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 ValueError: cannot add a multiple of a row to itself If the ring is not specified, and a scale parameter is given, the base ring for the matrix is chosen to contain the scale parameter. Otherwise, if no ring is given, the default is the integers. sage: E = elementary_matrix(4, row1=1, row2=3) sage: E.parent() Full MatrixSpace of 4 by 4 dense matrices over Integer Ring sage: E = elementary_matrix(4, row1=1, scale=4/3) sage: E.parent() Full MatrixSpace of 4 by 4 dense matrices over Rational Field sage: E = elementary_matrix(4, row1=1, scale=I) sage: E.parent() Full MatrixSpace of 4 by 4 dense matrices over Symbolic Ring sage: E = elementary_matrix(4, row1=1, scale=CDF(I)) sage: E.parent() Full MatrixSpace of 4 by 4 dense matrices over Complex Double Field sage: E = elementary_matrix(4, row1=1, scale=QQbar(I)) sage: E.parent() Full MatrixSpace of 4 by 4 dense matrices over Algebraic Field Returned matrices have a dense implementation by default, but a sparse implementation may be requested. sage: E = elementary_matrix(4, row1=0, row2=1) sage: E.is_dense() True sage: E = elementary_matrix(4, row1=0, row2=1, sparse=True) sage: E.is_sparse() True And the ridiculously small cases. The zero-row matrix cannot be built since then there are no rows to manipulate. sage: elementary_matrix(QQ, 1, row1=0, row2=0) [1] sage: elementary_matrix(QQ, 0, row1=0, row2=0) Traceback (most recent call last): ... ValueError: size of elementary matrix must be 1 or greater, not 0 TESTS: sage: E = elementary_matrix(’junk’, 5, row1=3, row2=1, scale=12) Traceback (most recent call last): ... TypeError: optional first parameter must be a ring, not junk sage: E = elementary_matrix(5, row1=3, scale=’junk’) Traceback (most recent call last): ... TypeError: scale must be an element of some ring, not junk sage: E = elementary_matrix(ZZ, 5, row1=3, col2=3, scale=12) Traceback (most recent call last): ... 34 Chapter 2. Matrix Constructor
Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1 ValueError: received an unexpected keyword: col2=3 sage: E = elementary_matrix(QQ, row1=3, scale=12) Traceback (most recent call last): ... ValueError: size of elementary matrix must be given sage: E = elementary_matrix(ZZ, 4/3, row1=3, row2=1, scale=12) Traceback (most recent call last): ... TypeError: size of elementary matrix must be an integer, not 4/3 sage: E = elementary_matrix(ZZ, -3, row1=3, row2=1, scale=12) Traceback (most recent call last): ... ValueError: size of elementary matrix must be 1 or greater, not -3 sage: E = elementary_matrix(ZZ, 5, row2=1, scale=12) Traceback (most recent call last): ... ValueError: row1 or col1 must be specified sage: E = elementary_matrix(ZZ, 5, row1=3, col1=3, scale=12) Traceback (most recent call last): ... ValueError: cannot specify both row1 and col1 sage: E = elementary_matrix(ZZ, 5, row1=4/3, row2=1, scale=12) Traceback (most recent call last): ... TypeError: row of elementary matrix must be an integer, not 4/3 sage: E = elementary_matrix(ZZ, 5, col1=5, col2=1, scale=12) Traceback (most recent call last): ... ValueError: column of elementary matrix must be positive and smaller than 5, not 5 sage: E = elementary_matrix(ZZ, 5, col1=3, col2=4/3, scale=12) Traceback (most recent call last): ... TypeError: column of elementary matrix must be an integer, not 4/3 sage: E = elementary_matrix(ZZ, 5, row1=3, row2=-1, scale=12) Traceback (most recent call last): ... ValueError: row of elementary matrix must be positive and smaller than 5, not -1 sage: E = elementary_matrix(ZZ, 5, row1=3, row2=1, scale=4/3) Traceback (most recent call last): ... TypeError: scale parameter of elementary matrix must an element of Integer Ring, not 4/3 sage: E = elementary_matrix(ZZ, 5, row1=3) Traceback (most recent call last): ... ValueError: insufficient parameters provided to construct elementary matrix sage: E = elementary_matrix(ZZ, 5, row1=3, row2=3, scale=12) 35
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