def test_dmp_ext_factor():
h = [QQ(1), QQ(0), QQ(-2)]
K = QQ.algebraic_field(sqrt(2))
assert dmp_ext_factor([], 0, K) == (ANP([], h, QQ), [])
assert dmp_ext_factor([[]], 1, K) == (ANP([], h, QQ), [])
f = [[ANP([QQ(1)], h, QQ)], [ANP([QQ(1)], h, QQ)]]
assert dmp_ext_factor(f, 1, K) == (ANP([QQ(1)], h, QQ), [(f, 1)])
g = [[ANP([QQ(2)], h, QQ)], [ANP([QQ(2)], h, QQ)]]
assert dmp_ext_factor(g, 1, K) == (ANP([QQ(2)], h, QQ), [(f, 1)])
f = [[ANP([QQ(1)], h, QQ)], [],
[ANP([QQ(-2)], h, QQ),
ANP([], h, QQ), ANP([], h, QQ)]]
assert dmp_ext_factor(f, 1, K) == \
(ANP([QQ(1)], h, QQ), [
([[ANP([QQ(1)], h, QQ)], [ANP([QQ(-1),QQ(0)], h, QQ), ANP([], h, QQ)]], 1),
([[ANP([QQ(1)], h, QQ)], [ANP([QQ( 1),QQ(0)], h, QQ), ANP([], h, QQ)]], 1),
])
f = [[ANP([QQ(2)], h, QQ)], [],
[ANP([QQ(-4)], h, QQ),
ANP([], h, QQ), ANP([], h, QQ)]]
assert dmp_ext_factor(f, 1, K) == \
(ANP([QQ(2)], h, QQ), [
([[ANP([QQ(1)], h, QQ)], [ANP([QQ(-1),QQ(0)], h, QQ), ANP([], h, QQ)]], 1),
([[ANP([QQ(1)], h, QQ)], [ANP([QQ( 1),QQ(0)], h, QQ), ANP([], h, QQ)]], 1),
])
def test_dmp_ext_factor():
h = [QQ(1),QQ(0),QQ(-2)]
K = QQ.algebraic_field(sqrt(2))
assert dmp_ext_factor([], 0, K) == (ANP([], h, QQ), [])
assert dmp_ext_factor([[]], 1, K) == (ANP([], h, QQ), [])
f = [[ANP([QQ(1)], h, QQ)], [ANP([QQ(1)], h, QQ)]]
assert dmp_ext_factor(f, 1, K) == (ANP([QQ(1)], h, QQ), [(f, 1)])
g = [[ANP([QQ(2)], h, QQ)], [ANP([QQ(2)], h, QQ)]]
assert dmp_ext_factor(g, 1, K) == (ANP([QQ(2)], h, QQ), [(f, 1)])
f = [[ANP([QQ(1)], h, QQ)], [], [ANP([QQ(-2)], h, QQ), ANP([], h, QQ), ANP([], h, QQ)]]
assert dmp_ext_factor(f, 1, K) == \
(ANP([QQ(1)], h, QQ), [
([[ANP([QQ(1)], h, QQ)], [ANP([QQ(-1),QQ(0)], h, QQ), ANP([], h, QQ)]], 1),
([[ANP([QQ(1)], h, QQ)], [ANP([QQ( 1),QQ(0)], h, QQ), ANP([], h, QQ)]], 1),
])
f = [[ANP([QQ(2)], h, QQ)], [], [ANP([QQ(-4)], h, QQ), ANP([], h, QQ), ANP([], h, QQ)]]
assert dmp_ext_factor(f, 1, K) == \
(ANP([QQ(2)], h, QQ), [
([[ANP([QQ(1)], h, QQ)], [ANP([QQ(-1),QQ(0)], h, QQ), ANP([], h, QQ)]], 1),
([[ANP([QQ(1)], h, QQ)], [ANP([QQ( 1),QQ(0)], h, QQ), ANP([], h, QQ)]], 1),
])
def test_dup_ext_factor():
h = [QQ(1), QQ(0), QQ(1)]
K = QQ.algebraic_field(I)
assert dup_ext_factor([], K) == (ANP([], h, QQ), [])
f = [ANP([QQ(1)], h, QQ), ANP([QQ(1)], h, QQ)]
assert dup_ext_factor(f, K) == (ANP([QQ(1)], h, QQ), [(f, 1)])
g = [ANP([QQ(2)], h, QQ), ANP([QQ(2)], h, QQ)]
