Coverage for /usr/lib/python3/dist-packages/sympy/polys/__init__.py: 100%

1"""Polynomial manipulation algorithms and algebraic objects. """ 

2 

3__all__ = [ 

4 'Poly', 'PurePoly', 'poly_from_expr', 'parallel_poly_from_expr', 'degree', 

5 'total_degree', 'degree_list', 'LC', 'LM', 'LT', 'pdiv', 'prem', 'pquo', 

6 'pexquo', 'div', 'rem', 'quo', 'exquo', 'half_gcdex', 'gcdex', 'invert', 

7 'subresultants', 'resultant', 'discriminant', 'cofactors', 'gcd_list', 

8 'gcd', 'lcm_list', 'lcm', 'terms_gcd', 'trunc', 'monic', 'content', 

9 'primitive', 'compose', 'decompose', 'sturm', 'gff_list', 'gff', 

10 'sqf_norm', 'sqf_part', 'sqf_list', 'sqf', 'factor_list', 'factor', 

11 'intervals', 'refine_root', 'count_roots', 'real_roots', 'nroots', 

12 'ground_roots', 'nth_power_roots_poly', 'cancel', 'reduced', 'groebner', 

13 'is_zero_dimensional', 'GroebnerBasis', 'poly', 

14 

15 'symmetrize', 'horner', 'interpolate', 'rational_interpolate', 'viete', 

16 

17 'together', 

18 

19 'BasePolynomialError', 'ExactQuotientFailed', 'PolynomialDivisionFailed', 

20 'OperationNotSupported', 'HeuristicGCDFailed', 'HomomorphismFailed', 

21 'IsomorphismFailed', 'ExtraneousFactors', 'EvaluationFailed', 

22 'RefinementFailed', 'CoercionFailed', 'NotInvertible', 'NotReversible', 

23 'NotAlgebraic', 'DomainError', 'PolynomialError', 'UnificationFailed', 

24 'GeneratorsError', 'GeneratorsNeeded', 'ComputationFailed', 

25 'UnivariatePolynomialError', 'MultivariatePolynomialError', 

26 'PolificationFailed', 'OptionError', 'FlagError', 

27 

28 'minpoly', 'minimal_polynomial', 'primitive_element', 'field_isomorphism', 

29 'to_number_field', 'isolate', 'round_two', 'prime_decomp', 

30 'prime_valuation', 'galois_group', 

31 

32 'itermonomials', 'Monomial', 

33 

34 'lex', 'grlex', 'grevlex', 'ilex', 'igrlex', 'igrevlex', 

35 

36 'CRootOf', 'rootof', 'RootOf', 'ComplexRootOf', 'RootSum', 

37 

38 'roots', 

39 

40 'Domain', 'FiniteField', 'IntegerRing', 'RationalField', 'RealField', 

41 'ComplexField', 'PythonFiniteField', 'GMPYFiniteField', 

42 'PythonIntegerRing', 'GMPYIntegerRing', 'PythonRational', 

43 'GMPYRationalField', 'AlgebraicField', 'PolynomialRing', 'FractionField', 

44 'ExpressionDomain', 'FF_python', 'FF_gmpy', 'ZZ_python', 'ZZ_gmpy', 

45 'QQ_python', 'QQ_gmpy', 'GF', 'FF', 'ZZ', 'QQ', 'ZZ_I', 'QQ_I', 'RR', 

46 'CC', 'EX', 'EXRAW', 

47 

48 'construct_domain', 

49 

50 'swinnerton_dyer_poly', 'cyclotomic_poly', 'symmetric_poly', 

51 'random_poly', 'interpolating_poly', 

52 

53 'jacobi_poly', 'chebyshevt_poly', 'chebyshevu_poly', 'hermite_poly', 

54 'hermite_prob_poly', 'legendre_poly', 'laguerre_poly', 

55 

56 'bernoulli_poly', 'bernoulli_c_poly', 'genocchi_poly', 'euler_poly', 

57 'andre_poly', 

58 

59 'apart', 'apart_list', 'assemble_partfrac_list', 

60 

61 'Options', 

62 

63 'ring', 'xring', 'vring', 'sring', 

64 

65 'field', 'xfield', 'vfield', 'sfield' 

