import sys
import mpmath
from sympy.release import __version__
from sympy.core.cache import lazy_function
from sympy.core import Add, AlgebraicNumber, Atom, AtomicExpr, Basic, Catalan, Derivative, Dict, Dummy, E, Eq, Equality, EulerGamma, Expr, Float, Function, FunctionClass, Ge, GoldenRatio, GreaterThan, Gt, I, Integer, Lambda, Le, LessThan, Lt, Mod, Mul, N, Ne, Number, NumberSymbol, PoleError, Pow, PrecisionExhausted, Rational, RealNumber, Rel, S, StrictGreaterThan, StrictLessThan, Subs, Symbol, SympifyError, TribonacciConstant, Tuple, Unequality, UnevaluatedExpr, Wild, WildFunction, arity, bottom_up, cacheit, comp, count_ops, default_sort_key, diff, evalf, evaluate, expand, expand_complex, expand_func, expand_log, expand_mul, expand_multinomial, expand_power_base, expand_power_exp, expand_trig, factor_nc, factor_terms, gcd_terms, integer_log, integer_nthroot, nan, nfloat, oo, ordered, pi, postorder_traversal, preorder_traversal, prod, seterr, symbols, sympify, use, var, vectorize, zoo, igcd, ilcm, mod_inverse
from sympy.logic import And, Equivalent, ITE, Implies, Nand, Nor, Not, Or, POSform, SOPform, Xor, bool_map, false, satisfiable, simplify_logic, to_cnf, to_dnf, to_nnf, true
from sympy.assumptions import AppliedPredicate, AssumptionsContext, Predicate, Q, ask, assuming, refine, register_handler, remove_handler
from sympy.polys import AlgebraicField, BasePolynomialError, CC, CRootOf, CoercionFailed, ComplexField, ComplexRootOf, ComputationFailed, Domain, DomainError, EX, EXRAW, EvaluationFailed, ExactQuotientFailed, ExpressionDomain, ExtraneousFactors, FF, FF_gmpy, FF_python, FiniteField, FlagError, FractionField, GF, GMPYFiniteField, GMPYIntegerRing, GMPYRationalField, GeneratorsError, GeneratorsNeeded, GroebnerBasis, HeuristicGCDFailed, HomomorphismFailed, IntegerRing, IsomorphismFailed, LC, LM, LT, Monomial, MultivariatePolynomialError, NotAlgebraic, NotInvertible, NotReversible, OperationNotSupported, OptionError, Options, PolificationFailed, Poly, PolynomialDivisionFailed, PolynomialError, PolynomialRing, PurePoly, PythonFiniteField, PythonIntegerRing, PythonRational, QQ, QQ_I, QQ_gmpy, QQ_python, RR, RationalField, RealField, RefinementFailed, RootOf, RootSum, UnificationFailed, UnivariatePolynomialError, ZZ, ZZ_I, ZZ_gmpy, ZZ_python, apart, apart_list, assemble_partfrac_list, cancel, chebyshevt_poly, chebyshevu_poly, cofactors, compose, construct_domain, content, count_roots, cyclotomic_poly, decompose, degree, degree_list, discriminant, div, exquo, factor, factor_list, field, field_isomorphism, galois_group, gcd, gcd_list, gcdex, gff, gff_list, grevlex, grlex, groebner, ground_roots, half_gcdex, hermite_poly, hermite_prob_poly, horner, igrevlex, igrlex, ilex, interpolate, interpolating_poly, intervals, invert, is_zero_dimensional, isolate, itermonomials, jacobi_poly, laguerre_poly, lcm, lcm_list, legendre_poly, lex, minimal_polynomial, minpoly, monic, nroots, nth_power_roots_poly, parallel_poly_from