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randomBlockMatrix -- create a block matrix with zero, identity and random blocks

Synopsis

Description

This function creates a block matrix with the block sizes (and degrees) determined by the modules in tarList and srcList. Each entry in the mats matrix indicates what should be placed at that block of the matrix: mats#r#c corresponds to a matrix with target tarList#r, and source srcList#c.

Each entry can be: random (giving a block which is random), the number 0 (a zero block), the number 1 (an identity block), or an actual matrix.

i1 : S = ZZ/101[a..d]

o1 = S

o1 : PolynomialRing
 
i2 : randomBlockMatrix({S^3, S^1}, {S^3, S^1}, {{random, random}, {0, 1}})

o2 = | 24  -29 -10 -22 |
     | -36 19  -29 -29 |
     | -30 19  -8  -24 |
     | 0   0   0   1   |

             4      4
o2 : Matrix S  <-- S
 
i3 : S = ZZ/101[a..d]

o3 = S

o3 : PolynomialRing
 
i4 : randomBlockMatrix({S^3, S^2}, {S^3, S^2, S^{2:-1}}, {{random, random, 0}, {0, 1, random}})

o4 = | -38 21 -47 -13 -28 0                0                |
     | -16 34 -39 -43 -47 0                0                |
     | 39  19 -18 -15 38  0                0                |
     | 0   0  0   1   0   2a+16b+22c+45d   19a-16b+7c+15d   |
     | 0   0  0   0   1   -34a-48b-47c+47d -23a+39b+43c-17d |

             5      7
o4 : Matrix S  <-- S

See also

Ways to use randomBlockMatrix :

For the programmer

The object randomBlockMatrix is a method function.