Description
For mathematical background of this package and some examples of use, see:
Steven V Sam, Computing inclusions of Schur modules, arXiv:0810.4666
Some other references:
Andrzej Daszkiewicz, On the Invariant Ideals of the Symmetric Algebra $S.(V \oplus \wedge^2 V)$, J. Algebra 125, 1989, 444-473.
David Eisenbud, Gunnar Fl\o ystad, and Jerzy Weyman, The existence of pure free resolutions, arXiv:0709.1529.
William Fulton, Young Tableaux: With Applications to Representation Theory and Geometry, London Math. Society Student Texts 35, 1997.
Jerzy Weyman, Cohomology of Vector Bundles and Syzygies, Cambridge University Press, 2002.
Let V be a vector space over K. If K has characteristic 0, then given the partition mu and the partition mu' obtained from mu by removing a single box, there is a unique (up to nonzero scalar) GL(V)-equivariant inclusion S_mu V -> V otimes S_mu' V, where S_mu refers to the irreducible representation of GL(V) with highest weight mu. This can be extended uniquely to a map of P = Sym(V)-modules P otimes S_mu V -> P otimes S_mu' V. The purpose of this package is to write down matrix representatives for these maps. The main function for doing so is
pieri. Here is an example of the use of the package PieriMaps, which is also designed to check whether the maps are being constructed correctly (important, since it is notoriously difficult to get the signs and coefficients right.) We will construct by hand the free resolution in 3 variables corresponding to the degree sequence (0,2,3,6). Let's start with the packaged code:
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
|
By the general theory from Eisenbud-Fl\o ystad-Weyman, each of these free modules should be essentially Schur functors corresponding to the following partitions.
i4 : needsPackage "SchurRings"
o4 = SchurRings
o4 : Package
|
i5 : schurRing(s,3)
o5 = schurRing (QQ, s, 3)
o5 : SchurRing
|
i6 : dim s_{2,2}
o6 = 6
|
i7 : dim s_{4,2}
o7 = 27
|
i8 : dim s_{4,3}
o8 = 24
|
i9 : dim s_{4,3,3}
o9 = 3
|
This package also provides a routine
schurRank for computing this dimension:
i10 : schurRank(3, {2,2})
o10 = 6
|
i11 : schurRank(3, {4,2})
o11 = 27
|
i12 : schurRank(3, {4,3})
o12 = 24
|
i13 : schurRank(3, {4,3,3})
o13 = 3
|
We now use
pieri to construct each of the maps of the resolution separately.
i14 : f1 = pieri({4,2,0},{1,1}, R)
o14 = | 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
o14 : Matrix R <-- R
|
i15 : f2 = pieri({4,3,0},{2}, R)
o15 = | 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
o15 : Matrix R <-- R
|
i16 : f3 = pieri({4,3,3},{3,3,3}, R)
o16 = | 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
o16 : Matrix R <-- R
|
Fix the degrees (i.e. make sure that the target of f2 is the source of f1, etc). Otherwise the test of exactness below would fail.
i17 : f1
o17 = | 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
o17 : Matrix R <-- R
|
i18 : f2 = map(source f1,,f2)
o18 = {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
o18 : Matrix R <-- R
|
i19 : f3 = map(source f2,,f3)
o19 = {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
o19 : Matrix R <-- R
|
i20 : f1 * f2
o20 = 0
6 24
o20 : Matrix R <-- R
|
i21 : f2 * f3
o21 = 0
27 3
o21 : Matrix R <-- R
|
Check that the complex is exact.
i22 : ker f1 == image f2
o22 = true
|
i23 : ker f2 == image f3
o23 = true
|
Looks great! Now let's try it modulo some prime numbers and see if we get exactness.
