-- -*- M2-comint -*- {* hash: -1939917111 *}
i1 : R = QQ[a,b,c];
i2 : f = pureFree({0,2,3,6}, R)
o2 = | 12a2 0 0 6ab 0 0 6ac 0 0 2b2 0 0 2bc 0 0
| 0 12a2 0 0 6ab 0 0 6ac 0 0 2b2 0 0 2bc 0
| 0 0 12a2 0 0 6ab 0 0 6ac 0 0 2b2 0 0 2bc
| 0 0 0 0 6a2 0 -12a2 0 0 0 8ab 0 -8ab 4ac 0
| 0 0 0 0 0 6a2 0 -3a2 0 0 0 8ab 0 -2ab 4ac
| 0 0 0 0 0 0 0 0 0 0 0 2a2 0 -a2 0
------------------------------------------------------------------------
2c2 0 0 0 0 0 0 0 0 0 0 0 |
0 2c2 0 0 0 0 0 0 0 0 0 0 |
0 0 2c2 0 0 0 0 0 0 0 0 0 |
-16ac 0 0 6b2 0 4bc 0 2c2 0 0 0 0 |
0 -4ac 0 0 6b2 -b2 4bc -2bc 2c2 0 0 0 |
2a2 0 0 0 6ab -2ab 2ac -2ac 0 12b2 6bc 2c2 |
6 27
o2 : Matrix R <--- R
i3 : betti res coker f
0 1 2 3
o3 = total: 6 27 24 3
0: 6 . . .
1: . 27 24 .
2: . . . .
3: . . . 3
o3 : BettiTally
i4 : schurRing(s,3)
o4 = schurRing (s, 3)
o4 : SchurRing
i5 : dim s_{2,2}
o5 = 6
i6 : dim s_{4,2}
o6 = 27
i7 : dim s_{4,3}
o7 = 24
i8 : dim s_{4,3,3}
o8 = 3
i9 : schurRank(3, {2,2})
o9 = 6
i10 : schurRank(3, {4,2})
o10 = 27
i11 : schurRank(3, {4,3})
o11 = 24
i12 : schurRank(3, {4,3,3})
o12 = 3
i13 : f1 = pieri({4,2,0},{1,1}, R)
o13 = | 12a2 0 0 6ab 0 0 6ac 0 0 2b2 0 0 2bc 0 0
| 0 12a2 0 0 6ab 0 0 6ac 0 0 2b2 0 0 2bc 0
| 0 0 12a2 0 0 6ab 0 0 6ac 0 0 2b2 0 0 2bc
| 0 0 0 0 6a2 0 -12a2 0 0 0 8ab 0 -8ab 4ac 0
| 0 0 0 0 0 6a2 0 -3a2 0 0 0 8ab 0 -2ab 4ac
| 0 0 0 0 0 0 0 0 0 0 0 2a2 0 -a2 0
-----------------------------------------------------------------------
2c2 0 0 0 0 0 0 0 0 0 0 0 |
0 2c2 0 0 0 0 0 0 0 0 0 0 |
0 0 2c2 0 0 0 0 0 0 0 0 0 |
-16ac 0 0 6b2 0 4bc 0 2c2 0 0 0 0 |
0 -4ac 0 0 6b2 -b2 4bc -2bc 2c2 0 0 0 |
2a2 0 0 0 6ab -2ab 2ac -2ac 0 12b2 6bc 2c2 |
6 27
o13 : Matrix R <--- R
i14 : f2 = pieri({4,3,0},{2}, R)
o14 = | 3b c 0 0 0 0 0 0 0 0 0 0 0
| 0 2b 2c 0 0 0 0 0 0 0 0 0 0
| 0 0 b 3c 0 0 0 0 0 0 0 0 0
| -6a 0 0 0 3/2b c 0 0 -3/2c 0 0 0 0
| 0 -4a 0 0 0 b 2c 0 0 -c 0 0 0
| 0 0 -2a 0 0 0 1/2b 3c 0 0 -1/2c 0 0
| 0 -2a 0 0 0 -1/2b 0 0 3b 1/2c 0 0 0
| 0 0 -4a 0 0 0 -b 0 0 2b c 0 0
| 0 0 0 -6a 0 0 0 -3/2b 0 0 b 3/2c 0
