sympy.core.basic.Basic method) rcollect() (in module sympy.simplify.simplify) re (class in sympy.functions.elementary.complexes) re() (in module mpmath) real_roots() (in module sympy.polys.polytools) (sympy.polys.polytools.Poly method) RealField (class in sympy.polys.domains) RealNumber (in module sympy.core.numbers) reconstruct() (in module sympy.solvers.diophantine) rect() (in module mpmath) recurrence_memo() (in module sympy.utilities.memoization) red_groebner() (in module sympy.polys.groebnertools) reduce() (sympy.core.sets.Intersection static method) (sympy.core.sets.Union static method) (sympy.polys.polytools.GroebnerBasis method) reduce_abs_inequalities() (in module sympy.solvers.inequalities) reduce_abs_inequality() (in module sympy.solvers.inequalities) reduce_element() (sympy.polys.agca.ideals.Ideal method) (sympy.polys.agca.modules.SubModule method) reduce_inequalities() (in module sympy.solvers.inequalities) reduce_rational_inequalities() (in module sympy.solvers.inequalities) reduced() (in module sympy.polys.polytools) ReferenceFrame (class in sympy.physics.vector.frame) refine() (in module sympy.assumptions.refine) (sympy.core.expr.Expr method) refine_abs() (in module sympy.assumptions.refine) refine_exp() (in module sympy.assumptions.refine) refine_Pow() (in module sympy.assumptions.refine) refine_Relational() (in module sympy.assumptions.refine) refine_root() (in module sympy.polys.polytools) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) RefinementFailed (class in sympy.polys.polyerrors) reflect() (sympy.geometry.ellipse.Circle method) (sympy.geometry.ellipse.Ellipse method) (sympy.geometry.polygon.RegularPolygon method) register_handler() (in module sympy.assumptions.ask) RegularPolygon (class in sympy.geometry.polygon) Rel (in module sympy.core.relational) rem() (in module sympy.polys.polytools) (sympy.polys.domains.domain.Domain method) (sympy.polys.domains.field.Field method) (sympy.polys.domains.ring.Ring method) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) remove_handler() (in module sympy.assumptions.ask) removeO() (sympy.core.expr.Expr method) render() (sympy.printing.pretty.stringpict.stringPict method) reorder() (sympy.polys.polytools.Poly method) rep_expectation() (in module sympy.physics.quantum.represent)

rep_innerproduct() (in module sympy.physics.quantum.represent) replace() (sympy.core.basic.Basic method) (sympy.matrices.matrices.MatrixBase method) (sympy.polys.polytools.Poly method) Reporter (class in sympy.utilities.runtests) represent() (in module sympy.physics.quantum.represent) reprify() (sympy.printing.repr.ReprPrinter method) ReprPrinter (class in sympy.printing.repr) reset() (sympy.combinatorics.polyhedron.Polyhedron method) reshape() (in module sympy.utilities.iterables) (sympy.matrices.sparse.SparseMatrix method) residue() (in module sympy.series.residues) restrict_codomain() (sympy.polys.agca.homomorphisms.ModuleHomomorphism method) restrict_domain() (sympy.polys.agca.homomorphisms.ModuleHomomorphism method) Result (class in sympy.utilities.codegen) result_variables (sympy.utilities.codegen.Routine attribute) resultant() (in module sympy.polys.polytools) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) retract() (sympy.polys.polytools.Poly method) reverse_order() (sympy.concrete.products.Product method) (sympy.concrete.summations.Sum method) ReversedGradedLexOrder (class in sympy.polys.orderings) revert() (sympy.polys.domains.domain.Domain method) (sympy.polys.domains.field.Field method) (sympy.polys.domains.ring.Ring method) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) rewrite() (in module sympy.series.gruntz) (sympy.core.basic.Basic method) rf() (in module mpmath) rgamma() (in module mpmath) RGS (sympy.combinatorics.partitions.Partition attribute) RGS_enum() (in module sympy.combinatorics.partitions) RGS_generalized() (in module sympy.combinatorics.partitions) RGS_rank() (in module sympy.combinatorics.partitions) RGS_unrank() (in module sympy.combinatorics.partitions) rhs() (sympy.physics.mechanics.kane.KanesMethod method) (sympy.physics.mechanics.lagrange.LagrangesMethod method) richardson() (in module mpmath) (in module sympy.series.acceleration) Ridder (class in mpmath.calculus.optimization) riemann_cyclic() (in module sympy.tensor.tensor) riemann_cyclic_replace() (in module sympy.tensor.tensor) riemannr() (in module mpmath) right (sympy.core.sets.Interval attribute) right() (sympy.printing.pretty.stringpict.stringPict method) right_open (sympy.core.sets.Interval attribute) RigidBody (class in sympy.physics.mechanics.rigidbody) Ring (class in sympy.polys.domains.ring) RisingFactorial (class in sympy.functions.combinatorial.factorials) Rk (in module sympy.physics.quantum.qft) RkGate (class in sympy.physics.quantum.qft) RL (sympy.matrices.sparse.SparseMatrix attribute) rmul() (sympy.combinatorics.permutations.Permutation static method) rmul_with_af() (sympy.combinatorics.permutations.Permutation static method) root (in module sympy.printing.pretty.pretty_symbology) root() (in module mpmath) (in module sympy.functions.elementary.miscellaneous) (sympy.polys.polytools.Poly method) (sympy.printing.pretty.stringpict.stringPict method) RootOf (class in sympy.polys.rootoftools) roots() (in module sympy.polys.polyroots) RootSum (class in sympy.polys.rootoftools) rot_axis1() (in module sympy.matrices.dense) rot_axis2() (in module sympy.matrices.dense) rot_axis3() (in module sympy.matrices.dense) rotate() (sympy.combinatorics.polyhedron.Polyhedron method) (sympy.geometry.curve.Curve method) (sympy.geometry.ellipse.Ellipse method) (sympy.geometry.entity.GeometryEntity method) (sympy.geometry.point.Point method) (sympy.geometry.polygon.RegularPolygon method) rotate_left() (in module sympy.utilities.iterables) rotate_right() (in module sympy.utilities.iterables) Rotation (class in sympy.physics.quantum.spin) rotation (sympy.geometry.polygon.RegularPolygon attribute) round() (sympy.core.expr.Expr method) RoundFunction (class in sympy.functions.elementary.integers) Routine (class in sympy.utilities.codegen) row() (sympy.matrices.sparse.SparseMatrix method) row_del() (sympy.matrices.dense.MutableDenseMatrix method) (sympy.matrices.sparse.MutableSparseMatrix method) row_insert() (sympy.matrices.matrices.MatrixBase method) row_join() (sympy.matrices.matrices.MatrixBase method) (sympy.matrices.sparse.MutableSparseMatrix method) row_list() (sympy.matrices.sparse.SparseMatrix method) row_op() (sympy.matrices.dense.MutableDenseMatrix method) (sympy.matrices.sparse.MutableSparseMatrix method) row_structure_symbolic_cholesky() (sympy.matrices.sparse.SparseMatrix method) row_swap() (sympy.matrices.dense.MutableDenseMatrix method) (sympy.matrices.sparse.MutableSparseMatrix method) rref() (sympy.matrices.matrices.MatrixBase method) rs_swap() (in module sympy.stats.rv) rsa_private_key() (in module sympy.crypto.crypto) rsa_public_key() (in module sympy.crypto.crypto) rsolve() (in module sympy.solvers.recurr) rsolve_hyper() (in module sympy.solvers.recurr) rsolve_poly() (in module sympy.solvers.recurr) rsolve_ratio() (in module sympy.solvers.recurr) run() (sympy.utilities.runtests.SymPyDocTestRunner method) run_all_tests() (in module sympy.utilities.runtests) run_in_subprocess_with_hash_randomization() (in module sympy.utilities.runtests) runs() (in module sympy.utilities.iterables) (sympy.combinatorics.permutations.Permutation method)