i24 : p = 32003
o24 = 32003
|
i25 : R = ZZ/p[a,b,c];
|
i26 : f1 = pieri({4,2,0},{1,1},R)
o26 = | 7012a2+6250ab-5379b2+12089ac-8371bc-3669c2
| 3630a2-5863ab-8195b2+3219ac-14676bc+10443c2
| -12738a2-14389ab-3669b2+14830ac+10443bc+4994c2
| 1962a2+704ab+42b2
| 3a2
| 0
-----------------------------------------------------------------------
9770a2-3164ab+14689b2+12630ac+661bc+10959c2
-6841a2-2950ab-13606b2-14090ac-15537bc+8572c2
15976a2-1642ab-2725b2-14788ac+7543bc-1774c2
3793a2+6938ab+14609b2+9266ac-12554bc+1946c2
5403a2+4637ab-2058ac+1946bc+86c2
a2-12863ab
-----------------------------------------------------------------------
1642a2+15650ab+932b2+4677ac-13229bc+10676c2
5880a2+12908ab+12962b2-12390ac+2856bc+4469c2
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3554a2+8755ab-5997b2-15690ac+6585bc-1155c2
12831a2-7437ab+b2-15850ac-1155bc+5350c2
102a2-9646ab
-----------------------------------------------------------------------
-1128a2-6948ab+12866b2+4136ac+9742bc-3952c2
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3004a2-6111ab-10090b2-12960ac-556bc+4552c2
1723a2+2521ab+11439b2+7047ac-12864bc-3101c2
7431a2-12074ab+b2-13792ac-3101bc+5264c2
101a2+3217ab
-----------------------------------------------------------------------
7230a2-7752ab-6045b2-4786ac+6938bc-8543c2
12526a2-7587ab+12804b2+13972ac+8090bc-1035c2
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1985a2-8539ab+14392b2-11485ac+12244bc-6993c2
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99a2-3060ab
-----------------------------------------------------------------------
10499a2+15367ab-14668b2+2246ac+2607bc+4192c2
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10229a2-12217ab-11216b2+131ac-1421bc+7570c2
10095a2+15220ab-14490b2+1986ac+5349bc-10885c2
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97a2-9337ab
-----------------------------------------------------------------------
1047a2-9148ab-14489b2-12525ac-4085bc+2166c2
7697a2+1003ab-1637b2+4780ac+391bc+13521c2
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7088a2-7893ab+b2-1444ac-14777bc+4748c2
95a2-15614ab
-----------------------------------------------------------------------
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93a2+10112ab
-----------------------------------------------------------------------
3034a2-13972ab+4905b2-4278ac-5652bc-10955c2
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91a2+3835ab
-----------------------------------------------------------------------
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10974a2-15649ab-3280b2+1186ac+2373bc+9234c2
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14886a2-3252ab+10396b2-7748ac+9856bc+5550c2
8269a2-3518ab+b2+10906ac+5550bc+4232c2
89a2-2463ab
-----------------------------------------------------------------------
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87a2-9502ab
-----------------------------------------------------------------------
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14817a2+6672ab+10707b2-15387ac-5252bc-2188c2
15830a2+8648ab+b2-10655ac-2188bc+3889c2
85a2+1314ab
-----------------------------------------------------------------------
4524a2+12312ab-14403b2+7223ac-12012bc+3211c2
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2048a2-15003ab+58b2-5828ac+9823bc+10672c2
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1902a2+5587ab+6b2+ac