| 0 0 0 0 -9/2a 0 0 0 0 0 0 0 c
| 0 0 0 0 0 -3a 0 0 0 0 0 0 0
| 0 0 0 0 0 0 -3/2a 0 0 0 0 0 0
| 0 0 0 0 0 -3/2a 0 0 -9/2a 0 0 0 -b
| 0 0 0 0 0 0 -3a 0 0 -3a 0 0 0
| 0 0 0 0 0 0 0 -9/2a 0 0 -3/2a 0 0
| 0 0 0 0 0 0 0 0 0 -3/2a 0 0 0
| 0 0 0 0 0 0 0 0 0 0 -3a 0 0
| 0 0 0 0 0 0 0 0 0 0 0 -9/2a 0
| 0 0 0 0 0 0 0 0 0 0 0 0 -4/3a
| 0 0 0 0 0 0 0 0 0 0 0 0 0
| 0 0 0 0 0 0 0 0 0 0 0 0 0
| 0 0 0 0 0 0 0 0 0 0 0 0 0
| 0 0 0 0 0 0 0 0 0 0 0 0 0
| 0 0 0 0 0 0 0 0 0 0 0 0 0
| 0 0 0 0 0 0 0 0 0 0 0 0 0
| 0 0 0 0 0 0 0 0 0 0 0 0 0
| 0 0 0 0 0 0 0 0 0 0 0 0 0
-----------------------------------------------------------------------
0 0 0 0 0 0 0 0 0 0 0 |
0 0 0 0 0 0 0 0 0 0 0 |
0 0 0 0 0 0 0 0 0 0 0 |
0 0 0 0 0 0 0 0 0 0 0 |
0 0 0 0 0 0 0 0 0 0 0 |
0 0 0 0 0 0 0 0 0 0 0 |
0 0 0 0 0 0 0 0 0 0 0 |
0 0 0 0 0 0 0 0 0 0 0 |
0 0 0 0 0 0 0 0 0 0 0 |
0 0 0 0 0 0 0 0 0 0 0 |
2c 0 -c 0 0 0 0 0 0 0 0 |
0 3c 0 -1/2c 0 0 0 0 0 0 0 |
0 0 1/2c 0 0 0 0 0 0 0 0 |
-2b 0 b c 0 0 0 0 0 0 0 |
0 -3b 0 1/2b 3/2c 0 0 0 0 0 0 |
0 0 -1/2b 0 0 0 0 0 0 0 0 |
0 0 0 -b 0 0 0 0 0 0 0 |
0 0 0 0 -3/2b 0 0 0 0 0 0 |
0 0 0 0 0 2c 0 0 0 0 0 |
-a 0 1/3a 0 0 -1/2b 3c -1/2c 0 0 0 |
-2a 0 0 0 0 -3b 0 c 0 0 0 |
0 -3a 0 -a 0 0 -9/2b 0 3/2c 0 0 |
0 0 0 -2a 0 0 0 -2b 0 0 0 |
0 0 0 0 -3a 0 0 0 -3b 0 0 |
0 0 0 0 0 -1/4a 0 0 0 3c 0 |
0 0 0 0 0 0 -3/2a 1/6a 0 -6b 3/2c |
0 0 0 0 0 0 0 0 -3/2a 0 -9/2b |
27 24
o14 : Matrix R <--- R
i15 : f3 = pieri({4,3,3},{3,3,3}, R)
o15 = | 6c3 0 0 |
| -18bc2 0 0 |
| 18b2c 0 0 |
| -6b3 0 0 |
| 0 6c3 0 |
| 72/5ac2 -72/5bc2 18/5c3 |
| -144/5abc 54/5b2c -36/5bc2 |
| 72/5ab2 -12/5b3 18/5b2c |
| -72/5ac2 -18/5bc2 12/5c3 |
| 144/5abc 36/5b2c -54/5bc2 |
| -72/5ab2 -18/5b3 72/5b2c |
| 0 0 -6b3 |
| 0 27ac2 0 |
| -108/5a2c -162/5abc 108/5ac2 |
| -36/5a2b 36/5ab2 -54/5abc |
| -432/5a2c -108/5abc 162/5ac2 |
| 216/5a2b 54/5ab2 -216/5abc |
| 0 0 18ab2 |
| 0 18a2c 0 |
| -24/5a3 -36/5a2b 54/5a2c |
| -216/5a3 -54/5a2b 216/5a2c |
| 0 0 -18a2b |
| 0 3/2a3 0 |
| 0 0 6a3 |
24 3
o15 : Matrix R <--- R
