Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

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Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1 ... [ 0, 0,a^3, 0], ... [a^2 +4 , 0, 0,a + 2]]) sage: A.zigzag_form(subdivide=False) [ 0 a^3 + 2*a^2 + 2*a + 2 0 0] [ 1 2*a + 2 0 0] [ 0 0 a^3 0] [ 0 0 0 a^2 + 1] TESTS: sage: A = matrix(QQ, 2, 3, range(6)) sage: A.zigzag_form() Traceback (most recent call last): ... TypeError: matrix must be square, not 2 x 3 sage: A = matrix(Integers(6), 2, 2, range(4)) sage: A.zigzag_form() Traceback (most recent call last): ... TypeError: matrix entries must come from an exact field, not Ring of integers modulo 6 sage: A = matrix(RDF, 2, 2, range(4)) sage: A.zigzag_form() Traceback (most recent call last): ... TypeError: matrix entries must come from an exact field, not Real Double Field sage: A = matrix(QQ, 2, range(4)) sage: A.zigzag_form(transformation=’junk’) Traceback (most recent call last): ... ValueError: ’transformation’ keyword must be True or False, not junk sage: A = matrix(QQ, 2, range(4)) sage: A.zigzag_form(subdivide=’garbage’) Traceback (most recent call last): ... ValueError: ’subdivide’ keyword must be True or False, not garbage Citations AUTHOR: •Rob Beezer (2011-06-09) sage.matrix.matrix2.cmp_pivots(x, y) Compare two sequences of pivot columns. •If x is shorter than y, return -1, i.e., x < y, “not as good”. •If x is longer than y, x > y, “better”. •If the length is the same then x is better, i.e., x > y if the entries of x are correspondingly >= those of y with one being greater. sage.matrix.matrix2.decomp_seq(v) This function is used internally be the decomposition matrix method. It takes a list of tuples and produces a sequence that is correctly sorted and prints with carriage returns. 268 Chapter 7. Base class for matrices, part 2
Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1 EXAMPLES: sage: from sage.matrix.matrix2 import decomp_seq sage: V = [(QQ^3, 2), (QQ^2, 1)] sage: decomp_seq(V) [ (Vector space of dimension 2 over Rational Field, 1), (Vector space of dimension 3 over Rational Field, 2) ] 269
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Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

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