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 Full MatrixSpace of 2 by 2 dense matrices over Real Field with 53 bits of precision Sometimes it is not possible to coerce into the base ring of self. A solution is to change the base ring of self to a more expansive ring. Here we mix the rationals with a ring of polynomials with rational coefficients. sage: R = PolynomialRing(QQ, ’y’) sage: A = matrix(QQ, 1, 2, [1,2]) sage: B = matrix(R, 1, 2, [’y’, ’y^2’]) sage: C = B.stack(A); C [ y y^2] [ 1 2] sage: C.parent() Full MatrixSpace of 2 by 2 dense matrices over Univariate Polynomial Ring in y over Rational sage: D = A.stack(B) Traceback (most recent call last): ... TypeError: not a constant polynomial sage: E = A.change_ring(R) sage: F = E.stack(B); F [ 1 2] [ y y^2] sage: F.parent() Full MatrixSpace of 2 by 2 dense matrices over Univariate Polynomial Ring in y over Rational TESTS: A legacy test from the original implementation. sage: M = Matrix(QQ, 2, 3, range(6)) sage: N = Matrix(QQ, 1, 3, [10,11,12]) sage: M.stack(N) [ 0 1 2] [ 3 4 5] [10 11 12] AUTHOR: •Rob Beezer (2011-03-19) - rewritten to mirror code for augment() submatrix(row=0, col=0, nrows=-1, ncols=-1) Return the matrix constructed from self using the specified range of rows and columns. INPUT: •row, col - index of the starting row and column. Indices start at zero. •nrows, ncols - (optional) number of rows and columns to take. If not provided, take all rows below and all columns to the right of the starting entry. SEE ALSO: The functions matrix_from_rows(), matrix_from_columns(), and matrix_from_rows_and_columns() allow one to select arbitrary subsets of rows and/or columns. EXAMPLES: Take the 3 × 3 submatrix starting from entry (1,1) in a 4 × 4 matrix: 116 Chapter 6. Base class for matrices, part 1
Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1 sage: m = matrix(4, [1..16]) sage: m.submatrix(1, 1) [ 6 7 8] [10 11 12] [14 15 16] Same thing, except take only two rows: sage: m.submatrix(1, 1, 2) [ 6 7 8] [10 11 12] And now take only one column: sage: m.submatrix(1, 1, 2, 1) [ 6] [10] You can take zero rows or columns if you want: sage: m.submatrix(1, 1, 0) [] sage: parent(m.submatrix(1, 1, 0)) Full MatrixSpace of 0 by 3 dense matrices over Integer Ring 117
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Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

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