i16 : f1
o16 = | 12a2 0 0 6ab 0 0 6ac 0 0 2b2 0 0 2bc 0 0
| 0 12a2 0 0 6ab 0 0 6ac 0 0 2b2 0 0 2bc 0
| 0 0 12a2 0 0 6ab 0 0 6ac 0 0 2b2 0 0 2bc
| 0 0 0 0 6a2 0 -12a2 0 0 0 8ab 0 -8ab 4ac 0
| 0 0 0 0 0 6a2 0 -3a2 0 0 0 8ab 0 -2ab 4ac
| 0 0 0 0 0 0 0 0 0 0 0 2a2 0 -a2 0
-----------------------------------------------------------------------
2c2 0 0 0 0 0 0 0 0 0 0 0 |
0 2c2 0 0 0 0 0 0 0 0 0 0 |
0 0 2c2 0 0 0 0 0 0 0 0 0 |
-16ac 0 0 6b2 0 4bc 0 2c2 0 0 0 0 |
0 -4ac 0 0 6b2 -b2 4bc -2bc 2c2 0 0 0 |
2a2 0 0 0 6ab -2ab 2ac -2ac 0 12b2 6bc 2c2 |
6 27
o16 : Matrix R <--- R
i17 : f2 = map(source f1,,f2)
o17 = {1} | 3b c 0 0 0 0 0 0 0 0 0 0
{1} | 0 2b 2c 0 0 0 0 0 0 0 0 0
{1} | 0 0 b 3c 0 0 0 0 0 0 0 0
{1} | -6a 0 0 0 3/2b c 0 0 -3/2c 0 0 0
{1} | 0 -4a 0 0 0 b 2c 0 0 -c 0 0
{1} | 0 0 -2a 0 0 0 1/2b 3c 0 0 -1/2c 0
{1} | 0 -2a 0 0 0 -1/2b 0 0 3b 1/2c 0 0
{1} | 0 0 -4a 0 0 0 -b 0 0 2b c 0
{1} | 0 0 0 -6a 0 0 0 -3/2b 0 0 b 3/2c
{1} | 0 0 0 0 -9/2a 0 0 0 0 0 0 0
{1} | 0 0 0 0 0 -3a 0 0 0 0 0 0
{1} | 0 0 0 0 0 0 -3/2a 0 0 0 0 0
{1} | 0 0 0 0 0 -3/2a 0 0 -9/2a 0 0 0
{1} | 0 0 0 0 0 0 -3a 0 0 -3a 0 0
{1} | 0 0 0 0 0 0 0 -9/2a 0 0 -3/2a 0
{1} | 0 0 0 0 0 0 0 0 0 -3/2a 0 0
{1} | 0 0 0 0 0 0 0 0 0 0 -3a 0
{1} | 0 0 0 0 0 0 0 0 0 0 0 -9/2a
{1} | 0 0 0 0 0 0 0 0 0 0 0 0
{1} | 0 0 0 0 0 0 0 0 0 0 0 0
{1} | 0 0 0 0 0 0 0 0 0 0 0 0
{1} | 0 0 0 0 0 0 0 0 0 0 0 0
{1} | 0 0 0 0 0 0 0 0 0 0 0 0
{1} | 0 0 0 0 0 0 0 0 0 0 0 0
{1} | 0 0 0 0 0 0 0 0 0 0 0 0
{1} | 0 0 0 0 0 0 0 0 0 0 0 0
{1} | 0 0 0 0 0 0 0 0 0 0 0 0
-----------------------------------------------------------------------
0 0 0 0 0 0 0 0 0 0 0 0 |
0 0 0 0 0 0 0 0 0 0 0 0 |
0 0 0 0 0 0 0 0 0 0 0 0 |
0 0 0 0 0 0 0 0 0 0 0 0 |
0 0 0 0 0 0 0 0 0 0 0 0 |
0 0 0 0 0 0 0 0 0 0 0 0 |
0 0 0 0 0 0 0 0 0 0 0 0 |
0 0 0 0 0 0 0 0 0 0 0 0 |
0 0 0 0 0 0 0 0 0 0 0 0 |
c 0 0 0 0 0 0 0 0 0 0 0 |
0 2c 0 -c 0 0 0 0 0 0 0 0 |
0 0 3c 0 -1/2c 0 0 0 0 0 0 0 |
-b 0 0 1/2c 0 0 0 0 0 0 0 0 |
0 -2b 0 b c 0 0 0 0 0 0 0 |
0 0 -3b 0 1/2b 3/2c 0 0 0 0 0 0 |