S

S (in module sympy.core.singleton) (in module sympy.physics.quantum.gate) Sample (class in sympy.statistics.distributions) sample() (in module sympy.stats) sample_iter() (in module sympy.stats) satisfiable() (in module sympy.logic.inference) saturate() (sympy.polys.agca.ideals.Ideal method) scalar_multiply() (sympy.matrices.sparse.SparseMatrix method) scale() (sympy.geometry.curve.Curve method) (sympy.geometry.ellipse.Circle method) (sympy.geometry.ellipse.Ellipse method) (sympy.geometry.entity.GeometryEntity method) (sympy.geometry.point.Point method) (sympy.geometry.polygon.RegularPolygon method) schreier_sims() (sympy.combinatorics.perm_groups.PermutationGroup method) schreier_sims_incremental() (sympy.combinatorics.perm_groups.PermutationGroup method) schreier_sims_random() (sympy.combinatorics.perm_groups.PermutationGroup method) schreier_vector() (sympy.combinatorics.perm_groups.PermutationGroup method) scorergi() (in module mpmath) scorerhi() (in module mpmath) sdm_add() (in module sympy.polys.distributedmodules) sdm_deg() (in module sympy.polys.distributedmodules) sdm_ecart() (in module sympy.polys.distributedmodules) sdm_from_dict() (in module sympy.polys.distributedmodules) sdm_from_vector() (in module sympy.polys.distributedmodules) sdm_groebner() (in module sympy.polys.distributedmodules) sdm_LC() (in module sympy.polys.distributedmodules) sdm_LM() (in module sympy.polys.distributedmodules) sdm_LT() (in module sympy.polys.distributedmodules) sdm_monomial_deg() (in module sympy.polys.distributedmodules) sdm_monomial_divides() (in module sympy.polys.distributedmodules) sdm_monomial_mul() (in module sympy.polys.distributedmodules) sdm_mul_term() (in module sympy.polys.distributedmodules) sdm_nf_mora() (in module sympy.polys.distributedmodules) sdm_spoly() (in module sympy.polys.distributedmodules) sdm_to_dict() (in module sympy.polys.distributedmodules) sdm_to_vector() (in module sympy.polys.distributedmodules) sdm_zero() (in module sympy.polys.distributedmodules) search() (sympy.ntheory.generate.Sieve method) search_function (sympy.physics.quantum.grover.OracleGate attribute) sec() (in module mpmath) Secant (class in mpmath.calculus.optimization) sech() (in module mpmath) secondzeta() (in module mpmath) Segment (class in sympy.geometry.line) select() (sympy.simplify.epathtools.EPath method) selections (sympy.combinatorics.graycode.GrayCode attribute) separate() (in module sympy.simplify.simplify) (sympy.core.expr.Expr method) separatevars() (in module sympy.simplify.simplify) series() (in module sympy.series.series) (sympy.core.expr.Expr method) Set (class in sympy.core.sets) set_acc() (sympy.physics.vector.point.Point method) set_ang_acc() (sympy.physics.vector.frame.ReferenceFrame method) set_ang_vel() (sympy.physics.vector.frame.ReferenceFrame method) set_comm() (sympy.tensor.tensor._TensorManager method) set_comms() (sympy.tensor.tensor._TensorManager method) set_domain() (sympy.polys.polytools.Poly method) set_global_settings() (sympy.printing.printer.Printer class method) set_modulus() (sympy.polys.polytools.Poly method) set_pos() (sympy.physics.vector.point.Point method) set_potential_energy() (sympy.physics.mechanics.particle.Particle method) (sympy.physics.mechanics.rigidbody.RigidBody method) set_vel() (sympy.physics.vector.point.Point method) seterr() (in module sympy.core.numbers) setup() (sympy.galgebra.vector.Vector static method) shanks() (in module mpmath) (in module sympy.series.acceleration) shape (sympy.matrices.matrices.MatrixBase attribute) (sympy.tensor.indexed.Indexed attribute) (sympy.tensor.indexed.IndexedBase attribute) ShapeError (class in sympy.matrices.matrices) Shi (class in sympy.functions.special.error_functions) shi() (in module mpmath) shift() (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) shor() (in module sympy.physics.quantum.shor) Si (class in sympy.functions.special.error_functions) si() (in module mpmath) sides (sympy.geometry.polygon.Polygon attribute) siegeltheta() (in module mpmath) siegelz() (in module mpmath) Sieve (class in sympy.ntheory.generate) sift() (in module sympy.utilities.iterables) sign (class in sympy.functions.elementary.complexes) sign() (in module mpmath) (in module sympy.series.gruntz) signature() (sympy.combinatorics.permutations.Permutation method) SimpleDomain (class in sympy.polys.domains.simpledomain) simplified() (in module sympy.solvers.diophantine) simplify() (in module sympy.simplify.simplify) (sympy.core.expr.Expr method) (sympy.functions.special.delta_functions.DiracDelta method) (sympy.matrices.dense.MutableDenseMatrix method) (sympy.matrices.matrices.MatrixBase method) (sympy.physics.vector.dyadic.Dyadic method) (sympy.physics.vector.vector.Vector method) simplify_gpgp() (sympy.physics.hep.gamma_matrices.GammaMatrixHead static method) simplify_index_permutations() (in module sympy.physics.secondquant) simplify_lines() (sympy.physics.hep.gamma_matrices.GammaMatrixHead static method) simplify_logic() (in module sympy.logic.boolalg) sin (class in sympy.functions.elementary.trigonometric) sin() (in module mpmath) sinc() (in module mpmath) sincpi() (in module mpmath) sine_transform() (in module sympy.integrals.transforms) SingleDomain (class in sympy.stats.rv) SinglePSpace (class in sympy.stats.rv) singular_values() (sympy.matrices.matrices.MatrixBase method) sinh (class in sympy.functions.elementary.hyperbolic) sinh() (in module mpmath) sinm() (in module mpmath) sinpi() (in module mpmath) size (sympy.combinatorics.permutations.Permutation attribute) (sympy.combinatorics.polyhedron.Polyhedron attribute) (sympy.combinatorics.prufer.Prufer attribute) (sympy.combinatorics.subsets.Subset attribute) SKIP() (in module sympy.utilities.pytest) skip() (sympy.combinatorics.graycode.GrayCode method) slice() (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) slope (sympy.geometry.line.LinearEntity attribute) smoothness() (in module sympy.ntheory.factor_) smoothness_p() (in module sympy.ntheory.factor_) solve() (in module sympy.solvers.solvers) (sympy.matrices.matrices.MatrixBase method) (sympy.matrices.sparse.SparseMatrix method) solve_congruence() (in module sympy.ntheory.modular) solve_least_squares() (sympy.matrices.matrices.MatrixBase method) (sympy.matrices.sparse.SparseMatrix method) solve_linear() (in module sympy.solvers.solvers) solve_linear_system() (in module sympy.solvers.solvers) solve_linear_system_LU() (in module sympy.solvers.solvers) solve_poly_inequality() (in module sympy.solvers.inequalities) solve_poly_system() (in module sympy.solvers.polysys) solve_rational_inequalities() (in module sympy.solvers.inequalities) solve_triangulated() (in module sympy.solvers.polysys) solve_undetermined_coeffs() (in module sympy.solvers.solvers) solve_univariate_inequality() (in module sympy.solvers.inequalities) SOPform() (in module