You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
81 lines
2.8 KiB
81 lines
2.8 KiB
from sympy.testing.pytest import warns_deprecated_sympy
|
|
|
|
from sympy.core.symbol import Symbol
|
|
from sympy.polys.polytools import Poly
|
|
from sympy.matrices import Matrix
|
|
from sympy.matrices.normalforms import (
|
|
invariant_factors,
|
|
smith_normal_form,
|
|
hermite_normal_form,
|
|
)
|
|
from sympy.polys.domains import ZZ, QQ
|
|
from sympy.core.numbers import Integer
|
|
|
|
|
|
def test_smith_normal():
|
|
m = Matrix([[12,6,4,8],[3,9,6,12],[2,16,14,28],[20,10,10,20]])
|
|
smf = Matrix([[1, 0, 0, 0], [0, 10, 0, 0], [0, 0, -30, 0], [0, 0, 0, 0]])
|
|
assert smith_normal_form(m) == smf
|
|
|
|
x = Symbol('x')
|
|
with warns_deprecated_sympy():
|
|
m = Matrix([[Poly(x-1), Poly(1, x),Poly(-1,x)],
|
|
[0, Poly(x), Poly(-1,x)],
|
|
[Poly(0,x),Poly(-1,x),Poly(x)]])
|
|
invs = 1, x - 1, x**2 - 1
|
|
assert invariant_factors(m, domain=QQ[x]) == invs
|
|
|
|
m = Matrix([[2, 4]])
|
|
smf = Matrix([[2, 0]])
|
|
assert smith_normal_form(m) == smf
|
|
|
|
|
|
def test_smith_normal_deprecated():
|
|
from sympy.polys.solvers import RawMatrix as Matrix
|
|
|
|
with warns_deprecated_sympy():
|
|
m = Matrix([[12, 6, 4,8],[3,9,6,12],[2,16,14,28],[20,10,10,20]])
|
|
setattr(m, 'ring', ZZ)
|
|
with warns_deprecated_sympy():
|
|
smf = Matrix([[1, 0, 0, 0], [0, 10, 0, 0], [0, 0, -30, 0], [0, 0, 0, 0]])
|
|
assert smith_normal_form(m) == smf
|
|
|
|
x = Symbol('x')
|
|
with warns_deprecated_sympy():
|
|
m = Matrix([[Poly(x-1), Poly(1, x),Poly(-1,x)],
|
|
[0, Poly(x), Poly(-1,x)],
|
|
[Poly(0,x),Poly(-1,x),Poly(x)]])
|
|
setattr(m, 'ring', QQ[x])
|
|
invs = (Poly(1, x, domain='QQ'), Poly(x - 1, domain='QQ'), Poly(x**2 - 1, domain='QQ'))
|
|
assert invariant_factors(m) == invs
|
|
|
|
with warns_deprecated_sympy():
|
|
m = Matrix([[2, 4]])
|
|
setattr(m, 'ring', ZZ)
|
|
with warns_deprecated_sympy():
|
|
smf = Matrix([[2, 0]])
|
|
assert smith_normal_form(m) == smf
|
|
|
|
|
|
def test_hermite_normal():
|
|
m = Matrix([[2, 7, 17, 29, 41], [3, 11, 19, 31, 43], [5, 13, 23, 37, 47]])
|
|
hnf = Matrix([[1, 0, 0], [0, 2, 1], [0, 0, 1]])
|
|
assert hermite_normal_form(m) == hnf
|
|
|
|
tr_hnf = Matrix([[37, 0, 19], [222, -6, 113], [48, 0, 25], [0, 2, 1], [0, 0, 1]])
|
|
assert hermite_normal_form(m.transpose()) == tr_hnf
|
|
|
|
m = Matrix([[8, 28, 68, 116, 164], [3, 11, 19, 31, 43], [5, 13, 23, 37, 47]])
|
|
hnf = Matrix([[4, 0, 0], [0, 2, 1], [0, 0, 1]])
|
|
assert hermite_normal_form(m) == hnf
|
|
assert hermite_normal_form(m, D=8) == hnf
|
|
assert hermite_normal_form(m, D=ZZ(8)) == hnf
|
|
assert hermite_normal_form(m, D=Integer(8)) == hnf
|
|
|
|
m = Matrix([[10, 8, 6, 30, 2], [45, 36, 27, 18, 9], [5, 4, 3, 2, 1]])
|
|
hnf = Matrix([[26, 2], [0, 9], [0, 1]])
|
|
assert hermite_normal_form(m) == hnf
|
|
|
|
m = Matrix([[2, 7], [0, 0], [0, 0]])
|
|
hnf = Matrix(3, 0, [])
|
|
assert hermite_normal_form(m) == hnf
|