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AdjointIdeal :: LRdecomposition

LRdecomposition -- LR decomposition

Synopsis

Description

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 = | 3/5 1    9/4 |
     | 3/4 3/10 1/7 |
     | 9/5 9/8  1   |

              3        3
o1 : Matrix QQ  <--- QQ
i2 : (perm,LR)=LRdecomposition(A,j->-j);
i3 : perm

o3 = {2, 0, 1}

o3 : List
i4 : P=transpose (id_(QQ^3))_perm

o4 = | 0 0 1 |
     | 1 0 0 |
     | 0 1 0 |

              3        3
o4 : Matrix QQ  <--- QQ
i5 : R=extractRightUpper(LR)

o5 = | 9/5 9/8 1         |
     | 0   5/8 23/12     |
     | 0   0   2047/8400 |

              3        3
o5 : Matrix QQ  <--- QQ
i6 : L=extractLeftLower(LR)

o6 = | 1    0       0 |
     | 1/3  1       0 |
     | 5/12 -27/100 1 |

              3        3
o6 : Matrix QQ  <--- QQ
i7 : L*R==P*A

o7 = true

See also

Ways to use LRdecomposition :