sympy.logic.boolalg) sort_key() (sympy.combinatorics.partitions.Partition method) (sympy.core.basic.Basic method) (sympy.core.sets.Set method) sorted_components() (sympy.tensor.tensor.TensMul method) (sympy.tensor.tensor.TIDS method) source (sympy.geometry.line.Ray attribute) source() (in module sympy.utilities.source) SparseMatrix (class in sympy.matrices.sparse) spherharm() (in module mpmath) spin() (sympy.geometry.polygon.RegularPolygon method) split() (sympy.tensor.tensor.TensMul method) split_list() (in module sympy.utilities.runtests) split_super_sub() (in module sympy.printing.conventions) split_symbols() (in module sympy.parsing.sympy_parser) split_symbols_custom() (in module sympy.parsing.sympy_parser) splot() (in module mpmath) spoly() (in module sympy.polys.groebnertools) sqf() (in module sympy.polys.polytools) sqf_list() (in module sympy.polys.polytools) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) sqf_list_include() (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) sqf_norm() (in module sympy.polys.polytools) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) sqf_part() (in module sympy.polys.polytools) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) sqr() (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) sqrt (class in sympy.functions.elementary.miscellaneous) sqrt() (in module mpmath) (sympy.polys.domains.domain.Domain method) sqrt_mod() (in module sympy.ntheory.residue_ntheory) sqrtdenest() (in module sympy.simplify.sqrtdenest) sqrtm() (in module mpmath) square_factor() (in module sympy.solvers.diophantine) srepr() (in module sympy.printing.repr) sstrrepr() (in module sympy.printing.str) stabilizer() (sympy.combinatorics.perm_groups.PermutationGroup method) stack() (sympy.printing.pretty.stringpict.stringPict static method) standard_transformations (in module sympy.parsing.sympy_parser) start (sympy.core.sets.Interval attribute) State (class in sympy.physics.quantum.state) state() (sympy.physics.secondquant.FixedBosonicBasis method) (sympy.physics.secondquant.VarBosonicBasis method) state_to_operators() (in module sympy.physics.quantum.operatorset) StateBase (class in sympy.physics.quantum.state) std() (in module sympy.stats) stieltjes() (in module mpmath) stirling() (in module sympy.functions.combinatorial.numbers) stirling1() (in module mpmath) stirling2() (in module mpmath) StopTokenizing (class in sympy.parsing.sympy_tokenize) str_array() (in module sympy.galgebra.stringarrays) str_combinations() (in module sympy.galgebra.stringarrays) StrictGreaterThan (class in sympy.core.relational) StrictLessThan (class in sympy.core.relational) stringify_expr() (in module sympy.parsing.sympy_parser) stringPict (class in sympy.printing.pretty.stringpict) strip() (sympy.tensor.tensor.TensExpr method) (sympy.tensor.tensor.TensorHead method) strong_gens (sympy.combinatorics.perm_groups.PermutationGroup attribute) StrPrinter (class in sympy.printing.str) struveh() (in module mpmath) struvel() (in module mpmath) StudentT() (in module sympy.stats) sturm() (in module sympy.polys.polytools) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) sub (in module sympy.printing.pretty.pretty_symbology) sub() (sympy.polys.domains.domain.Domain method) (sympy.polys.polyclasses.DMF method) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) sub_ground() (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) sub_paren() (in module sympy.galgebra.precedence) subdiagram_from_objects() (sympy.categories.Diagram method) subgroup_search() (sympy.combinatorics.perm_groups.PermutationGroup method) SubModule (class in sympy.polys.agca.modules) submodule() (sympy.polys.agca.modules.Module method) (sympy.polys.agca.modules.QuotientModule method) (sympy.polys.agca.modules.SubModule method) SubQuotientModule (class in sympy.polys.agca.modules) subresultants() (in module sympy.polys.polytools) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) Subs (class in sympy.core.function) subs() (sympy.core.basic.Basic method) (sympy.matrices.immutable.ImmutableSparseMatrix method) (sympy.matrices.matrices.MatrixBase method) (sympy.physics.vector.dyadic.Dyadic method) (sympy.physics.vector.vector.Vector method) Subset (class in sympy.combinatorics.subsets) subset (sympy.combinatorics.subsets.Subset attribute) subset() (sympy.core.sets.Set method) (sympy.polys.agca.ideals.Ideal method) (sympy.polys.agca.modules.Module method) subset_from_bitlist() (sympy.combinatorics.subsets.Subset class method) subset_indices() (sympy.combinatorics.subsets.Subset class method) subsets() (in module sympy.utilities.iterables) SubsSet (class in sympy.series.gruntz) substitute_dummies() (in module sympy.physics.secondquant) substitute_indices() (sympy.tensor.tensor.TensAdd method) (sympy.tensor.tensor.TensMul method) Sum (class in sympy.concrete.summations) sum_next() (mpmath.calculus.quadrature.QuadratureRule method) (mpmath.calculus.quadrature.TanhSinh method) sum_of_four_squares() (in module sympy.solvers.diophantine) sum_of_three_squares() (in module sympy.solvers.diophantine) sumap() (in module mpmath) sumem() (in module mpmath) summation() (in module sympy.concrete.summations) (mpmath.calculus.quadrature.QuadratureRule method) sup (in module sympy.printing.pretty.pretty_symbology) (sympy.core.sets.Set attribute) superfac() (in module mpmath) superposition_basis() (in module sympy.physics.quantum.grover) superset (sympy.combinatorics.subsets.Subset attribute) superset_size (sympy.combinatorics.subsets.Subset attribute) support() (sympy.combinatorics.permutations.Permutation method) SurfaceBaseSeries (class in sympy.plotting.plot) SurfaceOver2DRangeSeries (class in sympy.plotting.plot) SWAP (in module sympy.physics.quantum.gate) SwapGate (class in sympy.physics.quantum.gate) swinnerton_dyer_poly() (in module sympy.polys.specialpolys) symarray() (in module sympy.matrices.dense) symb_2txt (in module sympy.printing.pretty.pretty_symbology) Symbol (class in sympy.core.symbol) symbol (sympy.physics.secondquant.AntiSymmetricTensor attribute) Symbol() (sympy.assumptions.handlers.calculus.AskBoundedHandler static method) symbol_array() (in module sympy.galgebra.stringarrays) symbols() (in module sympy.core.symbol) symmetric() (sympy.combinatorics.generators static method) symmetric_poly() (in module sympy.polys.specialpolys) symmetric_residue() (in module sympy.ntheory.modular) SymmetricGroup() (in module sympy.combinatorics.named_groups) symmetrize() (in module sympy.polys.polyfuncs) sympify() (in module sympy.core.sympify) sympy (module) sympy.assumptions (module) sympy.assumptions.ask (module) sympy.assumptions.assume (module) sympy.assumptions.handlers (module) sympy.assumptions.handlers.calculus (module) sympy.assumptions.handlers.ntheory (module) sympy.assumptions.handlers.order (module) sympy.assumptions.handlers.sets (module)

