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Mini Shell
Mini Shell
from sympy.testing.pytest import raises
from sympy import Symbol, sympify
from sympy.polys.matrices.normalforms import invariant_factors, smith_normal_form
from sympy.polys.domains import ZZ, QQ
from sympy.polys.matrices import DomainMatrix
def test_smith_normal():
def DM(elems, domain):
conv = lambda e: domain.from_sympy(sympify(e))
elems = [[conv(e) for e in row] for row in elems]
return DomainMatrix(elems, (len(elems), len(elems[0])), domain)
m = DM([[12, 6, 4, 8], [3, 9, 6, 12], [2, 16, 14, 28], [20, 10, 10, 20]], ZZ)
smf = DM([[1, 0, 0, 0], [0, 10, 0, 0], [0, 0, -30, 0], [0, 0, 0, 0]], ZZ)
assert smith_normal_form(m).to_dense() == smf
x = Symbol('x')
m = DM([[x-1, 1, -1],
[ 0, x, -1],
[ 0, -1, x]], QQ[x])
dx = m.domain.gens[0]
assert invariant_factors(m) == (1, dx-1, dx**2-1)
zr = DomainMatrix([], (0, 2), ZZ)
zc = DomainMatrix([[], []], (2, 0), ZZ)
assert smith_normal_form(zr).to_dense() == zr
assert smith_normal_form(zc).to_dense() == zc
assert smith_normal_form(DM([[2, 4]], ZZ)).to_dense() == DM([[2, 0]], ZZ)
assert smith_normal_form(DM([[0, -2]], ZZ)).to_dense() == DM([[-2, 0]], ZZ)
assert smith_normal_form(DM([[0], [-2]], ZZ)).to_dense() == DM([[-2], [0]], ZZ)
m = DM([[3, 0, 0, 0], [0, 0, 0, 0], [0, 0, 2, 0]], ZZ)
snf = DM([[1, 0, 0, 0], [0, 6, 0, 0], [0, 0, 0, 0]], ZZ)
assert smith_normal_form(m).to_dense() == snf
raises(ValueError, lambda: smith_normal_form(DM([[1]], ZZ[x])))
Zerion Mini Shell 1.0