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130 lines
5.4 KiB
130 lines
5.4 KiB
5 months ago
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"""Polynomial manipulation algorithms and algebraic objects. """
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__all__ = [
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'Poly', 'PurePoly', 'poly_from_expr', 'parallel_poly_from_expr', 'degree',
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'total_degree', 'degree_list', 'LC', 'LM', 'LT', 'pdiv', 'prem', 'pquo',
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'pexquo', 'div', 'rem', 'quo', 'exquo', 'half_gcdex', 'gcdex', 'invert',
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'subresultants', 'resultant', 'discriminant', 'cofactors', 'gcd_list',
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'gcd', 'lcm_list', 'lcm', 'terms_gcd', 'trunc', 'monic', 'content',
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'primitive', 'compose', 'decompose', 'sturm', 'gff_list', 'gff',
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'sqf_norm', 'sqf_part', 'sqf_list', 'sqf', 'factor_list', 'factor',
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'intervals', 'refine_root', 'count_roots', 'real_roots', 'nroots',
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'ground_roots', 'nth_power_roots_poly', 'cancel', 'reduced', 'groebner',
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'is_zero_dimensional', 'GroebnerBasis', 'poly',
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'symmetrize', 'horner', 'interpolate', 'rational_interpolate', 'viete',
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'together',
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'BasePolynomialError', 'ExactQuotientFailed', 'PolynomialDivisionFailed',
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'OperationNotSupported', 'HeuristicGCDFailed', 'HomomorphismFailed',
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'IsomorphismFailed', 'ExtraneousFactors', 'EvaluationFailed',
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'RefinementFailed', 'CoercionFailed', 'NotInvertible', 'NotReversible',
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'NotAlgebraic', 'DomainError', 'PolynomialError', 'UnificationFailed',
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'GeneratorsError', 'GeneratorsNeeded', 'ComputationFailed',
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'UnivariatePolynomialError', 'MultivariatePolynomialError',
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'PolificationFailed', 'OptionError', 'FlagError',
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'minpoly', 'minimal_polynomial', 'primitive_element', 'field_isomorphism',
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'to_number_field', 'isolate', 'round_two', 'prime_decomp',
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'prime_valuation', 'galois_group',
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'itermonomials', 'Monomial',
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'lex', 'grlex', 'grevlex', 'ilex', 'igrlex', 'igrevlex',
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'CRootOf', 'rootof', 'RootOf', 'ComplexRootOf', 'RootSum',
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'roots',
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'Domain', 'FiniteField', 'IntegerRing', 'RationalField', 'RealField',
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'ComplexField', 'PythonFiniteField', 'GMPYFiniteField',
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'PythonIntegerRing', 'GMPYIntegerRing', 'PythonRational',
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'GMPYRationalField', 'AlgebraicField', 'PolynomialRing', 'FractionField',
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'ExpressionDomain', 'FF_python', 'FF_gmpy', 'ZZ_python', 'ZZ_gmpy',
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'QQ_python', 'QQ_gmpy', 'GF', 'FF', 'ZZ', 'QQ', 'ZZ_I', 'QQ_I', 'RR',
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'CC', 'EX', 'EXRAW',
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'construct_domain',
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'swinnerton_dyer_poly', 'cyclotomic_poly', 'symmetric_poly',
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'random_poly', 'interpolating_poly',
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'jacobi_poly', 'chebyshevt_poly', 'chebyshevu_poly', 'hermite_poly',
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'hermite_prob_poly', 'legendre_poly', 'laguerre_poly',
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'bernoulli_poly', 'bernoulli_c_poly', 'genocchi_poly', 'euler_poly',
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'andre_poly',
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'apart', 'apart_list', 'assemble_partfrac_list',
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'Options',
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'ring', 'xring', 'vring', 'sring',
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'field', 'xfield', 'vfield', 'sfield'
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]
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from .polytools import (Poly, PurePoly, poly_from_expr,
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parallel_poly_from_expr, degree, total_degree, degree_list, LC, LM,
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LT, pdiv, prem, pquo, pexquo, div, rem, quo, exquo, half_gcdex, gcdex,
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invert, subresultants, resultant, discriminant, cofactors, gcd_list,
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gcd, lcm_list, lcm, terms_gcd, trunc, monic, content, primitive,
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compose, decompose, sturm, gff_list, gff, sqf_norm, sqf_part,
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sqf_list, sqf, factor_list, factor, intervals, refine_root,
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count_roots, real_roots, nroots, ground_roots, nth_power_roots_poly,
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cancel, reduced, groebner, is_zero_dimensional, GroebnerBasis, poly)
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from .polyfuncs import (symmetrize, horner, interpolate,
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rational_interpolate, viete)
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from .rationaltools import together
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from .polyerrors import (BasePolynomialError, ExactQuotientFailed,
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PolynomialDivisionFailed, OperationNotSupported, HeuristicGCDFailed,
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HomomorphismFailed, IsomorphismFailed, ExtraneousFactors,
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EvaluationFailed, RefinementFailed, CoercionFailed, NotInvertible,
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NotReversible, NotAlgebraic, DomainError, PolynomialError,
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UnificationFailed, GeneratorsError, GeneratorsNeeded,
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ComputationFailed, UnivariatePolynomialError,
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MultivariatePolynomialError, PolificationFailed, OptionError,
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FlagError)
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from .numberfields import (minpoly, minimal_polynomial, primitive_element,
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field_isomorphism, to_number_field, isolate, round_two, prime_decomp,
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prime_valuation, galois_group)
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from .monomials import itermonomials, Monomial
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from .orderings import lex, grlex, grevlex, ilex, igrlex, igrevlex
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from .rootoftools import CRootOf, rootof, RootOf, ComplexRootOf, RootSum
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from .polyroots import roots
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from .domains import (Domain, FiniteField, IntegerRing, RationalField,
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RealField, ComplexField, PythonFiniteField, GMPYFiniteField,
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PythonIntegerRing, GMPYIntegerRing, PythonRational, GMPYRationalField,
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AlgebraicField, PolynomialRing, FractionField, ExpressionDomain,
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FF_python, FF_gmpy, ZZ_python, ZZ_gmpy, QQ_python, QQ_gmpy, GF, FF,
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ZZ, QQ, ZZ_I, QQ_I, RR, CC, EX, EXRAW)
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from .constructor import construct_domain
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from .specialpolys import (swinnerton_dyer_poly, cyclotomic_poly,
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symmetric_poly, random_poly, interpolating_poly)
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from .orthopolys import (jacobi_poly, chebyshevt_poly, chebyshevu_poly,
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hermite_poly, hermite_prob_poly, legendre_poly, laguerre_poly)
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from .appellseqs import (bernoulli_poly, bernoulli_c_poly, genocchi_poly,
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euler_poly, andre_poly)
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from .partfrac import apart, apart_list, assemble_partfrac_list
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from .polyoptions import Options
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from .rings import ring, xring, vring, sring
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from .fields import field, xfield, vfield, sfield
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