@@ -15,22 +15,22 @@ AUTHOR:
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# https://www.gnu.org/licenses/
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# *****************************************************************************
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from sage.matrix.constructor import identity_matrix
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- from sage.rings.polynomial.laurent_polynomial_ring_base import LaurentPolynomialRing_generic
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+
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cdef class Matrix_laurent_mpolynomial_dense(Matrix_generic_dense):
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"""
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Dense matrix over a Laurent multivariate polynomial ring over a field.
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"""
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def laurent_matrix_reduction (self ):
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"""
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- From a matrix `self` of Laurent polynomials, apply elementary operations
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- to obtain a matrix `P ` of polynomials such that the variables do not divide
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- no column and no row.
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+ From a matrix `` self` ` of Laurent polynomials, apply elementary operations
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+ to obtain a matrix ``P` ` of polynomials such that the variables do not divide
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+ any column and any row.
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OUTPUT:
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- Three matrices `L` , `P` , `R` such that ``self` equals `L P R`, where `L` and
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- `R ` are diagonal with monomial entries.
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+ Three matrices ``L`` , ``P`` , ``R`` such that ``self`` equals `` L P R``,
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+ where ``L`` and ``R` ` are diagonal with monomial entries.
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EXAMPLES:
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@@ -56,20 +56,22 @@ cdef class Matrix_laurent_mpolynomial_dense(Matrix_generic_dense):
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res = self .__copy__()
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for j, rw in enumerate (res.rows()):
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for t in R.gens():
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- n = min (mon.degree(t) for a in rw for cf , mon in a)
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+ n = min (mon.degree(t) for a in rw for _ , mon in a)
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res.rescale_row(j, t ** - n)
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mat_l.rescale_col(j, t ** n)
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for j, cl in enumerate (res.columns()):
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for t in R.gens():
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- n = min (mon.degree(t) for a in cl for cf , mon in a)
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+ n = min (mon.degree(t) for a in cl for _ , mon in a)
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res.rescale_col(j, t ** - n)
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mat_r.rescale_row(j, t ** n)
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res = res.change_ring(R.polynomial_ring())
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return mat_l, res, mat_r
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def _fitting_ideal (self , i ):
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r """
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- Return the `i`-th Fitting ideal of the matrix. This is the ideal generated
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+ Return the `i`-th Fitting ideal of the matrix.
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+
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+ This is the ideal generated
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by the `n - i` minors, where `n` is the number of columns.
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INPUT:
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