U Zʹj@sndZddlmZddlmZddlmZddlmZ m Z m Z dddZdd d Zdd d Z dd dddZ dS)z,Functions returning normal forms of matrices)ZZ)Poly) DomainMatrix)smith_normal_forminvariant_factorshermite_normal_formNcCsBt|dd}|dd}t|}|p*|}|dk r>||}|S)zConvert Matrix to DomainMatrixringNcSst|tr|S|SN) isinstancerZas_expr)er Y/var/www/html/bwave/python/venv/lib/python3.8/site-packages/sympy/matrices/normalforms.pyz_to_domain..)getattrZ applyfuncrZ from_MatrixZ convert_to)mdomainrdMr r r _to_domain s   rcCst||}t|S)a 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]]) )r_snf to_Matrix)rrrr r r rs rcsft||t}tfdd|D}t|drb|jjrb|jfddtfdd|D}|S)a9 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] https://web.archive.org/web/20200331143852/https://sierra.nmsu.edu/morandi/notes/SmithNormalForm.pdf c3s|]}j|VqdSr )rZto_sympy.0f)rr r <sz$invariant_factors..rcst|jjdS)N)r)rsymbolsr)r)Kr r rArz#invariant_factors..c3s|]}|VqdSr r r)to_polyr r rBs)r_invftuplehasattrrZis_PolynomialRing)rrZfactorsr )rrrr r.s   rFD check_rankcCs2|dk rt|stt|}t|j||dS)a Compute the Hermite Normal Form of a Matrix *A* of integers. Examples ======== >>> from sympy import Matrix >>> from sympy.matrices.normalforms import hermite_normal_form >>> m = Matrix([[12, 6, 4], [3, 9, 6], [2, 16, 14]]) >>> print(hermite_normal_form(m)) Matrix([[10, 0, 2], [0, 15, 3], [0, 0, 2]]) Parameters ========== A : $m \times n$ ``Matrix`` of integers. D : int, optional Let $W$ be the HNF of *A*. If known in advance, a positive integer *D* being any multiple of $\det(W)$ may be provided. In this case, if *A* also has rank $m$, then we may use an alternative algorithm that works mod *D* in order to prevent coefficient explosion. check_rank : boolean, optional (default=False) The basic assumption is that, if you pass a value for *D*, then you already believe that *A* has rank $m$, so we do not waste time checking it for you. If you do want this to be checked (and the ordinary, non-modulo *D* algorithm to be used if the check fails), then set *check_rank* to ``True``. Returns ======= ``Matrix`` The HNF of matrix *A*. Raises ====== DMDomainError If the domain of the matrix is not :ref:`ZZ`. DMShapeError If the mod *D* algorithm is used but the matrix has more rows than columns. References ========== .. [1] Cohen, H. *A Course in Computational Algebraic Number Theory.* (See Algorithms 2.4.5 and 2.4.8.) Nr!)rZof_typeint_hnfZ_repr)Ar"r#r r r rFs7 r)N)N)N)__doc__Zsympy.polys.domains.integerringrZsympy.polys.polytoolsrZsympy.polys.matricesrZ sympy.polys.matrices.normalformsrrrrrr%rr r r r s