_expr, pdiv, pexquo, poly, poly_from_expr, pquo, prem, prime_decomp, prime_valuation, primitive, primitive_element, quo, random_poly, rational_interpolate, real_roots, reduced, refine_root, rem, resultant, ring, rootof, roots, round_two, sfield, sqf, sqf_list, sqf_norm, sqf_part, sring, sturm, subresultants, swinnerton_dyer_poly, symmetric_poly, symmetrize, terms_gcd, to_number_field, together, total_degree, trunc, vfield, viete, vring, xfield, xring
from sympy.series import EmptySequence, Limit, O, Order, SeqAdd, SeqFormula, SeqMul, SeqPer, approximants, difference_delta, fourier_series, fps, gruntz, limit, limit_seq, residue, sequence, series
from sympy.functions import Abs, Chi, Ci, DiracDelta, E1, Ei, Eijk, FallingFactorial, Heaviside, Id, KroneckerDelta, LambertW, LeviCivita, Li, Max, Min, Piecewise, Rem, RisingFactorial, Shi, Si, SingularityFunction, Ynm, Ynm_c, Znm, acos, acosh, acot, acoth, acsc, acsch, adjoint, airyai, airyaiprime, airybi, airybiprime, andre, appellf1, arg, asec, asech, asin, asinh, assoc_laguerre, assoc_legendre, atan, atan2, atanh, bell, bernoulli, besseli, besselj, besselk, bessely, beta, betainc, betainc_regularized, binomial, bspline_basis, bspline_basis_set, carmichael, catalan, cbrt, ceiling, chebyshevt, chebyshevt_root, chebyshevu, chebyshevu_root, conjugate, cos, cosh, cot, coth, csc, csch, digamma, dirichlet_eta, elliptic_e, elliptic_f, elliptic_k, elliptic_pi, erf, erf2, erf2inv, erfc, erfcinv, erfi, erfinv, euler, exp, exp_polar, expint, factorial, factorial2, ff, fibonacci, floor, frac, fresnelc, fresnels, gamma, gegenbauer, genocchi, hankel1, hankel2, harmonic, hermite, hermite_prob, hn1, hn2, hyper, im, interpolating_spline, jacobi, jacobi_normalized, jn, jn_zeros, laguerre, legendre, lerchphi, li, ln, log, loggamma, lowergamma, lucas, marcumq, mathieuc, mathieucprime, mathieus, mathieusprime, meijerg, motzkin, multigamma, partition, periodic_argument, piecewise_exclusive, piecewise_fold, polar_lift, polarify, polygamma, polylog, principal_branch, re, real_root, rf, riemann_xi, root, sec, sech, sign, sin, sinc, sinh, sqrt, stieltjes, subfactorial, tan, tanh, transpose, tribonacci, trigamma, unbranched_argument, unpolarify, uppergamma, yn, zeta
from sympy.ntheory import Sieve, abundance, binomial_coefficients, binomial_coefficients_list, composite, compositepi, continued_fraction, continued_fraction_convergents, continued_fraction_iterator, continued_fraction_periodic, continued_fraction_reduce, cycle_length, discrete_log, divisor_count, divisors, egyptian_fraction, factorint, factorrat, is_abundant, is_amicable, is_deficient, is_mersenne_prime, is_nthpow_residue, is_perfect, is_primitive_root, is_quad_residue, isprime, mersenne_prime_exponent, multinomial_coefficients, multiplicity, n_order, nextprime, npartitions, nthroot_mod, perfect_power, pollard_pm1, pollard_rho, prevprime, prime, primefactors, primerange, primitive_root, primorial, proper_divisor_count, proper_divisors, quadratic_congruence, quadratic_residues, randprime, sieve, sqrt_mod, sqrt_mod_iter, totient, trailing, divisor_sigma, reduced_totient, primenu, primeomega, legendre_symbol,jacobi_symbol, mobius
