Solves the system R*x=b via backward substitution.
i1 : A=random(QQ^3,QQ^3)
o1 = | 1/7 3 2 |
| 3/4 5/3 4 |
| 2 3/7 1 |
3 3
o1 : Matrix QQ <--- QQ
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i2 : (perm,LR)=LRdecomposition(A,j->-j);
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i3 : LR
o3 = | 2 3/7 1 |
| 1/14 291/98 27/14 |
| 3/8 1771/3492 1027/388 |
3 3
o3 : Matrix QQ <--- QQ
|
i4 : P=transpose (id_(QQ^3))_perm
o4 = | 0 0 1 |
| 1 0 0 |
| 0 1 0 |
3 3
o4 : Matrix QQ <--- QQ
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i5 : R=extractRightUpper(LR)
o5 = | 2 3/7 1 |
| 0 291/98 27/14 |
| 0 0 1027/388 |
3 3
o5 : Matrix QQ <--- QQ
|
i6 : L=extractLeftLower(LR)
o6 = | 1 0 0 |
| 1/14 1 0 |
| 3/8 1771/3492 1 |
3 3
o6 : Matrix QQ <--- QQ
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i7 : L*R==P*A
o7 = true
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i8 : b=random(QQ^3,QQ^1);
3 1
o8 : Matrix QQ <--- QQ
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i9 : y=forwardSubstitution(LR,P*b)
o9 = | 9/2 |
| 5/28 |
| -971/3492 |
3 1
o9 : Matrix QQ <--- QQ
|
i10 : x=backwardSubstitution(LR,y)
o10 = | 21028/9243 |
| 791/6162 |
| -971/9243 |
3 1
o10 : Matrix QQ <--- QQ
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i11 : inverse(A)*b==x
o11 = true
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