-----------------------------------------------------------------------
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14598a2+2902ab+1380b2-13881ac+1458bc-9464c2
5137a2-3348ab+816b2+144ac+27bc+c2
-----------------------------------------------------------------------
8798a2+6400ab-5840b2-1845ac-5373bc+3153c2
5490a2-3378ab-15485b2-10675ac-10730bc+8660c2
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-----------------------------------------------------------------------
2831a2-3560ab+571b2-13064ac+1640bc-3083c2
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-----------------------------------------------------------------------
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-----------------------------------------------------------------------
15978a2+15978ab-3205b2-15047ac+11129bc-1579c2
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-----------------------------------------------------------------------
8a2+8ab-6399b2-9590ac+2115bc-5865c2
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-----------------------------------------------------------------------
4045a2+4045ab+809b2-2113ac+1696bc+1963c2
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-15500a2+12511ab-5323b2-1496ac+4892bc-10046c2
8205a2-1470ab+829b2+15722ac-9790bc-12374c2
15821a2-394ab+720b2+128ac+27bc+c2
-----------------------------------------------------------------------
15219a2+15219ab+15845b2-11552ac-1366bc-2180c2
4293a2-1686ab+6688b2-10945ac-10702bc+1327c2
4900a2+4550ab+10451b2+5419ac+1789bc-6152c2
-10585a2+213ab-7314b2-3964ac-4016bc-15700c2
-5979a2-11500ab+754b2+924ac-15450bc+1997c2
13622a2+1758ab+702b2+125ac+27bc+c2
-----------------------------------------------------------------------
-2422a2-2422ab-6885b2+7401ac+4968bc-5617c2
516a2-8522ab-3268b2+14073ac+8136bc-9874c2
-6986a2-6472ab-10454b2+11582ac-7971bc-5982c2
8679a2-941ab+3008b2-2798ac+11988bc-13214c2
2493a2+14054ab+688b2+3806ac-12970bc-2882c2
11864a2-2309ab+684b2+122ac+27bc+c2
-----------------------------------------------------------------------
6487a2+6487ab+7698b2-6463ac+10096bc+983c2
1235a2+15775ab-1860b2-10278ac-6994bc+15653c2
-9492a2+14649ab+5162b2+2860ac-12427bc+11060c2
-3302a2-15821ab-4033b2+10151ac-13273bc-4590c2
-12215a2-4361ab+582b2+7846ac-4366bc-11113c2
9642a2+11901ab+626b2+112ac+26bc+c2
-----------------------------------------------------------------------
-12758a2-12758ab+3849b2-15384ac+5255bc-6838c2
-11535a2+14459ab+12641b2-534ac-8196bc+6473c2
12756a2-4746ab+9071b2-3909ac-380bc-2164c2
13224a2-2459ab+12661b2+6309ac+15482bc-12673c2
-4479a2+12477ab+401b2-13706ac-12495bc-1648c2
6331a2+12532ab+494b2+89ac+23bc+c2
-----------------------------------------------------------------------
3849ac-7137bc+4496c2
3849a2-4713ab+13571b2-5152ac-1772bc-5389c2
-930a2-14501ab-3597b2-15426ac+13417bc-2977c2
-12411a2-13177ab+6020b2-7509ac+14376bc+4715c2
-11925a2-12616ab+135b2+5609ac+4813bc-9068c2
1785a2-3459ab+266b2+49ac+17bc+c2
-----------------------------------------------------------------------
-7344bc-4176c2 0 |
4717ab-9757ac+2927bc+11966c2 0 |
13571a2+13571ab-10087b2-10087ac-8418bc+4717c2 0 |
4717a2-2627ab+7344b2+7259ac+8259bc+15083c2 -10c2 |
2448a2-11272ab+25b2-8765ac+15125bc+3025c2 0 |
275a2+5961ab+110b2+21ac+11bc+c2 25b2+5ac+5bc+c2 |
6 27
o26 : Matrix R <-- R
|
i27 : betti res coker f1
0 1 2 3
o27 = total: 6 27 24 3
0: 6 . . .
1: . 27 24 .
2: . . . .