assert dup_ext_factor(g, K) == (ANP([QQ(2)], h, QQ), [(f, 1)])
f = [
ANP([QQ(7)], h, QQ),
ANP([], h, QQ),
ANP([], h, QQ),
ANP([], h, QQ),
ANP([QQ(1, 1)], h, QQ)
]
g = [
ANP([QQ(1)], h, QQ),
ANP([], h, QQ),
ANP([], h, QQ),
ANP([], h, QQ),
ANP([QQ(1, 7)], h, QQ)
]
assert dup_ext_factor(f, K) == (ANP([QQ(7)], h, QQ), [(g, 1)])
f = [
ANP([QQ(1)], h, QQ),
ANP([], h, QQ),
ANP([], h, QQ),
ANP([], h, QQ),
ANP([QQ(1)], h, QQ)
]
assert dup_ext_factor(f, K) == \
(ANP([QQ(1,1)], h, QQ), [
([ANP([QQ(1)], h, QQ), ANP([], h, QQ), ANP([QQ(-1),QQ(0)], h, QQ)], 1),
([ANP([QQ(1)], h, QQ), ANP([], h, QQ), ANP([QQ( 1),QQ(0)], h, QQ)], 1),
])
f = [
ANP([QQ(1)], h, QQ),
ANP([], h, QQ),
ANP([], h, QQ),
ANP([], h, QQ),
ANP([QQ(1)], h, QQ)
]
assert dup_ext_factor(f, K) == \
(ANP([QQ(1,1)], h, QQ), [
([ANP([QQ(1)], h, QQ), ANP([], h, QQ), ANP([QQ(-1),QQ(0)], h, QQ)], 1),
([ANP([QQ(1)], h, QQ), ANP([], h, QQ), ANP([QQ( 1),QQ(0)], h, QQ)], 1),
])
h = [QQ(1), QQ(0), QQ(-2)]
K = QQ.algebraic_field(sqrt(2))
f = [
ANP([QQ(1)], h, QQ),
ANP([], h, QQ),
ANP([], h, QQ),
ANP([], h, QQ),
ANP([QQ(1, 1)], h, QQ)
]
assert dup_ext_factor(f, K) == \
(ANP([QQ(1)], h, QQ), [
([ANP([QQ(1)], h, QQ), ANP([QQ(-1),QQ(0)], h, QQ), ANP([QQ(1)], h, QQ)], 1),
([ANP([QQ(1)], h, QQ), ANP([QQ( 1),QQ(0)], h, QQ), ANP([QQ(1)], h, QQ)], 1),
])
f = [ANP([QQ(1, 1)], h, QQ), ANP([2, 0], h, QQ), ANP([QQ(2, 1)], h, QQ)]
assert dup_ext_factor(f, K) == \
(ANP([QQ(1,1)], h, QQ), [
([ANP([1], h, QQ), ANP([1,0], h, QQ)], 2),
])
assert dup_ext_factor(dup_pow(f, 3, K), K) == \
(ANP([QQ(1,1)], h, QQ), [
([ANP([1], h, QQ), ANP([1,0], h, QQ)], 6),
])
f = dup_mul_ground(f, ANP([QQ(2, 1)], h, QQ), K)
assert dup_ext_factor(f, K) == \
(ANP([QQ(2,1)], h, QQ), [
([ANP([1], h, QQ), ANP([1,0], h, QQ)], 2),
])
assert dup_ext_factor(dup_pow(f, 3, K), K) == \
(ANP([QQ(8,1)], h, QQ), [
([ANP([1], h, QQ), ANP([1,0], h, QQ)], 6),
])
h = [QQ(1, 1), QQ(0, 1), QQ(1, 1)]
K = QQ.algebraic_field(I)
f = [ANP([QQ(4, 1)], h, QQ), ANP([], h, QQ), ANP([QQ(9, 1)], h, QQ)]
assert dup_ext_factor(f, K) == \
(ANP([QQ(4,1)], h, QQ), [
([ANP([QQ(1,1)], h, QQ), ANP([-QQ(3,2), QQ(0,1)], h, QQ)], 1),
([ANP([QQ(1,1)], h, QQ), ANP([ QQ(3,2), QQ(0,1)], h, QQ)], 1),
])
f = [
ANP([QQ(4, 1)], h, QQ),
ANP([QQ(8, 1)], h, QQ),
ANP([QQ(77, 1)], h, QQ),
ANP([QQ(18, 1)], h, QQ),
ANP([QQ(153, 1)], h, QQ)
]