from sympy.concrete import Product, Sum, product, summation
from sympy.discrete import convolution, covering_product, fft, fwht, ifft, ifwht, intersecting_product, intt, inverse_mobius_transform, mobius_transform, ntt
from sympy.simplify import EPath, FU, besselsimp, collect, collect_const, combsimp, cse, denom, epath, exptrigsimp, fraction, fu, gammasimp, hyperexpand, hypersimilar, hypersimp, kroneckersimp, logcombine, nsimplify, numer, posify, powdenest, powsimp, radsimp, ratsimp, ratsimpmodprime, rcollect, separatevars, signsimp, simplify, sqrtdenest, trigsimp
from sympy.sets import Complement, ComplexRegion, Complexes, ConditionSet, Contains, DisjointUnion, EmptySet, FiniteSet, ImageSet, Integers, Intersection, Interval, Naturals, Naturals0, OmegaPower, Ordinal, PowerSet, ProductSet, Range, Rationals, Reals, Set, SymmetricDifference, Union, UniversalSet, imageset, ord0
from sympy.solvers import check_assumptions, checkodesol, checkpdesol, checksol, classify_ode, classify_pde, decompogen, det_quick, diophantine, dsolve, failing_assumptions, homogeneous_order, inv_quick, linear_eq_to_matrix, linsolve, nonlinsolve, nsolve, ode_order, pde_separate, pde_separate_add, pde_separate_mul, pdsolve, reduce_abs_inequalities, reduce_abs_inequality, reduce_inequalities, rsolve, rsolve_hyper, rsolve_poly, rsolve_ratio, solve, solve_linear, solve_linear_system, solve_linear_system_LU, solve_poly_inequality, solve_poly_system, solve_rational_inequalities, solve_triangulated, solve_undetermined_coeffs, solve_univariate_inequality, solveset, substitution
from sympy.matrices import Adjoint, BlockDiagMatrix, BlockMatrix, DeferredVector, Determinant, DiagMatrix, DiagonalMatrix, DiagonalOf, DotProduct, FunctionMatrix, GramSchmidt, HadamardPower, HadamardProduct, Identity, ImmutableDenseMatrix, ImmutableMatrix, ImmutableSparseMatrix, Inverse, KroneckerProduct, MatAdd, MatMul, MatPow, Matrix, MatrixBase, MatrixExpr, MatrixPermute, MatrixSlice, MatrixSymbol, MutableDenseMatrix, MutableMatrix, MutableSparseMatrix, NonSquareMatrixError, OneMatrix, Permanent, PermutationMatrix, ShapeError, SparseMatrix, Trace, Transpose, ZeroMatrix, banded, block_collapse, blockcut, casoratian, det, diag, diagonalize_vector, eye, hadamard_product, hessian, jordan_cell, kronecker_product, list2numpy, matrix2numpy, matrix_multiply_elementwise, matrix_symbols, ones, per, randMatrix, rot_axis1, rot_axis2, rot_axis3, rot_ccw_axis1, rot_ccw_axis2, rot_ccw_axis3, rot_givens, symarray, trace, wronskian, zeros
from sympy.geometry import Circle, Curve, Ellipse, GeometryError, Line, Line2D, Line3D, Parabola, Plane, Point, Point2D, Point3D, Polygon, Ray, Ray2D, Ray3D, RegularPolygon, Segment, Segment2D, Segment3D, Triangle, are_similar, centroid, closest_points, convex_hull, deg, farthest_points, idiff, intersection, rad