sympy.assumptions.refine (module) sympy.calculus (module) sympy.categories (module) sympy.categories.diagram_drawing (module) sympy.combinatorics.generators (module) sympy.combinatorics.graycode (module) sympy.combinatorics.group_constructs (module) sympy.combinatorics.named_groups (module) sympy.combinatorics.partitions (module) sympy.combinatorics.perm_groups (module) sympy.combinatorics.permutations (module) sympy.combinatorics.polyhedron (module) sympy.combinatorics.prufer (module) sympy.combinatorics.subsets (module) sympy.combinatorics.tensor_can (module) sympy.combinatorics.testutil (module) sympy.combinatorics.util (module) sympy.core.add (module) sympy.core.basic (module) sympy.core.cache (module) sympy.core.compatibility (module) sympy.core.containers (module) sympy.core.evalf (module) sympy.core.expr (module) sympy.core.exprtools (module) sympy.core.function (module) sympy.core.mod (module) sympy.core.mul (module) sympy.core.multidimensional (module) sympy.core.numbers (module) sympy.core.power (module) sympy.core.relational (module) sympy.core.sets (module) sympy.core.singleton (module) sympy.core.symbol (module) sympy.core.sympify (module) sympy.crypto.crypto (module) sympy.diffgeom (module) sympy.functions (module) sympy.functions.special.bessel (module) sympy.functions.special.elliptic_integrals (module) sympy.functions.special.error_functions (module) sympy.functions.special.gamma_functions (module) sympy.functions.special.polynomials (module) sympy.functions.special.zeta_functions (module) sympy.galgebra (module) sympy.galgebra.debug (module) sympy.galgebra.ga (module) sympy.galgebra.ga.Com() (in module sympy.galgebra.ga) sympy.galgebra.ga.cross() (in module sympy.galgebra.ga) sympy.galgebra.ga.DD() (in module sympy.galgebra.ga) sympy.galgebra.ga.dual() (in module sympy.galgebra.ga) sympy.galgebra.ga.Fmt() (in module sympy.galgebra.ga) sympy.galgebra.ga.Format() (in module sympy.galgebra.ga) sympy.galgebra.ga.ga_print_off() (in module sympy.galgebra.ga) sympy.galgebra.ga.ga_print_on() (in module sympy.galgebra.ga) sympy.galgebra.ga.inv() (in module sympy.galgebra.ga) sympy.galgebra.ga.MV (class in sympy.galgebra.ga) sympy.galgebra.ga.MV.convert_from_blades() (in module sympy.galgebra.ga) sympy.galgebra.ga.MV.convert_to_blades() (in module sympy.galgebra.ga) sympy.galgebra.ga.MV.dd() (in module sympy.galgebra.ga) sympy.galgebra.ga.MV.diff() (in module sympy.galgebra.ga) sympy.galgebra.ga.MV.dual() (in module sympy.galgebra.ga) sympy.galgebra.ga.MV.even() (in module sympy.galgebra.ga) sympy.galgebra.ga.MV.exp() (in module sympy.galgebra.ga) sympy.galgebra.ga.MV.expand() (in module sympy.galgebra.ga) sympy.galgebra.ga.MV.factor() (in module sympy.galgebra.ga) sympy.galgebra.ga.MV.func() (in module sympy.galgebra.ga) sympy.galgebra.ga.MV.grade() (in module sympy.galgebra.ga) sympy.galgebra.ga.MV.inv() (in module sympy.galgebra.ga) sympy.galgebra.ga.MV.norm() (in module sympy.galgebra.ga), [1] sympy.galgebra.ga.MV.rev() (in module sympy.galgebra.ga) sympy.galgebra.ga.MV.scalar() (in module sympy.galgebra.ga) sympy.galgebra.ga.MV.set_coef() (in module sympy.galgebra.ga) sympy.galgebra.ga.MV.setup() (in module sympy.galgebra.ga) sympy.galgebra.ga.MV.simplify() (in module sympy.galgebra.ga) sympy.galgebra.ga.MV.subs() (in module sympy.galgebra.ga) sympy.galgebra.ga.MV.trigsimp() (in module sympy.galgebra.ga) sympy.galgebra.ga.Nga() (in module sympy.galgebra.ga) sympy.galgebra.ga.proj() (in module sympy.galgebra.ga) sympy.galgebra.ga.ReciprocalFrame() (in module sympy.galgebra.ga) sympy.galgebra.ga.refl() (in module sympy.galgebra.ga) sympy.galgebra.ga.rot() (in module sympy.galgebra.ga) sympy.galgebra.ga.ScalarFunction() (in module sympy.galgebra.ga) sympy.galgebra.manifold (module) sympy.galgebra.ncutil (module) sympy.galgebra.precedence (module) sympy.galgebra.precedence.define_precedence() (in module sympy.galgebra.ga), [1] sympy.galgebra.precedence.GAeval() (in module sympy.galgebra.ga), [1] sympy.galgebra.printing (module) sympy.galgebra.printing.Format() (in module sympy.galgebra.ga) sympy.galgebra.printing.GA_Printer() (in module sympy.galgebra.ga) sympy.galgebra.printing.Get_Program() (in module sympy.galgebra.ga) sympy.galgebra.printing.Print_Function() (in module sympy.galgebra.ga) sympy.galgebra.printing.xdvi() (in module sympy.galgebra.ga) sympy.galgebra.stringarrays (module) sympy.galgebra.vector (module) sympy.geometry (module) sympy.geometry.curve (module) sympy.geometry.ellipse (module) sympy.geometry.entity (module) sympy.geometry.line (module) sympy.geometry.point (module) sympy.geometry.polygon (module) sympy.geometry.util (module) sympy.integrals (module) sympy.integrals.meijerint_doc (module) sympy.integrals.transforms (module) sympy.logic (module) sympy.matrices (module) sympy.matrices.expressions (module) sympy.matrices.expressions.blockmatrix (module) sympy.matrices.immutable (module) sympy.matrices.matrices (module) sympy.matrices.sparse (module) sympy.ntheory.factor_ (module) sympy.ntheory.generate (module) sympy.ntheory.modular (module) sympy.ntheory.multinomial (module) sympy.ntheory.partitions_ (module) sympy.ntheory.primetest (module) sympy.ntheory.residue_ntheory (module) sympy.physics (module) sympy.physics.gaussopt (module) sympy.physics.hep.gamma_matrices (module) sympy.physics.hydrogen (module) sympy.physics.matrices (module) sympy.physics.mechanics.kane (module) sympy.physics.mechanics.lagrange (module) sympy.physics.mechanics.particle (module) sympy.physics.mechanics.rigidbody (module) sympy.physics.paulialgebra (module) sympy.physics.qho_1d (module) sympy.physics.quantum.anticommutator (module) sympy.physics.quantum.cartesian (module) sympy.physics.quantum.cg (module) sympy.physics.quantum.circuitplot (module) sympy.physics.quantum.commutator (module) sympy.physics.quantum.constants (module) sympy.physics.quantum.dagger (module) sympy.physics.quantum.gate (module) sympy.physics.quantum.grover (module) sympy.physics.quantum.hilbert (module) sympy.physics.quantum.innerproduct (module) sympy.physics.quantum.operator (module) sympy.physics.quantum.operatorset (module) sympy.physics.quantum.piab (module) sympy.physics.quantum.qapply (module) sympy.physics.quantum.qft (module) sympy.physics.quantum.qubit (module) sympy.physics.quantum.represent (module) sympy.physics.quantum.shor (module) sympy.physics.quantum.spin (module) sympy.physics.quantum.state (module) sympy.physics.quantum.tensorproduct (module) sympy.physics.secondquant (module) sympy.physics.sho (module) sympy.physics.units (module) sympy.physics.vector.functions (module) sympy.physics.vector.point (module) sympy.physics.wigner (module) sympy.plotting.plot (module) sympy.plotting.pygletplot (module) sympy.printing.ccode (module) sympy.printing.codeprinter (module) sympy.printing.conventions (module) sympy.printing.fcode (module) sympy.printing.gtk (module) sympy.printing.lambdarepr (module) sympy.printing.latex (module) sympy.printing.mathml (module) sympy.printing.precedence (module) sympy.printing.pretty.pretty (module) sympy.printing.pretty.pretty_symbology (module) sympy.printing.pretty.stringpict (module) sympy.printing.preview (module) sympy.printing.printer (module) sympy.printing.python (module) sympy.printing.repr (module) sympy.printing.str (module) sympy.printing.tree (module) sympy.series (module) sympy.sets.fancysets (module) sympy.simplify.cse_main (module), [1] sympy.simplify.epathtools (module) sympy.simplify.hyperexpand (module) sympy.simplify.hyperexpand_doc (module) sympy.simplify.simplify (module) sympy.simplify.sqrtdenest (module) sympy.simplify.traversaltools (module) sympy.solvers (module) sympy.solvers.inequalities (module) sympy.solvers.ode (module) sympy.solvers.pde (module) sympy.solvers.recurr (module) sympy.statistics (module) sympy.stats (module) sympy.stats.crv (module) sympy.stats.crv_types (module) sympy.stats.Die() (in module sympy.stats.crv_types) sympy.stats.frv (module) sympy.stats.frv_types (module) sympy.stats.Normal() (in module sympy.stats.crv_types) sympy.stats.rv (module) sympy.tensor (module) sympy.tensor.index_methods (module) sympy.tensor.indexed (module) sympy.tensor.tensor (module) sympy.utilities (module) sympy.utilities.autowrap (module) sympy.utilities.codegen (module) sympy.utilities.decorator (module) sympy.utilities.enumerative (module) sympy.utilities.iterables (module) sympy.utilities.lambdify (module) sympy.utilities.memoization (module) sympy.utilities.misc (module) sympy.utilities.pkgdata (module) sympy.utilities.pytest (module) sympy.utilities.randtest (module) sympy.utilities.runtests (module) sympy.utilities.source (module) sympy.utilities.timeutils (module) SymPyDocTestFinder (class in sympy.utilities.runtests) SymPyDocTestRunner (class in sympy.utilities.runtests) SymPyOutputChecker (class in sympy.utilities.runtests) sympytestfile() (in module sympy.utilities.runtests) SymPyTestResults (in module sympy.utilities.runtests) syzygy_module() (sympy.polys.agca.modules.SubModule method)