3: . . . 3
o27 : BettiTally
|
i28 : f2 = pieri({4,3,0},{2},R)
o28 = | 6986b+4510c -1451b-7220c 13064b+9527c
| 9020b-10741c -14440b+3016c -12949b-15317c
| 10631b+2953c 1508b+10808c 8343b+684c
| -13972a+14166b+3105c 2902a-9397b-5451c 5875a-5254b+4348c
| 13963a+923b+2263c -3123a-12640b-10200c -6105a-4110b+15487c
| 10741a+10088b-320c -3016a+9732b+14476c 15317a-12189b+420c
| -9020a+11176b+3043c 14440a-8058b-7439c 12949a-14861b+15883c
| -10521a-8004b-15157c -6032a+14786b+14710c -1369a-8099b+10532c
| -5906a-3207b+8650c 10387a-12207b+8371c -1368a+7689b+1079c
| -10495a-11636c -3812a-11660c 15762a-3966c
| -2769a+2034c 5917a+2034c 12330a+1147c
| 1739a+15880c 2807a+15880c 4564a+13355c
| -10840a+11636b-13565c 8524a+11660b-13565c -464a+3966b+11577c
| -14780a-2034b+11327c -13758a-2034b+11327c 9839a-1147b-4667c
| 10581a-15880b-270c -6807a-15880b-270c 7676a-13355b-10233c
| -9129a+13565b -9686a+13565b -15646a-11577b
| 13468a-11327b -12127a-11327b 407a+4667b
| 6053a+270b 6890a+270b -3237a+10233b
| 4847a-24c 4879a-24c 5288a-1392c
| -7163a+6b+2034c -7163a+6b+2034c 11569a+348b-2296c
| -6907a+36b-12204c -6907a+36b-12204c 7702a+2088b+13764c
| 15134a+6102b 15134a+6102b 9647a-6879b
| 9349a-7595b 9349a-7595b 9334a+4475b
| 540a 540a -11537a
| 3a 3a 174a
| 0 0 a
| 0 0 0
-----------------------------------------------------------------------
-15183b-7919c 4969b-6623c 15163b-9429c
-15838b-4094c -13246b+10515c 13145b-2015c
-2047b-12069c -10744b-5499c 14994b+30c
-1637a+7830b-12120c -9938a+8975b+14045c 1677a-13275b-6277c
-327a-10408b+12432c -5511a+13349b+6604c 5713a+7996b-3832c
4094a+11292b-3503c -10515a+11413b+7642c 2015a+15497b+8124c
15838a+8628b-15635c 13246a+7935b-12479c -13145a-7455b+907c
8188a+10885b-5888c 10973a-8736b+10767c 4030a+4637b+4339c
-7865a+13337b+7255c 10998a+12255b+10478c -60a+7193b-12886c
8513a+14347c 5078a+11453c 7822a-12082c
-779a-299c -8044a-4319c 8015a-8243c
-1873a+13436c -2236a-2363c -14488a+13760c
10476a-14347b-648c -1934a-11453b+1094c 9193a+12082b-15937c
-5945a+299b+9117c 6396a+4319b+11574c -2415a+8243b+247c
2501a-13436b-10053c 4315a+2363b-9603c -13948a-13760b-9333c
14902a+648b 5434a-1094b -2721a+15937b
-14339a-9117b -298a-11574b -13017a-247b
10238a+10053b 569a+9603b 6655a+9333b
2206a-1376c -4603a-1336c -5226a-1312c
-15636a+344b-3652c -3539a+334b-7042c 4100a+328b-9076c
1595a+2064b-10103c 2131a+2004b+10237c 8114a+1968b-9562c
-11110a-10947b -14998a+10886b 1871a+4784b
13769a-11797b 8855a+11529b -494a-12879b
-11897a -12797a -13337a
172a 167a 164a
a a a
0 0 0
-----------------------------------------------------------------------
-15488b-2190c -6016b-15512c -10796b-3322c
-4380b+3603c 979b+8643c -6644b+13540c
-14200b+3911c -11680b+13264c 6770b+594c
-1027a+13161b+1107c 12032a+12462b+8085c -10411a-8151b+73c
8760a-6030b+5120c -1958a+13732b+1140c 13288a+11081b+15412c
-3603a+3224b-8085c -8643a+188b+1322c -13540a-146b+14592c
4380a-11259b+3888c -979a+4428b-194c 6644a+474b-7998c
-7206a+9104b+401c 14717a-1152b-7492c 4923a+303b+6218c