0 0 0 -1/2b 0 0 0 0 0 0 0 0 |
0 0 0 0 -b 0 0 0 0 0 0 0 |
0 0 0 0 0 -3/2b 0 0 0 0 0 0 |
-4/3a 0 0 0 0 0 2c 0 0 0 0 0 |
0 -a 0 1/3a 0 0 -1/2b 3c -1/2c 0 0 0 |
0 -2a 0 0 0 0 -3b 0 c 0 0 0 |
0 0 -3a 0 -a 0 0 -9/2b 0 3/2c 0 0 |
0 0 0 0 -2a 0 0 0 -2b 0 0 0 |
0 0 0 0 0 -3a 0 0 0 -3b 0 0 |
0 0 0 0 0 0 -1/4a 0 0 0 3c 0 |
0 0 0 0 0 0 0 -3/2a 1/6a 0 -6b 3/2c |
0 0 0 0 0 0 0 0 0 -3/2a 0 -9/2b |
27 24
o17 : Matrix R <--- R
i18 : f3 = map(source f2,,f3)
o18 = {2} | 6c3 0 0 |
{2} | -18bc2 0 0 |
{2} | 18b2c 0 0 |
{2} | -6b3 0 0 |
{2} | 0 6c3 0 |
{2} | 72/5ac2 -72/5bc2 18/5c3 |
{2} | -144/5abc 54/5b2c -36/5bc2 |
{2} | 72/5ab2 -12/5b3 18/5b2c |
{2} | -72/5ac2 -18/5bc2 12/5c3 |
{2} | 144/5abc 36/5b2c -54/5bc2 |
{2} | -72/5ab2 -18/5b3 72/5b2c |
{2} | 0 0 -6b3 |
{2} | 0 27ac2 0 |
{2} | -108/5a2c -162/5abc 108/5ac2 |
{2} | -36/5a2b 36/5ab2 -54/5abc |
{2} | -432/5a2c -108/5abc 162/5ac2 |
{2} | 216/5a2b 54/5ab2 -216/5abc |
{2} | 0 0 18ab2 |
{2} | 0 18a2c 0 |
{2} | -24/5a3 -36/5a2b 54/5a2c |
{2} | -216/5a3 -54/5a2b 216/5a2c |
{2} | 0 0 -18a2b |
{2} | 0 3/2a3 0 |
{2} | 0 0 6a3 |
24 3
o18 : Matrix R <--- R
i19 : f1 * f2
o19 = 0
6 24
o19 : Matrix R <--- R
i20 : f2 * f3
o20 = 0
27 3
o20 : Matrix R <--- R
i21 : ker f1 == image f2
o21 = true
i22 : ker f2 == image f3
o22 = true
i23 : p = 32003
o23 = 32003
i24 : R = ZZ/p[a,b,c];
i25 : f1 = pieri({4,2,0},{1,1},R)
o25 = | a2 ab b2 0 ac bc 0 0 c2 0 0 0 0 -bc 0 0 -c2 0 0 0
| 0 0 0 a2 2ab b2 0 2ac 4bc 0 c2 0 ab 0 0 -2ac -2bc 0 -c2 0
| 0 0 0 0 0 0 a2 ab b2 ac bc c2 0 0 0 0 0 0 0 0
| 0 0 0 0 0 0 0 0 0 0 0 0 a2 4ab b2 0 4ac 4bc 0 c2
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a2 2ab 0 2ac bc
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ab 0 0
-----------------------------------------------------------------------
0 0 0 0 0 0 0 |
0 -2bc 0 0 0 0 0 |
0 0 0 0 0 0 0 |
0 -4ac -4bc 0 -2c2 0 0 |
c2 2ab b2 0 0 0 0 |
0 a2 2ab b2 ac bc c2 |
6 27
o25 : Matrix R <--- R
i26 : betti res coker f1
0 1 2 3
o26 = total: 6 27 24 3
0: 6 . . .
1: . 27 24 .
2: . . . .
