91 lines
3.1 KiB
Python
91 lines
3.1 KiB
Python
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"""
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Tests for the sympy.polys.matrices.eigen module
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"""
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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.matrices.dense import Matrix
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from sympy.polys.agca.extensions import FiniteExtension
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from sympy.polys.domains import QQ
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from sympy.polys.polytools import Poly
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from sympy.polys.rootoftools import CRootOf
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from sympy.polys.matrices.domainmatrix import DomainMatrix
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from sympy.polys.matrices.eigen import dom_eigenvects, dom_eigenvects_to_sympy
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def test_dom_eigenvects_rational():
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# Rational eigenvalues
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A = DomainMatrix([[QQ(1), QQ(2)], [QQ(1), QQ(2)]], (2, 2), QQ)
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rational_eigenvects = [
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(QQ, QQ(3), 1, DomainMatrix([[QQ(1), QQ(1)]], (1, 2), QQ)),
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(QQ, QQ(0), 1, DomainMatrix([[QQ(-2), QQ(1)]], (1, 2), QQ)),
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]
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assert dom_eigenvects(A) == (rational_eigenvects, [])
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# Test converting to Expr:
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sympy_eigenvects = [
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(S(3), 1, [Matrix([1, 1])]),
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(S(0), 1, [Matrix([-2, 1])]),
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]
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assert dom_eigenvects_to_sympy(rational_eigenvects, [], Matrix) == sympy_eigenvects
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def test_dom_eigenvects_algebraic():
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# Algebraic eigenvalues
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A = DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ)
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Avects = dom_eigenvects(A)
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# Extract the dummy to build the expected result:
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lamda = Avects[1][0][1].gens[0]
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irreducible = Poly(lamda**2 - 5*lamda - 2, lamda, domain=QQ)
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K = FiniteExtension(irreducible)
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KK = K.from_sympy
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algebraic_eigenvects = [
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(K, irreducible, 1, DomainMatrix([[KK((lamda-4)/3), KK(1)]], (1, 2), K)),
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]
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assert Avects == ([], algebraic_eigenvects)
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# Test converting to Expr:
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sympy_eigenvects = [
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(S(5)/2 - sqrt(33)/2, 1, [Matrix([[-sqrt(33)/6 - S(1)/2], [1]])]),
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(S(5)/2 + sqrt(33)/2, 1, [Matrix([[-S(1)/2 + sqrt(33)/6], [1]])]),
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]
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assert dom_eigenvects_to_sympy([], algebraic_eigenvects, Matrix) == sympy_eigenvects
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def test_dom_eigenvects_rootof():
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# Algebraic eigenvalues
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A = DomainMatrix([
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[0, 0, 0, 0, -1],
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[1, 0, 0, 0, 1],
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[0, 1, 0, 0, 0],
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[0, 0, 1, 0, 0],
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[0, 0, 0, 1, 0]], (5, 5), QQ)
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Avects = dom_eigenvects(A)
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# Extract the dummy to build the expected result:
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lamda = Avects[1][0][1].gens[0]
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irreducible = Poly(lamda**5 - lamda + 1, lamda, domain=QQ)
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K = FiniteExtension(irreducible)
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KK = K.from_sympy
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algebraic_eigenvects = [
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(K, irreducible, 1,
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DomainMatrix([
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[KK(lamda**4-1), KK(lamda**3), KK(lamda**2), KK(lamda), KK(1)]
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], (1, 5), K)),
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]
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assert Avects == ([], algebraic_eigenvects)
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# Test converting to Expr (slow):
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l0, l1, l2, l3, l4 = [CRootOf(lamda**5 - lamda + 1, i) for i in range(5)]
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sympy_eigenvects = [
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(l0, 1, [Matrix([-1 + l0**4, l0**3, l0**2, l0, 1])]),
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(l1, 1, [Matrix([-1 + l1**4, l1**3, l1**2, l1, 1])]),
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(l2, 1, [Matrix([-1 + l2**4, l2**3, l2**2, l2, 1])]),
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(l3, 1, [Matrix([-1 + l3**4, l3**3, l3**2, l3, 1])]),
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(l4, 1, [Matrix([-1 + l4**4, l4**3, l4**2, l4, 1])]),
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]
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assert dom_eigenvects_to_sympy([], algebraic_eigenvects, Matrix) == sympy_eigenvects
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