114 lines
3.6 KiB
Python
114 lines
3.6 KiB
Python
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from sympy.abc import x
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from sympy.core.numbers import (I, Rational)
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from sympy.core.singleton import S
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from sympy.functions.elementary.miscellaneous import sqrt
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from sympy.polys import Poly, cyclotomic_poly
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from sympy.polys.domains import FF, QQ
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from sympy.polys.matrices import DomainMatrix, DM
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from sympy.polys.matrices.exceptions import DMRankError
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from sympy.polys.numberfields.utilities import (
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AlgIntPowers, coeff_search, extract_fundamental_discriminant,
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isolate, supplement_a_subspace,
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)
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from sympy.printing.lambdarepr import IntervalPrinter
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from sympy.testing.pytest import raises
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def test_AlgIntPowers_01():
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T = Poly(cyclotomic_poly(5))
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zeta_pow = AlgIntPowers(T)
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raises(ValueError, lambda: zeta_pow[-1])
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for e in range(10):
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a = e % 5
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if a < 4:
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c = zeta_pow[e]
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assert c[a] == 1 and all(c[i] == 0 for i in range(4) if i != a)
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else:
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assert zeta_pow[e] == [-1] * 4
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def test_AlgIntPowers_02():
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T = Poly(x**3 + 2*x**2 + 3*x + 4)
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m = 7
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theta_pow = AlgIntPowers(T, m)
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for e in range(10):
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computed = theta_pow[e]
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coeffs = (Poly(x)**e % T + Poly(x**3)).rep.rep[1:]
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expected = [c % m for c in reversed(coeffs)]
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assert computed == expected
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def test_coeff_search():
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C = []
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search = coeff_search(2, 1)
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for i, c in enumerate(search):
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C.append(c)
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if i == 12:
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break
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assert C == [[1, 1], [1, 0], [1, -1], [0, 1], [2, 2], [2, 1], [2, 0], [2, -1], [2, -2], [1, 2], [1, -2], [0, 2], [3, 3]]
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def test_extract_fundamental_discriminant():
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# To extract, integer must be 0 or 1 mod 4.
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raises(ValueError, lambda: extract_fundamental_discriminant(2))
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raises(ValueError, lambda: extract_fundamental_discriminant(3))
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# Try many cases, of different forms:
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cases = (
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(0, {}, {0: 1}),
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(1, {}, {}),
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(8, {2: 3}, {}),
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(-8, {2: 3, -1: 1}, {}),
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(12, {2: 2, 3: 1}, {}),
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(36, {}, {2: 1, 3: 1}),
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(45, {5: 1}, {3: 1}),
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(48, {2: 2, 3: 1}, {2: 1}),
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(1125, {5: 1}, {3: 1, 5: 1}),
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)
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for a, D_expected, F_expected in cases:
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D, F = extract_fundamental_discriminant(a)
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assert D == D_expected
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assert F == F_expected
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def test_supplement_a_subspace_1():
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M = DM([[1, 7, 0], [2, 3, 4]], QQ).transpose()
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# First supplement over QQ:
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B = supplement_a_subspace(M)
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assert B[:, :2] == M
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assert B[:, 2] == DomainMatrix.eye(3, QQ).to_dense()[:, 0]
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# Now supplement over FF(7):
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M = M.convert_to(FF(7))
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B = supplement_a_subspace(M)
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assert B[:, :2] == M
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# When we work mod 7, first col of M goes to [1, 0, 0],
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# so the supplementary vector cannot equal this, as it did
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# when we worked over QQ. Instead, we get the second std basis vector:
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assert B[:, 2] == DomainMatrix.eye(3, FF(7)).to_dense()[:, 1]
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def test_supplement_a_subspace_2():
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M = DM([[1, 0, 0], [2, 0, 0]], QQ).transpose()
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with raises(DMRankError):
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supplement_a_subspace(M)
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def test_IntervalPrinter():
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ip = IntervalPrinter()
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assert ip.doprint(x**Rational(1, 3)) == "x**(mpi('1/3'))"
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assert ip.doprint(sqrt(x)) == "x**(mpi('1/2'))"
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def test_isolate():
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assert isolate(1) == (1, 1)
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assert isolate(S.Half) == (S.Half, S.Half)
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assert isolate(sqrt(2)) == (1, 2)
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assert isolate(-sqrt(2)) == (-2, -1)
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assert isolate(sqrt(2), eps=Rational(1, 100)) == (Rational(24, 17), Rational(17, 12))
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assert isolate(-sqrt(2), eps=Rational(1, 100)) == (Rational(-17, 12), Rational(-24, 17))
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raises(NotImplementedError, lambda: isolate(I))
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