3: . . . 3
o26 : BettiTally
i27 : f2 = pieri({4,3,0},{2},R)
o27 = | -b -c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
| 0 -2b -2c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
| 0 0 -b -c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
| 2a 0 0 0 -b -3c -2c 0 0 0 0 0 0 0 0 0 0 0 0
| 0 4a 0 0 0 -2b -2b -4c 0 6c 0 0 0 0 0 0 0 0 0
| 0 0 2a 0 0 0 0 -b -2c b c 0 0 0 0 0 0 0 0
| 0 2a 0 0 0 3b b 0 0 -c 0 0 0 0 0 0 0 0 0
| 0 0 4a 0 0 0 0 2b 0 -6b -2c 0 0 0 0 0 0 0 0
| 0 0 0 2a 0 0 0 0 b 0 -2b -c 0 0 0 0 0 0 0
| 0 0 0 0 3a 0 0 0 0 0 0 0 -3c 0 0 0 0 0 0
| 0 0 0 0 0 6a 6a 0 0 0 0 0 0 -4c -6c 0 0 0 0
| 0 0 0 0 0 0 0 3a 0 -3a 0 0 0 0 0 -c c 0 0
| 0 0 0 0 0 0 3a 0 0 0 0 0 3b 3c 3c 0 0 0 0
| 0 0 0 0 0 0 0 6a 0 0 0 0 0 4b 6b 0 -2c 0 0
| 0 0 0 0 0 0 0 0 3a 0 3a 0 0 0 0 b -b 0 -c
| 0 0 0 0 0 0 0 0 0 3a 0 0 0 -3b -3b 0 0 0 0
| 0 0 0 0 0 0 0 0 0 0 6a 0 0 0 0 0 2b 0 0
| 0 0 0 0 0 0 0 0 0 0 0 3a 0 0 0 0 0 0 b
| 0 0 0 0 0 0 0 0 0 0 0 0 4a 0 0 0 0 0 0
| 0 0 0 0 0 0 0 0 0 0 0 0 0 a 2a 0 0 c 0
| 0 0 0 0 0 0 0 0 0 0 0 0 0 -2a 0 0 0 -6c 0
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a 2a 3b 0
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4a 12b 0
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2a
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-----------------------------------------------------------------------
0 0 0 0 0 |
0 0 0 0 0 |
0 0 0 0 0 |
0 0 0 0 0 |
0 0 0 0 0 |
0 0 0 0 0 |
0 0 0 0 0 |
0 0 0 0 0 |
0 0 0 0 0 |
0 0 0 0 0 |
0 0 0 0 0 |
0 0 0 0 0 |
0 0 0 0 0 |
0 0 0 0 0 |
0 0 0 0 0 |
0 0 0 0 0 |
0 0 0 0 0 |
0 0 0 0 0 |
-8c 0 0 0 0 |
2b -3c 0 0 0 |
12b 6c 0 0 0 |
0 0 0 -c 0 |
0 -12b 0 0 0 |
0 0 0 2b 0 |
a 0 -c 0 0 |
0 a 2b 0 -c |
0 0 0 a 3b |
27 24
o27 : Matrix R <--- R
i28 : f3 = pieri({4,3,3},{3,3,3},R)
o28 = | -5c3 0 0 |
| 15bc2 0 0 |
| -15b2c 0 0 |
| 5b3 0 0 |
| 0 20c3 0 |
| -12ac2 -48bc2 3c3 |
| 24abc 36b2c -6bc2 |
| -12ab2 -8b3 3b2c |
| 12ac2 -12bc2 2c3 |
| -24abc 24b2c -9bc2 |
| 12ab2 -12b3 12b2c |
| 0 0 -5b3 |
| 0 90ac2 0 |
| 18a2c -108abc 18ac2 |
| 6a2b 24ab2 -9abc |
| 72a2c -72abc 27ac2 |
| -36a2b 36ab2 -36abc |
| 0 0 15ab2 |
| 0 60a2c 0 |
| 4a3 -24a2b 9a2c |
| 36a3 -36a2b 36a2c |
| 0 0 -15a2b |
| 0 5a3 0 |
| 0 0 5a3 |
24 3
o28 : Matrix R <--- R
i29 : f2 = map(source f1,,f2)
o29 = | -b -c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