from sympy.utilities import capture, dict_merge, filldedent, flatten, group, has_dups, has_variety, lambdify, memoize_property, numbered_symbols, postfixes, prefixes, public, reshape, rotations, sift, subsets, take, threaded, timed, topological_sort, unflatten, variations, xthreaded, cartes
from sympy.integrals import CosineTransform, FourierTransform, HankelTransform, Integral, InverseCosineTransform, InverseFourierTransform, InverseHankelTransform, InverseLaplaceTransform, InverseMellinTransform, InverseSineTransform, LaplaceTransform, MellinTransform, SineTransform, cosine_transform, fourier_transform, hankel_transform, integrate, inverse_cosine_transform, inverse_fourier_transform, inverse_hankel_transform, inverse_laplace_transform, inverse_mellin_transform, inverse_sine_transform, laplace_transform, line_integrate, mellin_transform, sine_transform, singularityintegrate
from sympy.tensor import Array, DenseNDimArray, Idx, ImmutableDenseNDimArray, ImmutableSparseNDimArray, Indexed, IndexedBase, MutableDenseNDimArray, MutableSparseNDimArray, NDimArray, SparseNDimArray, derive_by_array, get_contraction_structure, get_indices, permutedims, shape, tensorcontraction, tensordiagonal, tensorproduct
from sympy.parsing import parse_expr
from sympy.calculus import AccumBounds, apply_finite_diff, differentiate_finite, euler_equations, finite_diff_weights, is_convex, is_decreasing, is_increasing, is_monotonic, is_strictly_decreasing, is_strictly_increasing, maximum, minimum, not_empty_in, periodicity, singularities, stationary_points
from sympy.algebras import Quaternion
from sympy.printing import StrPrinter, TableForm, ccode, cxxcode, dotprint, fcode, glsl_code, jscode, julia_code, latex, maple_code, mathematica_code, mathml, multiline_latex, octave_code, pager_print, pprint, pprint_try_use_unicode, pprint_use_unicode, pretty, pretty_print, preview, print_ccode, print_fcode, print_glsl, print_gtk, print_jscode, print_latex, print_maple_code, print_mathml, print_python, print_rcode, print_tree, pycode, python, rcode, rust_code, smtlib_code, srepr, sstr, sstrrepr
from sympy.plotting import plot, plot_backends, plot_implicit, plot_parametric, textplot
from sympy.interactive import init_printing, init_session, interactive_traversal

if sys.version_info < (3, 8):
    ...
if 'dev' in __version__:
    def enable_warnings() -> None:
        ...
    
SYMPY_DEBUG: bool = ...
test = ...
doctest = ...
__all__ = ['__version__', 'sympify', 'SympifyError', 'cacheit', 'Basic', 'Atom', 'preorder_traversal', 'S', 'Expr', 'AtomicExpr', 'UnevaluatedExpr', 'Symbol', 'Wild', 'Dummy', 'symbols', 'var', 'Number', 'Float', 'Rational', 'Integer', 'NumberSymbol', 'RealNumber', 'igcd', 'ilcm', 'seterr', 'E', 'I', 'nan', 'oo', 'pi', 'zoo', 'AlgebraicNumber', 'comp', 'mod_inverse', 'Pow', 'integer_nthroot', 'integer_log', 'Mul', 'prod', 'Add', 'Mod', 'Rel', 'Eq', 'Ne', 'Lt', 'Le', 'Gt', 'Ge', 