assert dup_ext_factor(f, K) == \
(ANP([QQ(4,1)], h, QQ), [
([ANP([QQ(1,1)], h, QQ), ANP([-QQ(4,1), QQ(1,1)], h, QQ)], 1),
([ANP([QQ(1,1)], h, QQ), ANP([-QQ(3,2), QQ(0,1)], h, QQ)], 1),
([ANP([QQ(1,1)], h, QQ), ANP([ QQ(3,2), QQ(0,1)], h, QQ)], 1),
([ANP([QQ(1,1)], h, QQ), ANP([ QQ(4,1), QQ(1,1)], h, QQ)], 1),
])
"""Tests for classes defining properties of ground domains, e.g. ZZ, QQ, ZZ[x] ... """
from sympy.polys.algebratools import ZZ, QQ, RR, PolynomialRing, FractionField, EX
from sympy.polys.polyerrors import (
UnificationFailed,
GeneratorsNeeded,
DomainError,
)
from sympy import S, sqrt, sin, oo
from sympy.abc import x, y
from sympy.utilities.pytest import raises
ALG = QQ.algebraic_field(sqrt(2) + sqrt(3))
def test_Algebra__unify():
assert ZZ.unify(ZZ) == ZZ
assert QQ.unify(QQ) == QQ
assert ZZ.unify(QQ) == QQ
assert QQ.unify(ZZ) == QQ
assert EX.unify(EX) == EX
assert ZZ.unify(EX) == EX
assert QQ.unify(EX) == EX
assert EX.unify(ZZ) == EX
assert EX.unify(QQ) == EX
def test_dup_ext_factor():
h = [QQ(1),QQ(0),QQ(1)]
K = QQ.algebraic_field(I)
assert dup_ext_factor([], K) == (ANP([], h, QQ), [])
f = [ANP([QQ(1)], h, QQ), ANP([QQ(1)], h, QQ)]
assert dup_ext_factor(f, K) == (ANP([QQ(1)], h, QQ), [(f, 1)])
g = [ANP([QQ(2)], h, QQ), ANP([QQ(2)], h, QQ)]
assert dup_ext_factor(g, K) == (ANP([QQ(2)], h, QQ), [(f, 1)])
f = [ANP([QQ(7)], h, QQ), ANP([], h, QQ), ANP([], h, QQ), ANP([], h, QQ), ANP([QQ(1,1)], h, QQ)]
g = [ANP([QQ(1)], h, QQ), ANP([], h, QQ), ANP([], h, QQ), ANP([], h, QQ), ANP([QQ(1,7)], h, QQ)]
assert dup_ext_factor(f, K) == (ANP([QQ(7)], h, QQ), [(g, 1)])
f = [ANP([QQ(1)], h, QQ), ANP([], h, QQ), ANP([], h, QQ), ANP([], h, QQ), ANP([QQ(1)], h, QQ)]
assert dup_ext_factor(f, K) == \
(ANP([QQ(1,1)], h, QQ), [
([ANP([QQ(1)], h, QQ), ANP([], h, QQ), ANP([QQ(-1),QQ(0)], h, QQ)], 1),
([ANP([QQ(1)], h, QQ), ANP([], h, QQ), ANP([QQ( 1),QQ(0)], h, QQ)], 1),
])
f = [ANP([QQ(1)], h, QQ), ANP([], h, QQ), ANP([], h, QQ), ANP([], h, QQ), ANP([QQ(1)], h, QQ)]
assert dup_ext_factor(f, K) == \
(ANP([QQ(1,1)], h, QQ), [
([ANP([QQ(1)], h, QQ), ANP([], h, QQ), ANP([QQ(-1),QQ(0)], h, QQ)], 1),
([ANP([QQ(1)], h, QQ), ANP([], h, QQ), ANP([QQ( 1),QQ(0)], h, QQ)], 1),
])
h = [QQ(1),QQ(0),QQ(-2)]
K = QQ.algebraic_field(sqrt(2))
f = [ANP([QQ(1)], h, QQ), ANP([], h, QQ), ANP([], h, QQ), ANP([], h, QQ), ANP([QQ(1,1)], h, QQ)]
