| """Polynomial manipulation algorithms and algebraic objects. """ | |
| __all__ = [ | |
| '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', 'all_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', | |
| 'bernoulli_poly', 'bernoulli_c_poly', 'genocchi_poly', 'euler_poly', | |
| 'andre_poly', | |
| 'apart', 'apart_list', 'assemble_partfrac_list', | |
| 'Options', | |
| 'ring', 'xring', 'vring', 'sring', | |
| 'field', 'xfield', 'vfield', 'sfield' | |
| ] | |
| from .polytools import (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, all_roots, real_roots, nroots, ground_roots, | |
| nth_power_roots_poly, cancel, reduced, groebner, is_zero_dimensional, | |
| GroebnerBasis, poly) | |
| from .polyfuncs import (symmetrize, horner, interpolate, | |
| rational_interpolate, viete) | |
| from .rationaltools import together | |
| from .polyerrors import (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) | |
| from .numberfields import (minpoly, minimal_polynomial, primitive_element, | |
| field_isomorphism, to_number_field, isolate, round_two, prime_decomp, | |
| prime_valuation, galois_group) | |
| from .monomials import itermonomials, Monomial | |
| from .orderings import lex, grlex, grevlex, ilex, igrlex, igrevlex | |
| from .rootoftools import CRootOf, rootof, RootOf, ComplexRootOf, RootSum | |
| from .polyroots import roots | |
| from .domains import (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) | |
| from .constructor import construct_domain | |
| from .specialpolys import (swinnerton_dyer_poly, cyclotomic_poly, | |
| symmetric_poly, random_poly, interpolating_poly) | |
| from .orthopolys import (jacobi_poly, chebyshevt_poly, chebyshevu_poly, | |
| hermite_poly, hermite_prob_poly, legendre_poly, laguerre_poly) | |
| from .appellseqs import (bernoulli_poly, bernoulli_c_poly, genocchi_poly, | |
| euler_poly, andre_poly) | |
| from .partfrac import apart, apart_list, assemble_partfrac_list | |
| from .polyoptions import Options | |
| from .rings import ring, xring, vring, sring | |
| from .fields import field, xfield, vfield, sfield | |