'Equality', 'GreaterThan', 'LessThan', 'Unequality', 'StrictGreaterThan', 'StrictLessThan', 'vectorize', 'Lambda', 'WildFunction', 'Derivative', 'diff', 'FunctionClass', 'Function', 'Subs', 'expand', 'PoleError', 'count_ops', 'expand_mul', 'expand_log', 'expand_func', 'expand_trig', 'expand_complex', 'expand_multinomial', 'nfloat', 'expand_power_base', 'expand_power_exp', 'arity', 'PrecisionExhausted', 'N', 'evalf', 'Tuple', 'Dict', 'gcd_terms', 'factor_terms', 'factor_nc', 'evaluate', 'Catalan', 'EulerGamma', 'GoldenRatio', 'TribonacciConstant', 'bottom_up', 'use', 'postorder_traversal', 'default_sort_key', 'ordered', 'to_cnf', 'to_dnf', 'to_nnf', 'And', 'Or', 'Not', 'Xor', 'Nand', 'Nor', 'Implies', 'Equivalent', 'ITE', 'POSform', 'SOPform', 'simplify_logic', 'bool_map', 'true', 'false', 'satisfiable', 'AppliedPredicate', 'Predicate', 'AssumptionsContext', 'assuming', 'Q', 'ask', 'register_handler', 'remove_handler', 'refine', 'Poly', 'PurePoly', 'poly_from_expr', 'parallel_poly_from_expr', 'degree', 'total_degree', 'degree_list', 'LC', 'LM', 'LT', 'pdiv', 'prem', 'pquo', 'pexquo', 'div', 'rem', 'quo', 'exquo', 'half_gcdex', 'gcdex', 'invert', 'subresultants', 'resultant', 'discriminant', 'cofactors', 'gcd_list', 'gcd', 'lcm_list', 'lcm', 'terms_gcd', 'trunc', 'monic', 'content', 'primitive', 'compose', 'decompose', 'sturm', 'gff_list', 'gff', 'sqf_norm', 'sqf_part', 'sqf_list', 'sqf', 'factor_list', 'factor', 'intervals', 'refine_root', 'count_roots', 'real_roots', 'nroots', 'ground_roots', 'nth_power_roots_poly', 'cancel', 'reduced', 'groebner', 'is_zero_dimensional', 'GroebnerBasis', 'poly', 'symmetrize', 'horner', 'interpolate', 'rational_interpolate', 'viete', 'together', 'BasePolynomialError', 'ExactQuotientFailed', 'PolynomialDivisionFailed', 'OperationNotSupported', 'HeuristicGCDFailed', 'HomomorphismFailed', 'IsomorphismFailed', 'ExtraneousFactors', 'EvaluationFailed', 'RefinementFailed', 'CoercionFailed', 'NotInvertible', 'NotReversible', 'NotAlgebraic', 'DomainError', 'PolynomialError', 'UnificationFailed', 'GeneratorsError', 'GeneratorsNeeded', 'ComputationFailed', 'UnivariatePolynomialError', 'MultivariatePolynomialError', 'PolificationFailed', 'OptionError', 'FlagError', 'minpoly', 'minimal_polynomial', 'primitive_element', 'field_isomorphism', 'to_number_field', 'isolate', 'round_two', 'prime_decomp', 'prime_valuation', 'galois_group', 'itermonomials', 'Monomial', 'lex', 'grlex', 'grevlex', 'ilex', 'igrlex', 'igrevlex', 'CRootOf', 'rootof', 'RootOf', 'ComplexRootOf', 'RootSum', 'roots', 'Domain', 'FiniteField', 'IntegerRing', 'RationalField', 'RealField', 'ComplexField', 'PythonFiniteField', 'GMPYFiniteField', 'PythonIntegerRing', 'GMPYIntegerRing', 'PythonRational', 'GMPYRationalField', 'AlgebraicField', 'PolynomialRing', 'FractionField', 'ExpressionDomain', 'FF_python', 'FF_gmpy', 'ZZ_python', 'ZZ_gmpy', 'QQ_python', 'QQ_gmpy', 'GF', 'FF', 'ZZ', 'QQ', 'ZZ_I', 'QQ_I', 'RR', 'CC', 'EX', 'EXRAW', 