Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
[ 1 0 0 -76/157]
[ 0 1 0 -5/157]
[ 0 0 1 238/157]
[ 0 0 0 0]
sage: a.echelon_form(algorithm=’multimodular’)
[ 1 0 0 -76/157]
[ 0 1 0 -5/157]
[ 0 0 1 238/157]
[ 0 0 0 0]
The result is an immutable matrix, so if you want to modify the result then you need to make a copy. This
checks that Trac #10543 is fixed.
sage: A = matrix(QQ, 2, range(6))
sage: E = A.echelon_form()
sage: E.is_mutable()
False
sage: F = copy(E)
sage: F[0,0] = 50
sage: F
[50 0 -1]
[ 0 1 2]
echelonize(algorithm=’default’, height_guess=None, proof=None, **kwds)
INPUT:
•algorithm
•‘default’ (default): use heuristic choice
•‘padic’: an algorithm based on the IML p-adic solver.
•‘multimodular’: uses a multimodular algorithm the uses linbox modulo many primes.
•‘classical’: just clear each column using Gauss elimination
•height_guess, **kwds - all passed to the multimodular algorithm; ignored by the p-adic algorithm.
•proof - bool or None (default: None, see proof.linear_algebra or sage.structure.proof). Passed to the
multimodular algorithm. Note that the Sage global default is proof=True.
OUTPUT:
•matrix - the reduced row echelon for of self.
EXAMPLES:
sage: a = matrix(QQ, 4, range(16)); a[0,0] = 1/19; a[0,1] = 1/5; a
[1/19 1/5 2 3]
[ 4 5 6 7]
[ 8 9 10 11]
[ 12 13 14 15]
sage: a.echelonize(); a
[ 1 0 0 -76/157]
[ 0 1 0 -5/157]
[ 0 0 1 238/157]
[ 0 0 0 0]
344 Chapter 18. Dense matrices over the rational field