| 0 -2b -2c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
| 0 0 -b -c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
| 2a 0 0 0 -b -3c -2c 0 0 0 0 0 0 0 0 0 0 0 0
| 0 4a 0 0 0 -2b -2b -4c 0 6c 0 0 0 0 0 0 0 0 0
| 0 0 2a 0 0 0 0 -b -2c b c 0 0 0 0 0 0 0 0
| 0 2a 0 0 0 3b b 0 0 -c 0 0 0 0 0 0 0 0 0
| 0 0 4a 0 0 0 0 2b 0 -6b -2c 0 0 0 0 0 0 0 0
| 0 0 0 2a 0 0 0 0 b 0 -2b -c 0 0 0 0 0 0 0
| 0 0 0 0 3a 0 0 0 0 0 0 0 -3c 0 0 0 0 0 0
| 0 0 0 0 0 6a 6a 0 0 0 0 0 0 -4c -6c 0 0 0 0
| 0 0 0 0 0 0 0 3a 0 -3a 0 0 0 0 0 -c c 0 0
| 0 0 0 0 0 0 3a 0 0 0 0 0 3b 3c 3c 0 0 0 0
| 0 0 0 0 0 0 0 6a 0 0 0 0 0 4b 6b 0 -2c 0 0
| 0 0 0 0 0 0 0 0 3a 0 3a 0 0 0 0 b -b 0 -c
| 0 0 0 0 0 0 0 0 0 3a 0 0 0 -3b -3b 0 0 0 0
| 0 0 0 0 0 0 0 0 0 0 6a 0 0 0 0 0 2b 0 0
| 0 0 0 0 0 0 0 0 0 0 0 3a 0 0 0 0 0 0 b
| 0 0 0 0 0 0 0 0 0 0 0 0 4a 0 0 0 0 0 0
| 0 0 0 0 0 0 0 0 0 0 0 0 0 a 2a 0 0 c 0
| 0 0 0 0 0 0 0 0 0 0 0 0 0 -2a 0 0 0 -6c 0
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a 2a 3b 0
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4a 12b 0
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2a
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-----------------------------------------------------------------------
0 0 0 0 0 |
0 0 0 0 0 |
0 0 0 0 0 |
0 0 0 0 0 |
0 0 0 0 0 |
0 0 0 0 0 |
0 0 0 0 0 |
0 0 0 0 0 |
0 0 0 0 0 |
0 0 0 0 0 |
0 0 0 0 0 |
0 0 0 0 0 |
0 0 0 0 0 |
0 0 0 0 0 |
0 0 0 0 0 |
0 0 0 0 0 |
0 0 0 0 0 |
0 0 0 0 0 |
-8c 0 0 0 0 |
2b -3c 0 0 0 |
12b 6c 0 0 0 |
0 0 0 -c 0 |
0 -12b 0 0 0 |
0 0 0 2b 0 |
a 0 -c 0 0 |
0 a 2b 0 -c |
0 0 0 a 3b |
27 24
o29 : Matrix R <--- R
i30 : f3 = map(source f2,,f3)
o30 = {1} | -5c3 0 0 |
{1} | 15bc2 0 0 |
{1} | -15b2c 0 0 |
{1} | 5b3 0 0 |
{1} | 0 20c3 0 |
{1} | -12ac2 -48bc2 3c3 |
{1} | 24abc 36b2c -6bc2 |
{1} | -12ab2 -8b3 3b2c |
{1} | 12ac2 -12bc2 2c3 |
{1} | -24abc 24b2c -9bc2 |
{1} | 12ab2 -12b3 12b2c |
{1} | 0 0 -5b3 |
{1} | 0 90ac2 0 |
{1} | 18a2c -108abc 18ac2 |
{1} | 6a2b 24ab2 -9abc |
{1} | 72a2c -72abc 27ac2 |
{1} | -36a2b 36ab2 -36abc |
{1} | 0 0 15ab2 |
{1} | 0 60a2c 0 |
{1} | 4a3 -24a2b 9a2c |
{1} | 36a3 -36a2b 36a2c |
{1} | 0 0 -15a2b |
{1} | 0 5a3 0 |
{1} | 0 0 5a3 |
24 3
o30 : Matrix R <--- R
i31 : f1 * f2
o31 = | -a2b -2ab2+3a2c -b3 -b2c+2ac2 0 -2abc
