-- -*- M2-comint -*- {* hash: -371636807 *}
i1 : kk = ZZ/101
o1 = kk
o1 : QuotientRing
i2 : A = matrix"1,2,3,4;1,3,6,10;19,7,11,13" ** kk
o2 = | 1 2 3 4 |
| 1 3 6 10 |
| 19 7 11 13 |
3 4
o2 : Matrix kk <--- kk
i3 : (P,L,U) = LUdecomposition A
o3 = ({0, 1, 2}, | 1 0 0 |, | 1 2 3 4 |)
| 1 1 0 | | 0 1 3 6 |
| 19 -31 1 | | 0 0 47 22 |
o3 : Sequence
i4 : Q = id_(kk^3) _ P
o4 = | 1 0 0 |
| 0 1 0 |
| 0 0 1 |
3 3
o4 : Matrix kk <--- kk
i5 : Q * L * U == matrix A
o5 = true
i6 : A = matrix"1,2,3,4,5,6;1,3,6,12,13,16;19,7,11,47,48,21" ** RR
o6 = | 1 2 3 4 5 6 |
| 1 3 6 12 13 16 |
| 19 7 11 47 48 21 |
3 6
o6 : Matrix RR <--- RR
53 53
i7 : (P,L,U) = LUdecomposition A
o7 = ({2, 1, 0}, | 1 0 0 |, | 19 7 11 47 48
| .0526316 1 0 | | 0 2.63158 5.42105 9.52632 10.4737
| .0526316 .62 1 | | 0 0 -.94 -4.38 -4.02
------------------------------------------------------------------------
21 |)
14.8947 |
-4.34 |
o7 : Sequence
i8 : Q = id_ (RR^3) _ P
o8 = | 0 0 1 |
| 0 1 0 |
| 1 0 0 |
3 3
o8 : Matrix RR <--- RR
53 53
i9 : Q * L * U - A
o9 = | 0 -2.22045e-16 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
3 6
o9 : Matrix RR <--- RR
53 53
i10 : clean(1e-15,oo)
o10 = 0
3 6
o10 : Matrix RR <--- RR
53 53
i11 : A = mutableMatrix(CC,5,10, Dense=>true)
o11 = 0
o11 : MutableMatrix
i12 : printingPrecision = 2
o12 = 2
i13 : setRandomSeed 0
o13 = 0
i14 : fillMatrix A
o14 = | .83+.27i .64+.14i .014+.33i .12+.86i .76+.02i .41+.088i .12+.78i .98+.79i .4+.12i .06+.57i |
| .44+.48i .45+.077i .12+.72i .8+.77i .19+.73i .014+.18i .97+.42i .05+.55i .18+.53i 1+.32i |
| .084+.19i .4+.52i .13+.28i .88+.03i .3+.49i .86+.04i .7+.5i .7+.78i .37+.41i .56+.16i |
| .83+.04i .34+.26i .39+.97i .4+.6i .77+.28i .9+.84i .73+.88i .23+.99i .56+.89i .3+i |
| .88+.44i .24+.77i .82+.62i .32+.7i .39+.49i .58+.45i .94+.87i .19+.85i .093+.017i .34+.83i |
o14 : MutableMatrix
i15 : (P,L,U) = LUdecomposition A;
i16 : Q = id_(CC^5) _ P
o16 = | 0 0 0 0 1 |
| 0 1 0 0 0 |
| 0 0 0 1 0 |
| 0 0 1 0 0 |
| 1 0 0 0 0 |
5 5
o16 : Matrix CC <--- CC
53 53
i17 : matrix Q * matrix L * matrix U - matrix A
o17 = | -1.1e-16 0 -2.2e-16+5.6e-17i 0 0
| 0 0 8.3e-17-1.1e-16i 0 0
| -2.8e-17i -1.1e-16i 5.6e-17 0 0
| -1.1e-16-5.6e-17i 5.6e-17+5.6e-17i 0 0 0
| 0 0 0 0 0
-----------------------------------------------------------------------
0 -2.2e-16+1.1e-16i 1.1e-16 0
2.8e-17+5.6e-17i -5.6e-17i 0 0
-1.1e-16+2.8e-17i 1.1e-16i -1.1e-16 -5.6e-17-5.6e-17i
0 -1.1e-16 2.8e-17-1.1e-16i 0
0 0 0 0
-----------------------------------------------------------------------
0 |
1.1e-16-1.1e-16i |
-1.7e-16i |
-1.1e-16i |
0 |
5 10
o17 : Matrix CC <--- CC
53 53
i18 : clean(1e-15,oo)
o18 = 0
5 10
o18 : Matrix CC <--- CC
53 53
i19 :
