1"""Polynomial manipulation algorithms and algebraic objects.""" 2 3from .polytools import (Poly, PurePoly, 4 parallel_poly_from_expr, degree, LC, 5 LM, LT, div, rem, quo, 6 exquo, half_gcdex, gcdex, invert, subresultants, 7 resultant, discriminant, cofactors, gcd, 8 lcm, terms_gcd, trunc, monic, content, 9 primitive, compose, decompose, 10 sqf_norm, sqf_part, sqf_list, sqf, factor_list, 11 factor, count_roots, real_roots, nroots, 12 cancel, reduced, groebner, GroebnerBasis, poly) 13from .polyfuncs import symmetrize, horner, interpolate, viete 14from .rationaltools import together 15from .polyerrors import (BasePolynomialError, 16 ExactQuotientFailed, PolynomialDivisionFailed, 17 OperationNotSupported, HeuristicGCDFailed, 18 HomomorphismFailed, IsomorphismFailed, 19 ExtraneousFactors, EvaluationFailed, 20 RefinementFailed, CoercionFailed, NotInvertible, 21 NotReversible, NotAlgebraic, DomainError, 22 PolynomialError, UnificationFailed, 23 GeneratorsError, GeneratorsNeeded, ComputationFailed, 24 UnivariatePolynomialError, MultivariatePolynomialError, 25 PolificationFailed, OptionError, FlagError) 26from .numberfields import (minimal_polynomial, 27 primitive_element, field_isomorphism) 28from .monomials import Monomial, itermonomials 29from .orderings import (lex, grlex, grevlex, ilex, 30 igrlex, igrevlex) 31from .rootoftools import RootOf, RootSum 32from .polyroots import roots 33from .constructor import construct_domain 34from .specialpolys import (swinnerton_dyer_poly, 35 cyclotomic_poly, symmetric_poly, 36 random_poly, interpolating_poly) 37from .orthopolys import (jacobi_poly, chebyshevt_poly, 38 chebyshevu_poly, hermite_poly, legendre_poly, 39 laguerre_poly, spherical_bessel_fn) 40from .partfrac import apart, apart_list, assemble_partfrac_list 41from .polyoptions import Options 42from .rings import PolynomialRing, ring 43from .fields import FractionField, field 44from .univar import UnivarPolynomialRing 45 46 47__all__ = ('Poly', 'PurePoly', 48 'parallel_poly_from_expr', 'degree', 'LC', 49 'LM', 'LT', 'div', 'rem', 'quo', 'exquo', 'half_gcdex', 50 'gcdex', 'invert', 'subresultants', 'resultant', 'discriminant', 51 'cofactors', 'gcd', 'lcm', 'terms_gcd', 52 'trunc', 'monic', 'content', 'primitive', 'compose', 'decompose', 53 'sqf_norm', 'sqf_part', 'sqf_list', 'sqf', 'factor_list', 54 'factor', 'count_roots', 'real_roots', 'nroots', 'cancel', 55 'reduced', 'groebner', 'GroebnerBasis', 'poly', 'symmetrize', 56 'horner', 'interpolate', 'viete', 'together', 'BasePolynomialError', 57 'ExactQuotientFailed', 'PolynomialDivisionFailed', 58 'OperationNotSupported', 'HeuristicGCDFailed', 59 'HomomorphismFailed', 'IsomorphismFailed', 'ExtraneousFactors', 60 'EvaluationFailed', 'RefinementFailed', 'CoercionFailed', 61 'NotInvertible', 'NotReversible', 'NotAlgebraic', 'DomainError', 62 'PolynomialError', 'UnificationFailed', 'GeneratorsError', 63 'GeneratorsNeeded', 'ComputationFailed', 'UnivariatePolynomialError', 64 'MultivariatePolynomialError', 'PolificationFailed', 'OptionError', 65 'FlagError', 'minimal_polynomial', 'primitive_element', 66 'field_isomorphism', 'Monomial', 'itermonomials', 'lex', 'grlex', 67 'grevlex', 'ilex', 'igrlex', 'igrevlex', 'RootOf', 'RootSum', 68 'roots', 'construct_domain', 'swinnerton_dyer_poly', 69 'cyclotomic_poly', 'symmetric_poly', 'random_poly', 70 'interpolating_poly', 'jacobi_poly', 'chebyshevt_poly', 71 'chebyshevu_poly', 'hermite_poly', 'legendre_poly', 72 'laguerre_poly', 'spherical_bessel_fn', 'apart', 'apart_list', 73 'assemble_partfrac_list', 'Options', 'PolynomialRing', 'ring', 74 'FractionField', 'field', 'UnivarPolynomialRing') 75