'construct_domain', 'swinnerton_dyer_poly', 'cyclotomic_poly', 'symmetric_poly', 'random_poly', 'interpolating_poly', 'jacobi_poly', 'chebyshevt_poly', 'chebyshevu_poly', 'hermite_poly', 'hermite_prob_poly', 'legendre_poly', 'laguerre_poly', 'apart', 'apart_list', 'assemble_partfrac_list', 'Options', 'ring', 'xring', 'vring', 'sring', 'field', 'xfield', 'vfield', 'sfield', 'Order', 'O', 'limit', 'Limit', 'gruntz', 'series', 'approximants', 'residue', 'EmptySequence', 'SeqPer', 'SeqFormula', 'sequence', 'SeqAdd', 'SeqMul', 'fourier_series', 'fps', 'difference_delta', 'limit_seq', 'factorial', 'factorial2', 'rf', 'ff', 'binomial', 'RisingFactorial', 'FallingFactorial', 'subfactorial', 'carmichael', 'fibonacci', 'lucas', 'motzkin', 'tribonacci', 'harmonic', 'bernoulli', 'bell', 'euler', 'catalan', 'genocchi', 'andre', 'partition', 'sqrt', 'root', 'Min', 'Max', 'Id', 'real_root', 'Rem', 'cbrt', 're', 'im', 'sign', 'Abs', 'conjugate', 'arg', 'polar_lift', 'periodic_argument', 'unbranched_argument', 'principal_branch', 'transpose', 'adjoint', 'polarify', 'unpolarify', 'sin', 'cos', 'tan', 'sec', 'csc', 'cot', 'sinc', 'asin', 'acos', 'atan', 'asec', 'acsc', 'acot', 'atan2', 'exp_polar', 'exp', 'ln', 'log', 'LambertW', 'sinh', 'cosh', 'tanh', 'coth', 'sech', 'csch', 'asinh', 'acosh', 'atanh', 'acoth', 'asech', 'acsch', 'floor', 'ceiling', 'frac', 'Piecewise', 'piecewise_fold', 'piecewise_exclusive', 'erf', 'erfc', 'erfi', 'erf2', 'erfinv', 'erfcinv', 'erf2inv', 'Ei', 'expint', 'E1', 'li', 'Li', 'Si', 'Ci', 'Shi', 'Chi', 'fresnels', 'fresnelc', 'gamma', 'lowergamma', 'uppergamma', 'polygamma', 'loggamma', 'digamma', 'trigamma', 'multigamma', 'dirichlet_eta', 'zeta', 'lerchphi', 'polylog', 'stieltjes', 'Eijk', 'LeviCivita', 'KroneckerDelta', 'SingularityFunction', 'DiracDelta', 'Heaviside', 'bspline_basis', 'bspline_basis_set', 'interpolating_spline', 'besselj', 'bessely', 'besseli', 'besselk', 'hankel1', 'hankel2', 'jn', 'yn', 'jn_zeros', 'hn1', 'hn2', 'airyai', 'airybi', 'airyaiprime', 'airybiprime', 'marcumq', 'hyper', 'meijerg', 'appellf1', 'legendre', 'assoc_legendre', 'hermite', 'hermite_prob', 'chebyshevt', 'chebyshevu', 'chebyshevu_root', 'chebyshevt_root', 'laguerre', 'assoc_laguerre', 'gegenbauer', 'jacobi', 'jacobi_normalized', 'Ynm', 'Ynm_c', 'Znm', 'elliptic_k', 'elliptic_f', 'elliptic_e', 'elliptic_pi', 'beta', 'mathieus', 'mathieuc', 'mathieusprime', 'mathieucprime', 'riemann_xi', 'betainc', 'betainc_regularized', 'nextprime', 'prevprime', 'prime', 'primerange', 'randprime', 'Sieve', 'sieve', 'primorial', 'cycle_length', 'composite', 'compositepi', 'isprime', 'divisors', 'proper_divisors', 'factorint', 'multiplicity', 'perfect_power', 'pollard_pm1', 'pollard_rho', 'primefactors', 'totient', 'trailing', 'divisor_count', 'proper_divisor_count', 'divisor_sigma', 'factorrat', 'reduced_totient', 'primenu', 'primeomega', 'mersenne_prime_exponent', 'is_perfect', 'is_mersenne_prime', 'is_abundant', 'is_deficient', 