T

T (in module sympy.physics.quantum.gate) (sympy.matrices.expressions.MatrixExpr attribute) (sympy.matrices.matrices.MatrixBase attribute) t (sympy.physics.quantum.shor.CMod attribute) table() (sympy.matrices.matrices.MatrixBase method) take() (in module sympy.utilities.iterables) tan (class in sympy.functions.elementary.trigonometric) tan() (in module mpmath) tangent_lines() (sympy.geometry.ellipse.Ellipse method) tanh (class in sympy.functions.elementary.hyperbolic) tanh() (in module mpmath) TanhSinh (class in mpmath.calculus.quadrature) targets (sympy.physics.quantum.gate.CGate attribute) (sympy.physics.quantum.gate.CNotGate attribute) (sympy.physics.quantum.gate.Gate attribute) (sympy.physics.quantum.gate.UGate attribute) (sympy.physics.quantum.grover.OracleGate attribute) taufrom() (in module mpmath) taylor() (in module mpmath) taylor_term() (sympy.core.expr.Expr method) (sympy.functions.elementary.exponential.exp static method) (sympy.functions.elementary.exponential.log static method) (sympy.functions.elementary.hyperbolic.sinh static method) TC() (sympy.polys.polyclasses.ANP method) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) TensAdd (class in sympy.tensor.tensor) TensExpr (class in sympy.tensor.tensor) TensMul (class in sympy.tensor.tensor) tensor_indices() (in module sympy.tensor.tensor) tensor_mul() (in module sympy.tensor.tensor) tensor_product_simp() (in module sympy.physics.quantum.tensorproduct) TensorHead (class in sympy.tensor.tensor) TensorIndex (class in sympy.tensor.tensor) TensorIndexType (class in sympy.tensor.tensor) TensorProduct (class in sympy.diffgeom) (class in sympy.physics.quantum.tensorproduct) TensorSymmetry (class in sympy.tensor.tensor) TensorType (class in sympy.tensor.tensor) terminal_width() (sympy.printing.pretty.stringpict.stringPict method) terms() (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) terms_gcd() (in module sympy.polys.polytools) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) termwise() (sympy.polys.polytools.Poly method) test() (in module sympy.utilities.runtests) test_derivative_numerically() (in module sympy.utilities.randtest) test_numerically() (in module sympy.utilities.randtest) TGate (class in sympy.physics.quantum.gate) ThinLens (class in sympy.physics.gaussopt) threaded() (in module sympy.utilities.decorator) threaded_factory() (in module sympy.utilities.decorator) TIDS (class in sympy.tensor.tensor) time (sympy.physics.quantum.state.TimeDepState attribute) time_derivative() (in module sympy.physics.vector.functions) timed() (in module sympy.utilities.timeutils) TimeDepBra (class in sympy.physics.quantum.state) TimeDepKet (class in sympy.physics.quantum.state) TimeDepState (class in sympy.physics.quantum.state) timing() (in module mpmath) to_algebraic_integer() (sympy.polys.numberfields.AlgebraicNumber method) to_cnf() (in module sympy.logic.boolalg) to_dict() (sympy.polys.polyclasses.ANP method) (sympy.polys.polyclasses.DMP method)

