i1 : R = QQ[x,y];
|
i2 : F = R^{1,2,3}
3
o2 = R
o2 : R-module, free, degrees {-1, -2, -3}
|
i3 : G = R^{10,20,30}
3
o3 = R
o3 : R-module, free, degrees {-10, -20, -30}
|
i4 : f = flip(F,G)
o4 = {-11} | 1 0 0 0 0 0 0 0 0 |
{-12} | 0 0 0 1 0 0 0 0 0 |
{-13} | 0 0 0 0 0 0 1 0 0 |
{-21} | 0 1 0 0 0 0 0 0 0 |
{-22} | 0 0 0 0 1 0 0 0 0 |
{-23} | 0 0 0 0 0 0 0 1 0 |
{-31} | 0 0 1 0 0 0 0 0 0 |
{-32} | 0 0 0 0 0 1 0 0 0 |
{-33} | 0 0 0 0 0 0 0 0 1 |
9 9
o4 : Matrix R <-- R
|
i5 : isHomogeneous f
o5 = true
|
i6 : target f
9
o6 = R
o6 : R-module, free, degrees {-11, -12, -13, -21, -22, -23, -31, -32, -33}
|
i7 : source f
9
o7 = R
o7 : R-module, free, degrees {-11, -21, -31, -12, -22, -32, -13, -23, -33}
|
i8 : target f === G**F
o8 = true
|
i9 : source f === F**G
o9 = true
|
i10 : u = x * F_0
o10 = | x |
| 0 |
| 0 |
3
o10 : R
|
i11 : v = y * G_1
o11 = | 0 |
| y |
| 0 |
3
o11 : R
|
i12 : u ** v
o12 = | 0 |
| xy |
| 0 |
| 0 |
| 0 |
| 0 |
| 0 |
| 0 |
| 0 |
9
o12 : R
|
i13 : v ** u
o13 = | 0 |
| 0 |
| 0 |
| xy |
| 0 |
| 0 |
| 0 |
| 0 |
| 0 |
9
o13 : R
|
i14 : f * (u ** v)
o14 = | 0 |
| 0 |
| 0 |
| xy |
| 0 |
| 0 |
| 0 |
| 0 |
| 0 |
9
o14 : R
|
i15 : f * (u ** v) === v ** u
o15 = true
|