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 [||13||17 19 23 29] [++--++-----------] [++--++-----------] [||31||37 41 43 47] [++--++-----------] [||53||59 61 67 71] [||73||79 83 89 97] sage: M.subdivision(0,0) [] sage: M.subdivision(2,4) [37 41 43 47] AUTHORS: •Robert Bradshaw (2007-06-14) subdivision(i, j) Returns an immutable copy of the (i,j)th submatrix of self, according to a previously set subdivision. Before a subdivision is set, the only valid arguments are (0,0) which returns self. EXAMPLE: sage: M = matrix(3, 4, range(12)) sage: M.subdivide(1,2); M [ 0 1| 2 3] [-----+-----] [ 4 5| 6 7] [ 8 9|10 11] sage: M.subdivision(0,0) [0 1] sage: M.subdivision(0,1) [2 3] sage: M.subdivision(1,0) [4 5] [8 9] It handles size-zero subdivisions as well. sage: M = matrix(3, 4, range(12)) sage: M.subdivide([0],[0,2,2,4]); M [+-----++-----+] [| 0 1|| 2 3|] [| 4 5|| 6 7|] [| 8 9||10 11|] sage: M.subdivision(0,0) [] sage: M.subdivision(1,1) [0 1] [4 5] [8 9] sage: M.subdivision(1,2) [] sage: M.subdivision(1,0) [] sage: M.subdivision(0,1) [] subdivision_entry(i, j, x, y) Returns the x,y entry of the i,j submatrix of self. 258 Chapter 7. Base class for matrices, part 2
Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1 EXAMPLES: sage: M = matrix(5, 5, range(25)) sage: M.subdivide(3,3); M [ 0 1 2| 3 4] [ 5 6 7| 8 9] [10 11 12|13 14] [--------+-----] [15 16 17|18 19] [20 21 22|23 24] sage: M.subdivision_entry(0,0,1,2) 7 sage: M.subdivision(0,0)[1,2] 7 sage: M.subdivision_entry(0,1,0,0) 3 sage: M.subdivision_entry(1,0,0,0) 15 sage: M.subdivision_entry(1,1,1,1) 24 Even though this entry exists in the matrix, the index is invalid for the submatrix. sage: M.subdivision_entry(0,0,4,0) Traceback (most recent call last): ... IndexError: Submatrix 0,0 has no entry 4,0 subdivisions() Returns the current subdivision of self. EXAMPLES: sage: M = matrix(5, 5, range(25)) sage: M.subdivisions() ([], []) sage: M.subdivide(2,3) sage: M.subdivisions() ([2], [3]) sage: N = M.parent()(1) sage: N.subdivide(M.subdivisions()); N [1 0 0|0 0] [0 1 0|0 0] [-----+---] [0 0 1|0 0] [0 0 0|1 0] [0 0 0|0 1] subs(in_dict=None, **kwds) EXAMPLES: sage: var(’a,b,d,e’) (a, b, d, e) sage: m = matrix([[a,b], [d,e]]) sage: m.substitute(a=1) [1 b] [d e] sage: m.subs(a=b, b=d) [b d] [d e] 259
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