to_dnf() (in module sympy.logic.boolalg) to_exact() (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) to_field() (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) to_indices() (sympy.tensor.tensor.TIDS method) to_list() (sympy.polys.polyclasses.ANP method) to_matrix() (sympy.physics.vector.dyadic.Dyadic method) (sympy.physics.vector.vector.Vector method) to_number_field() (in module sympy.polys.numberfields) to_prufer() (sympy.combinatorics.prufer.Prufer static method) to_rational() (sympy.polys.domains.RealField method) to_ring() (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) to_sympy() (sympy.polys.domains.AlgebraicField method) (sympy.polys.domains.ExpressionDomain method) (sympy.polys.domains.FiniteField method) (sympy.polys.domains.FractionField method) (sympy.polys.domains.PolynomialRing method) (sympy.polys.domains.RealField method) (sympy.polys.domains.domain.Domain method) to_sympy_dict() (sympy.polys.polyclasses.ANP method) (sympy.polys.polyclasses.DMP method) to_sympy_list() (sympy.polys.polyclasses.ANP method) to_tree() (sympy.combinatorics.prufer.Prufer static method) to_tuple() (sympy.polys.polyclasses.ANP method) (sympy.polys.polyclasses.DMP method) together() (in module sympy.polys.rationaltools) (sympy.core.expr.Expr method) TokenError (class in sympy.parsing.sympy_tokenize) tokenize() (in module sympy.parsing.sympy_tokenize) tolist() (sympy.matrices.sparse.SparseMatrix method) topological_sort() (in module sympy.utilities.iterables) total_degree() (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) totient() (in module sympy.ntheory.factor_) Trace (class in sympy.matrices.expressions) trailing() (in module sympy.ntheory.factor_) transform() (sympy.geometry.point.Point method) (sympy.integrals.Integral method) (sympy.statistics.distributions.PDF method) transform_nodes() (mpmath.calculus.quadrature.QuadratureRule method) transformation_to_DN() (in module sympy.solvers.diophantine) transitivity_degree (sympy.combinatorics.perm_groups.PermutationGroup attribute) translate() (sympy.geometry.curve.Curve method) (sympy.geometry.entity.GeometryEntity method) (sympy.geometry.point.Point method) Transpose (class in sympy.matrices.expressions) transpose() (sympy.matrices.expressions.blockmatrix.BlockMatrix method) transpositions() (sympy.combinatorics.permutations.Permutation method) tree() (in module sympy.printing.tree) tree_cse() (in module sympy.simplify.cse_main) tree_repr (sympy.combinatorics.prufer.Prufer attribute) Triangle (class in sympy.geometry.polygon) Triangular() (in module sympy.stats) trigamma() (in module sympy.functions.special.gamma_functions) trigintegrate() (sympy.integrals static method) TrigSimp() (in module sympy.galgebra.vector) trigsimp() (in module sympy.simplify.simplify) (sympy.core.expr.Expr method) trunc() (in module sympy.polys.polytools) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) tsolve() (in module sympy.solvers.solvers) Tuple (class in sympy.core.containers) tuple_count() (sympy.core.containers.Tuple method) twinprime (mpmath.mp attribute) twoform_to_matrix() (in module sympy.diffgeom) TwoQubitGate (class in sympy.physics.quantum.gate)

U

U() (in module sympy.printing.pretty.pretty_symbology) ufuncify() (in module sympy.utilities.autowrap) UGate (class in sympy.physics.quantum.gate) uncouple() (in module sympy.physics.quantum.spin) Unequality (class in sympy.core.relational) unflatten() (in module sympy.utilities.iterables) UnificationFailed (class in sympy.polys.polyerrors) Uniform (class in sympy.statistics.distributions) Uniform() (in module sympy.stats) UniformSum() (in module sympy.stats) unify() (sympy.polys.domains.domain.Domain method) (sympy.polys.polyclasses.ANP method) (sympy.polys.polyclasses.DMP method) (sympy.polys.polytools.Poly method) Union (class in sympy.core.sets) union() (sympy.core.sets.Set method) (sympy.polys.agca.ideals.Ideal method) (sympy.polys.agca.modules.SubModule method) (sympy.series.gruntz.SubsSet method) uniq() (in module sympy.utilities.iterables) Unit (class in sympy.physics.units) unit (sympy.polys.polytools.Poly attribute) UnitaryOperator (class in sympy.physics.quantum.operator)

unitroots() (in module mpmath) UnivariatePolynomialError (class in sympy.polys.polyerrors) UniversalSet (class in sympy.core.sets) unparse_paren() (in module sympy.galgebra.precedence) unrank() (sympy.combinatorics.graycode.GrayCode class method) (sympy.combinatorics.prufer.Prufer class method) unrank_binary() (sympy.combinatorics.subsets.Subset class method) unrank_gray() (sympy.combinatorics.subsets.Subset class method) unrank_lex() (sympy.combinatorics.permutations.Permutation class method) unrank_nonlex() (sympy.combinatorics.permutations.Permutation class method) unrank_trotterjohnson() (sympy.combinatorics.permutations.Permutation class method) unrestricted_necklace() (in module sympy.utilities.iterables) untokenize() (in module sympy.parsing.sympy_tokenize) upper (sympy.physics.secondquant.AntiSymmetricTensor attribute) (sympy.tensor.indexed.Idx attribute) upper_triangular_solve() (sympy.matrices.matrices.MatrixBase method) uppergamma (class in sympy.functions.special.gamma_functions) use() (in module sympy.simplify.traversaltools)