'is_amicable', 'abundance', 'npartitions', 'is_primitive_root', 'is_quad_residue', 'legendre_symbol', 'jacobi_symbol', 'n_order', 'sqrt_mod', 'quadratic_residues', 'primitive_root', 'nthroot_mod', 'is_nthpow_residue', 'sqrt_mod_iter', 'mobius', 'discrete_log', 'quadratic_congruence', 'binomial_coefficients', 'binomial_coefficients_list', 'multinomial_coefficients', 'continued_fraction_periodic', 'continued_fraction_iterator', 'continued_fraction_reduce', 'continued_fraction_convergents', 'continued_fraction', 'egyptian_fraction', 'product', 'Product', 'summation', 'Sum', 'fft', 'ifft', 'ntt', 'intt', 'fwht', 'ifwht', 'mobius_transform', 'inverse_mobius_transform', 'convolution', 'covering_product', 'intersecting_product', 'simplify', 'hypersimp', 'hypersimilar', 'logcombine', 'separatevars', 'posify', 'besselsimp', 'kroneckersimp', 'signsimp', 'nsimplify', 'FU', 'fu', 'sqrtdenest', 'cse', 'epath', 'EPath', 'hyperexpand', 'collect', 'rcollect', 'radsimp', 'collect_const', 'fraction', 'numer', 'denom', 'trigsimp', 'exptrigsimp', 'powsimp', 'powdenest', 'combsimp', 'gammasimp', 'ratsimp', 'ratsimpmodprime', 'Set', 'Interval', 'Union', 'EmptySet', 'FiniteSet', 'ProductSet', 'Intersection', 'imageset', 'DisjointUnion', 'Complement', 'SymmetricDifference', 'ImageSet', 'Range', 'ComplexRegion', 'Reals', 'Contains', 'ConditionSet', 'Ordinal', 'OmegaPower', 'ord0', 'PowerSet', 'Naturals', 'Naturals0', 'UniversalSet', 'Integers', 'Rationals', 'Complexes', 'solve', 'solve_linear_system', 'solve_linear_system_LU', 'solve_undetermined_coeffs', 'nsolve', 'solve_linear', 'checksol', 'det_quick', 'inv_quick', 'check_assumptions', 'failing_assumptions', 'diophantine', 'rsolve', 'rsolve_poly', 'rsolve_ratio', 'rsolve_hyper', 'checkodesol', 'classify_ode', 'dsolve', 'homogeneous_order', 'solve_poly_system', 'solve_triangulated', 'pde_separate', 'pde_separate_add', 'pde_separate_mul', 'pdsolve', 'classify_pde', 'checkpdesol', 'ode_order', 'reduce_inequalities', 'reduce_abs_inequality', 'reduce_abs_inequalities', 'solve_poly_inequality', 'solve_rational_inequalities', 'solve_univariate_inequality', 'decompogen', 'solveset', 'linsolve', 'linear_eq_to_matrix', 'nonlinsolve', 'substitution', 'ShapeError', 'NonSquareMatrixError', 'GramSchmidt', 'casoratian', 'diag', 'eye', 'hessian', 'jordan_cell', 'list2numpy', 'matrix2numpy', 'matrix_multiply_elementwise', 'ones', 'randMatrix', 'rot_axis1', 'rot_axis2', 'rot_axis3', 'symarray', 'wronskian', 'zeros', 'MutableDenseMatrix', 'DeferredVector', 'MatrixBase', 'Matrix', 'MutableMatrix', 'MutableSparseMatrix', 'banded', 'ImmutableDenseMatrix', 'ImmutableSparseMatrix', 'ImmutableMatrix', 'SparseMatrix', 'MatrixSlice', 'BlockDiagMatrix', 'BlockMatrix', 'FunctionMatrix', 'Identity', 'Inverse', 'MatAdd', 'MatMul', 'MatPow', 'MatrixExpr', 'MatrixSymbol', 'Trace', 'Transpose', 'ZeroMatrix', 'OneMatrix', 'blockcut', 'block_collapse', 'matrix_symbols', 'Adjoint', 'hadamard_product', 'HadamardProduct', 