| 2a3 8a2b 2ab2+8a2c 8abc -a2b -4ab2-3a2c+6ac2
| 0 2a3 4a2b 2ab2 3a2c 3a2b+6abc
| 0 0 0 0 0 0
| 0 0 0 0 0 0
| 0 0 0 0 0 0
-----------------------------------------------------------------------
-2abc -6abc-b2c-4ac2 -bc2 b2c+6ac2 -6ac2-bc2
3a2b-4ab2-2a2c+6ac2 -b3-4abc 2b2c b3-6a2c -12abc-7b2c-4ac2
a2b+6abc 2ab2+3ac2 b3 -6ab2-a2c-3ac2 -2b3-2abc
3a3 24a2b 3ab2 0 3ab2+24a2c
0 0 0 3a3 12a2b
0 0 0 0 0
-----------------------------------------------------------------------
-c3 0 -4b2c -6b2c 0 0
-4bc2 3ab2-4ac2 9abc-4c3 9abc-6c3 -2abc -4abc-4b2c
-b2c -3ac2 -4bc2 -6bc2 -c3 c3
12abc 3a2b 16ab2+3a2c+ac2 24ab2+3a2c+2ac2 b3-4a2c -b3-8a2c-16abc
0 8a2c -3a2b+abc-2ac2 -3a2b+2abc 2a2b 4a2b+8ab2
-3a2b 0 0 0 a3 2a3+8a2b
-----------------------------------------------------------------------
0 0 0 0 0
-6b2c 0 8c3 0 0
0 0 0 0 0
-12abc-48b2c+c3 3b2c -2ac2+2bc2 48b2c-3c3 2c3
6ab2+12b3+bc2-6c3 0 2b2c-16ac2+12bc2 -12b3-3bc2+6c3 0
3a2b+24ab2 ab2 a2c -24ab2+abc 2b2c-ac2
-----------------------------------------------------------------------
0 0 |
2bc2 0 |
0 0 |
4ac2 0 |
-2abc 0 |
2b3-a2c+ac2 2bc2 |
6 24
o31 : Matrix R <--- R
i32 : f2 * f3
o32 = | -10bc3 0
| 0 0
| 10b3c 0
| -48abc2+26ac3 -72b2c2+124bc3
| -60abc2 -40b3c+240b2c2
| 12ab3-42ab2c-24ac3 8b4+12b3c+24bc3
| 24ab2c+18abc2 36b3c-168b2c2
| -24ab3+60ab2c -16b4-120b3c
| -14ab3+12abc2 24b4-12b2c2
| 0 -210ac3
| 108a2bc-144a2c2 72ab2c+144abc2
| -36a2b2+36a2bc-72a2c2 -24ab3-36ab2c+72abc2
| 90a2bc+54a2c2 180ab2c-54abc2
| -36a2b2+144a2bc 96ab3-504ab2c
| 72a2b2+72a2bc+36a2c2 -72ab3-72ab2c-60a2c2-36abc2
| -18a2b2-126a2bc -72ab3+396ab2c
| 0 0
| 0 60a2bc
| -32a3c 192a2bc+360a2c2
| 20a3b-90a3c 0
| 48a3b+180a3c -288a2b2
| -72a3b+72a3c 72a2b2-5a3c-72a2bc
| -576a3b 576a2b2
| 0 10a3b+120a3c
| 4a4 -24a3b
| 36a4 -36a3b
| 0 5a4
-----------------------------------------------------------------------
0 |
0 |
0 |
12bc3-9c4 |
-60bc3 |
-3b3c+3b2c2-4c4 |
-6b2c2+18bc3 |
6b3c+30b2c2 |
-19b3c+2bc3 |
0 |
18abc2-54ac3 |
9ab2c-9abc2-27ac3 |
-45abc2+54ac3 |
-36ab2c+144abc2 |
72ab2c+27abc2+6ac3 |
27ab2c-81abc2 |
0 |
-15ab3 |
-72a2c2 |
15ab2c-90a2c2 |
108a2bc-90ab2c+180a2c2 |
45ab3-72a2bc+27a2c2 |
180ab3-576a2bc |
0 |
9a3c+15a2bc |
-30a2b2+31a3c |
15a3b |
27 3
o32 : Matrix R <--- R
i33 : ker f1 == image f2
o33 = false
i34 : ker f2 == image f3
o34 = false
i35 :