assert dup_ext_factor(f, K) == \
(ANP([QQ(1)], h, QQ), [
([ANP([QQ(1)], h, QQ), ANP([QQ(-1),QQ(0)], h, QQ), ANP([QQ(1)], h, QQ)], 1),
([ANP([QQ(1)], h, QQ), ANP([QQ( 1),QQ(0)], h, QQ), ANP([QQ(1)], h, QQ)], 1),
])
f = [ANP([QQ(1,1)], h, QQ), ANP([2,0], h, QQ), ANP([QQ(2,1)], h, QQ)]
assert dup_ext_factor(f, K) == \
(ANP([QQ(1,1)], h, QQ), [
([ANP([1], h, QQ), ANP([1,0], h, QQ)], 2),
])
assert dup_ext_factor(dup_pow(f, 3, K), K) == \
(ANP([QQ(1,1)], h, QQ), [
([ANP([1], h, QQ), ANP([1,0], h, QQ)], 6),
])
f = dup_mul_ground(f, ANP([QQ(2,1)], h, QQ), K)
assert dup_ext_factor(f, K) == \
(ANP([QQ(2,1)], h, QQ), [
([ANP([1], h, QQ), ANP([1,0], h, QQ)], 2),
])
assert dup_ext_factor(dup_pow(f, 3, K), K) == \
(ANP([QQ(8,1)], h, QQ), [
([ANP([1], h, QQ), ANP([1,0], h, QQ)], 6),
])
h = [QQ(1,1), QQ(0,1), QQ(1,1)]
K = QQ.algebraic_field(I)
f = [ANP([QQ(4,1)], h, QQ), ANP([], h, QQ), ANP([QQ(9,1)], h, QQ)]
assert dup_ext_factor(f, K) == \
(ANP([QQ(4,1)], h, QQ), [
([ANP([QQ(1,1)], h, QQ), ANP([-QQ(3,2), QQ(0,1)], h, QQ)], 1),
([ANP([QQ(1,1)], h, QQ), ANP([ QQ(3,2), QQ(0,1)], h, QQ)], 1),
])
f = [ANP([QQ(4,1)], h, QQ), ANP([QQ(8,1)], h, QQ), ANP([QQ(77,1)], h, QQ), ANP([QQ(18,1)], h, QQ), ANP([QQ(153,1)], h, QQ)]
assert dup_ext_factor(f, K) == \
(ANP([QQ(4,1)], h, QQ), [
([ANP([QQ(1,1)], h, QQ), ANP([-QQ(4,1), QQ(1,1)], h, QQ)], 1),
([ANP([QQ(1,1)], h, QQ), ANP([-QQ(3,2), QQ(0,1)], h, QQ)], 1),
([ANP([QQ(1,1)], h, QQ), ANP([ QQ(3,2), QQ(0,1)], h, QQ)], 1),
([ANP([QQ(1,1)], h, QQ), ANP([ QQ(4,1), QQ(1,1)], h, QQ)], 1),
])
"""Tests for classes defining properties of ground domains, e.g. ZZ, QQ, ZZ[x] ... """
from sympy.polys.algebratools import ZZ, QQ, RR, PolynomialRing, FractionField, EX
from sympy.polys.polyerrors import (UnificationFailed, GeneratorsNeeded,
DomainError,)
from sympy import S, sqrt, sin, oo
from sympy.abc import x, y
from sympy.utilities.pytest import raises
ALG = QQ.algebraic_field(sqrt(2)+sqrt(3))
def test_Algebra__unify():
assert ZZ.unify(ZZ) == ZZ
assert QQ.unify(QQ) == QQ
assert ZZ.unify(QQ) == QQ
assert QQ.unify(ZZ) == QQ
assert EX.unify(EX) == EX
assert ZZ.unify(EX) == EX
assert QQ.unify(EX) == EX
assert EX.unify(ZZ) == EX
assert EX.unify(QQ) == EX
assert ZZ.poly_ring('x').unify(EX) == EX
assert ZZ.frac_field('x').unify(EX) == EX
assert EX.unify(ZZ.poly_ring('x')) == EX
assert EX.unify(ZZ.frac_field('x')) == EX