V

v1pt_theory() (sympy.physics.vector.point.Point method) v2pt_theory() (sympy.physics.vector.point.Point method) values() (sympy.core.containers.Dict method) (sympy.matrices.matrices.MatrixBase method) var() (in module sympy.core.symbol) VarBosonicBasis (class in sympy.physics.secondquant) variable_map() (sympy.physics.vector.frame.ReferenceFrame method) variables (sympy.core.function.Lambda attribute) (sympy.core.function.Subs attribute) (sympy.physics.quantum.operator.DifferentialOperator attribute) (sympy.physics.quantum.state.Wavefunction attribute) (sympy.utilities.codegen.Routine attribute) variance() (in module sympy.stats) variations() (in module sympy.utilities.iterables) vec() (sympy.matrices.matrices.MatrixBase method) vech() (sympy.matrices.matrices.MatrixBase method) Vector (class in sympy.galgebra.vector) (class in sympy.physics.vector.vector) vectorize (class in sympy.core.multidimensional)

vectors_in_basis() (in module sympy.diffgeom) vel() (sympy.physics.vector.point.Point method) vertices (sympy.combinatorics.polyhedron.Polyhedron attribute) (sympy.geometry.polygon.Polygon attribute) (sympy.geometry.polygon.RegularPolygon attribute) (sympy.geometry.polygon.Triangle attribute) VF() (in module sympy.printing.pretty.pretty_symbology) viete() (in module sympy.polys.polyfuncs) vlatex() (in module sympy.physics.vector.printing) vobj() (in module sympy.printing.pretty.pretty_symbology) VonMises() (in module sympy.stats) vpprint() (in module sympy.physics.vector.printing) vprint() (in module sympy.physics.vector.printing) vradius (sympy.geometry.ellipse.Circle attribute) (sympy.geometry.ellipse.Ellipse attribute) vstack() (sympy.matrices.matrices.MatrixBase class method) VTIDS (class in sympy.tensor.tensor)

W

w (sympy.physics.gaussopt.BeamParameter attribute) w_0 (sympy.physics.gaussopt.BeamParameter attribute) waist2rayleigh() (in module sympy.physics.gaussopt) waist_approximation_limit (sympy.physics.gaussopt.BeamParameter attribute) Wavefunction (class in sympy.physics.quantum.state) webere() (in module mpmath) WedgeProduct (class in sympy.diffgeom) Weibull() (in module sympy.stats) WGate (class in sympy.physics.quantum.grover) where() (in module sympy.stats) whitm() (in module mpmath) whitw() (in module mpmath) wicks() (in module sympy.physics.secondquant) width (sympy.categories.diagram_drawing.DiagramGrid attribute) width() (sympy.printing.pretty.stringpict.stringPict method)

Wigner3j (class in sympy.physics.quantum.cg) Wigner6j (class in sympy.physics.quantum.cg) Wigner9j (class in sympy.physics.quantum.cg) wigner_3j() (in module sympy.physics.wigner) wigner_6j() (in module sympy.physics.wigner) wigner_9j() (in module sympy.physics.wigner) WignerD (class in sympy.physics.quantum.spin) WignerSemicircle() (in module sympy.stats) Wild (class in sympy.core.symbol) WildFunction (class in sympy.core.function) workdps() (in module mpmath) workprec() (in module mpmath) write() (sympy.utilities.codegen.CodeGen method) (sympy.utilities.runtests.PyTestReporter method) wronskian() (in module sympy.matrices.dense)

X

X (in module sympy.physics.quantum.gate) x (sympy.geometry.point.Point attribute) (sympy.physics.vector.frame.ReferenceFrame attribute) XBra (class in sympy.physics.quantum.cartesian) xdirection (sympy.geometry.line.Ray attribute) xdvi() (in module sympy.galgebra.printing) XGate (class in sympy.physics.quantum.gate) XKet (class in sympy.physics.quantum.cartesian) xobj() (in module sympy.printing.pretty.pretty_symbology)

XOp (class in sympy.physics.quantum.cartesian) Xor (class in sympy.logic.boolalg) xreplace() (sympy.core.basic.Basic method) xstr() (in module sympy.printing.pretty.pretty_symbology) xsym() (in module sympy.printing.pretty.pretty_symbology) xthreaded() (in module sympy.utilities.decorator) xypic_draw_diagram() (in module sympy.categories.diagram_drawing) XypicDiagramDrawer (class in sympy.categories.diagram_drawing)

Y

Y (in module sympy.physics.quantum.gate) y (sympy.geometry.point.Point attribute) (sympy.physics.vector.frame.ReferenceFrame attribute) ydirection (sympy.geometry.line.Ray attribute) YGate (class in sympy.physics.quantum.gate)

yn (class in sympy.functions.special.bessel) Ynm (class in sympy.functions.special.spherical_harmonics) Ynm_c() (in module sympy.functions.special.spherical_harmonics) YOp (class in sympy.physics.quantum.cartesian)

Z

Z (in module sympy.physics.quantum.gate) z (sympy.physics.vector.frame.ReferenceFrame attribute) Zero (class in sympy.core.numbers) zero (sympy.polys.polytools.Poly attribute) ZeroMatrix (class in sympy.matrices.expressions) zeros() (in module sympy.matrices.dense) (sympy.matrices.sparse.SparseMatrix class method) zeta (class in sympy.functions.special.zeta_functions)

zeta() (in module mpmath) zetazero() (in module mpmath) ZGate (class in sympy.physics.quantum.gate) zip_row_op() (sympy.matrices.dense.MutableDenseMatrix method) (sympy.matrices.sparse.MutableSparseMatrix method) Znm (class in sympy.functions.special.spherical_harmonics) ZOp (class in sympy.physics.quantum.cartesian)