'HadamardPower', 'Determinant', 'det', 'diagonalize_vector', 'DiagMatrix', 'DiagonalMatrix', 'DiagonalOf', 'trace', 'DotProduct', 'kronecker_product', 'KroneckerProduct', 'PermutationMatrix', 'MatrixPermute', 'Permanent', 'per', 'rot_ccw_axis1', 'rot_ccw_axis2', 'rot_ccw_axis3', 'rot_givens', 'Point', 'Point2D', 'Point3D', 'Line', 'Ray', 'Segment', 'Line2D', 'Segment2D', 'Ray2D', 'Line3D', 'Segment3D', 'Ray3D', 'Plane', 'Ellipse', 'Circle', 'Polygon', 'RegularPolygon', 'Triangle', 'rad', 'deg', 'are_similar', 'centroid', 'convex_hull', 'idiff', 'intersection', 'closest_points', 'farthest_points', 'GeometryError', 'Curve', 'Parabola', 'flatten', 'group', 'take', 'subsets', 'variations', 'numbered_symbols', 'cartes', 'capture', 'dict_merge', 'prefixes', 'postfixes', 'sift', 'topological_sort', 'unflatten', 'has_dups', 'has_variety', 'reshape', 'rotations', 'filldedent', 'lambdify', 'threaded', 'xthreaded', 'public', 'memoize_property', 'timed', 'integrate', 'Integral', 'line_integrate', 'mellin_transform', 'inverse_mellin_transform', 'MellinTransform', 'InverseMellinTransform', 'laplace_transform', 'inverse_laplace_transform', 'LaplaceTransform', 'InverseLaplaceTransform', 'fourier_transform', 'inverse_fourier_transform', 'FourierTransform', 'InverseFourierTransform', 'sine_transform', 'inverse_sine_transform', 'SineTransform', 'InverseSineTransform', 'cosine_transform', 'inverse_cosine_transform', 'CosineTransform', 'InverseCosineTransform', 'hankel_transform', 'inverse_hankel_transform', 'HankelTransform', 'InverseHankelTransform', 'singularityintegrate', 'IndexedBase', 'Idx', 'Indexed', 'get_contraction_structure', 'get_indices', 'shape', 'MutableDenseNDimArray', 'ImmutableDenseNDimArray', 'MutableSparseNDimArray', 'ImmutableSparseNDimArray', 'NDimArray', 'tensorproduct', 'tensorcontraction', 'tensordiagonal', 'derive_by_array', 'permutedims', 'Array', 'DenseNDimArray', 'SparseNDimArray', 'parse_expr', 'euler_equations', 'singularities', 'is_increasing', 'is_strictly_increasing', 'is_decreasing', 'is_strictly_decreasing', 'is_monotonic', 'finite_diff_weights', 'apply_finite_diff', 'differentiate_finite', 'periodicity', 'not_empty_in', 'AccumBounds', 'is_convex', 'stationary_points', 'minimum', 'maximum', 'Quaternion', 'pager_print', 'pretty', 'pretty_print', 'pprint', 'pprint_use_unicode', 'pprint_try_use_unicode', 'latex', 'print_latex', 'multiline_latex', 'mathml', 'print_mathml', 'python', 'print_python', 'pycode', 'ccode', 'print_ccode', 'smtlib_code', 'glsl_code', 'print_glsl', 'cxxcode', 'fcode', 'print_fcode', 'rcode', 'print_rcode', 'jscode', 'print_jscode', 'julia_code', 'mathematica_code', 'octave_code', 'rust_code', 'print_gtk', 'preview', 'srepr', 'print_tree', 'StrPrinter', 'sstr', 'sstrrepr', 'TableForm', 'dotprint', 'maple_code', 'print_maple_code', 'plot', 'textplot', 'plot_backends', 'plot_implicit', 'plot_parametric', 'init_session', 'init_printing', 'interactive_traversal', 'test', 'doctest']