66] 

67 

68from .polytools import (Poly, PurePoly, poly_from_expr, 

69 parallel_poly_from_expr, degree, total_degree, degree_list, LC, LM, 

70 LT, pdiv, prem, pquo, pexquo, div, rem, quo, exquo, half_gcdex, gcdex, 

71 invert, subresultants, resultant, discriminant, cofactors, gcd_list, 

72 gcd, lcm_list, lcm, terms_gcd, trunc, monic, content, primitive, 

73 compose, decompose, sturm, gff_list, gff, sqf_norm, sqf_part, 

74 sqf_list, sqf, factor_list, factor, intervals, refine_root, 

75 count_roots, real_roots, nroots, ground_roots, nth_power_roots_poly, 

76 cancel, reduced, groebner, is_zero_dimensional, GroebnerBasis, poly) 

77 

78from .polyfuncs import (symmetrize, horner, interpolate, 

79 rational_interpolate, viete) 

80 

81from .rationaltools import together 

82 

83from .polyerrors import (BasePolynomialError, ExactQuotientFailed, 

84 PolynomialDivisionFailed, OperationNotSupported, HeuristicGCDFailed, 

85 HomomorphismFailed, IsomorphismFailed, ExtraneousFactors, 

86 EvaluationFailed, RefinementFailed, CoercionFailed, NotInvertible, 

87 NotReversible, NotAlgebraic, DomainError, PolynomialError, 

88 UnificationFailed, GeneratorsError, GeneratorsNeeded, 

89 ComputationFailed, UnivariatePolynomialError, 

90 MultivariatePolynomialError, PolificationFailed, OptionError, 

91 FlagError) 

92 

93from .numberfields import (minpoly, minimal_polynomial, primitive_element, 

94 field_isomorphism, to_number_field, isolate, round_two, prime_decomp, 

95 prime_valuation, galois_group) 

96 

97from .monomials import itermonomials, Monomial 

98 

99from .orderings import lex, grlex, grevlex, ilex, igrlex, igrevlex 

100 

101from .rootoftools import CRootOf, rootof, RootOf, ComplexRootOf, RootSum 

102 

103from .polyroots import roots 

104 

105from .domains import (Domain, FiniteField, IntegerRing, RationalField, 

106 RealField, ComplexField, PythonFiniteField, GMPYFiniteField, 

107 PythonIntegerRing, GMPYIntegerRing, PythonRational, GMPYRationalField, 

108 AlgebraicField, PolynomialRing, FractionField, ExpressionDomain, 

109 FF_python, FF_gmpy, ZZ_python, ZZ_gmpy, QQ_python, QQ_gmpy, GF, FF, 

110 ZZ, QQ, ZZ_I, QQ_I, RR, CC, EX, EXRAW) 

111 

112from .constructor import construct_domain 

113 

114from .specialpolys import (swinnerton_dyer_poly, cyclotomic_poly, 

115 symmetric_poly, random_poly, interpolating_poly) 

116 

117from .orthopolys import (jacobi_poly, chebyshevt_poly, chebyshevu_poly, 

118 hermite_poly, hermite_prob_poly, legendre_poly, laguerre_poly) 

119 

120from .appellseqs import (bernoulli_poly, bernoulli_c_poly, genocchi_poly, 

121 euler_poly, andre_poly) 

122 

123from .partfrac import apart, apart_list, assemble_partfrac_list 

124 

125from .polyoptions import Options 

126 

127from .rings import ring, xring, vring, sring 

128 

129from .fields import field, xfield, vfield, sfield