Current File : //proc/self/root/lib/python3/dist-packages/sympy/matrices/normalforms.py
'''Functions returning normal forms of matrices'''
from sympy.polys.polytools import Poly
from sympy.polys.matrices import DomainMatrix
from sympy.polys.matrices.normalforms import (
smith_normal_form as _snf,
invariant_factors as _invf,
)
def _to_domain(m, domain=None):
"""Convert Matrix to DomainMatrix"""
# XXX: deprecated support for RawMatrix:
ring = getattr(m, "ring", None)
m = m.applyfunc(lambda e: e.as_expr() if isinstance(e, Poly) else e)
dM = DomainMatrix.from_Matrix(m)
domain = domain or ring
if domain is not None:
dM = dM.convert_to(domain)
return dM
def smith_normal_form(m, domain=None):
'''
Return the Smith Normal Form of a matrix `m` over the ring `domain`.
This will only work if the ring is a principal ideal domain.
Examples
========
>>> from sympy import Matrix, ZZ
>>> from sympy.matrices.normalforms import smith_normal_form
>>> m = Matrix([[12, 6, 4], [3, 9, 6], [2, 16, 14]])
>>> print(smith_normal_form(m, domain=ZZ))
Matrix([[1, 0, 0], [0, 10, 0], [0, 0, -30]])
'''
dM = _to_domain(m, domain)
return _snf(dM).to_Matrix()
def invariant_factors(m, domain=None):
'''
Return the tuple of abelian invariants for a matrix `m`
(as in the Smith-Normal form)
References
==========
[1] https://en.wikipedia.org/wiki/Smith_normal_form#Algorithm
[2] http://sierra.nmsu.edu/morandi/notes/SmithNormalForm.pdf
'''
dM = _to_domain(m, domain)
factors = _invf(dM)
factors = tuple(dM.domain.to_sympy(f) for f in factors)
# XXX: deprecated.
if hasattr(m, "ring"):
if m.ring.is_PolynomialRing:
K = m.ring
to_poly = lambda f: Poly(f, K.symbols, domain=K.domain)
factors = tuple(to_poly(f) for f in factors)
return factors
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