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"""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
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