Does the PA=LR decomposition on the matrix A, pivoting by the minimal value of pivotfunction. L can be extracted by the function extractLeftLower, R by extractRightUpper. This has been implemented with fields of rational functions in mind.
i1 : A=random(QQ^3,QQ^3)
o1 = | 9/2 1/2 3/2 |
| 1/2 1 3/4 |
| 9/4 3/4 7/4 |
3 3
o1 : Matrix QQ <--- QQ
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i2 : (perm,LR)=LRdecomposition(A,j->-j);
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i3 : perm
o3 = {0, 1, 2}
o3 : List
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i4 : P=transpose (id_(QQ^3))_perm
o4 = | 1 0 0 |
| 0 1 0 |
| 0 0 1 |
3 3
o4 : Matrix QQ <--- QQ
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i5 : R=extractRightUpper(LR)
o5 = | 9/2 1/2 3/2 |
| 0 17/18 7/12 |
| 0 0 47/68 |
3 3
o5 : Matrix QQ <--- QQ
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i6 : L=extractLeftLower(LR)
o6 = | 1 0 0 |
| 1/9 1 0 |
| 1/2 9/17 1 |
3 3
o6 : Matrix QQ <--- QQ
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i7 : L*R==P*A
o7 = true
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