-7822a+12344b+6148c 5475a-6280b-1448c -1188a+13369b-8693c
-7480a-6710c -5383a-4866c -7550a-6982c
-13913a-13787c -9193a+11052c -1240a+2268c
-9672a-2120c -564a+14003c 438a-1877c
-1547a+6710b+241c -5536a+4866b-14378c -1641a+6982b+4212c
-10669a+13787b-11080c 36a-11052b+9596c -15142a-2268b-1731c
-12777a+2120b-9063c 14874a-14003b-8793c 12126a+1877b-8523c
-11664a-241b 582a+14378b -8009a-4212b
-1203a+11080b -9527a-9596b 13349a+1731b
13559a+9063b 4344a+8793b -5924a+8523b
-1721a-1288c 6488a-1264c -12026a-1240c
12147a+322b-11110c -11401a+316b-13144c -2538a+310b-15178c
13305a+1932b+2642c -14299a+1896b+14846c -10692a+1860b-4953c
-13263a-1318b 3606a-7420b -11528a-13522b
-9843a-5284b 12811a+2311b 3462a+9906b
-13877a -14417a -14957a
161a 158a 155a
a a a
0 0 0
-----------------------------------------------------------------------
-5877b-6258c -8813b-14176c 9247b+1060c
-12516b+12885c 3651b-8309c 2120b+10717c
-9559b+5151c 11847b-9902c -10643b+15903c
11754a-5269b-13526c -14377a+10506b-6944c 13509a+1070b-4108c
-6971a-4888b+6606c -7302a-12365b+14458c -4240a+14466b-7935c
-12885a-6457b+8767c 8309a+3644b+324c -10717a+5242b+6182c
12516a-12283b+15786c -3651a+11342b+59c -2120a-2088b-1550c
6233a+12052b+3081c -15385a-7052b+12629c 10569a+15319b+7046c
-10302a+5928b+11394c -12199a+1309b-9825c 197a-13808b+9463c
15807a-13490c 485a+7187c -3210a-5592c
14664a-8136c 5092a+11835c -11395a-9899c
-12632a+14246c -10932a-1634c -15726a+14484c
13421a+13490b-7995c -13194a-7187b+13013c -13415a+5592b+9233c
8032a+8136b-13058c 9785a-11835b+7618c 9851a+9899b-3711c
-12082a-14246b-8253c -4899a+1634b-7983c -9125a-14484b-7713c
-15355a+7995b -177a-13013b 4650a-9233b
-9243a+13058b -5884a-7618b 10865a+3711b
-2179a+8253b -2528a+7983b 3614a+7713b
7319a-1216c 1085a-1192c 7456a-1168c
6733a+304b+14791c -15589a+298b+12757c -3462a+292b+10723c
-7877a+1824b+7251c -5858a+1788b-12548c -8567a+1752b-344c
5341a+12379b -9793a+6277b 7084a+175b
-5887a-14502b -15236a-6907b 7422a+688b
-15497a 15966a 15426a
152a 149a 146a
a a a
0 0 0
-----------------------------------------------------------------------
8346b+14184c -9595b+9348c -13631b+10629c
-3635b+3555c -13307b+15643c -10745b+3953c
-14224b+9547c -8180b+3540c -14025b-10748c
15311a+7734b-3965c -12813a+9990b-9574c -4741a+2846b+13893c
7270a-8118b+15295c -5389a-15886b+2496c -10513a+4749b+11970c
-3555a+11902b-6621c -15643a+1686b+83c -3953a+11113b-5917c
3635a-4247b+155c 13307a-4681b+2124c 10745a-4661b-15762c
-7110a+8819b-14645c 717a+5124b-523c -7906a+10735b+15973c
12909a-15674b-15693c -7080a+7567b+10712c -10507a-9064b+15358c
8801a-643c 2033a-10155c -8538a+8235c
-7649a-5644c 15655a+15019c -14247a-9613c
-3703a-1484c -5058a+13376c -1336a-1110c
-7367a+643b-6563c 10762a+10155b+14319c 4307a-8235b+12905c
-8336a+5644b-15074c 9143a-15019b+14327c -4109a+9613b+15512c
2879a+1484b-7443c 9053a-13376b-6634c 12940a+1110b-2619c
-465a+6563b -6372a-14319b 15283a-12905b
11932a+15074b 1569a-14327b -15916a-15512b
15076a+7443b -133a+6634b -14071a+2619b
11525a-1144c 13540a-1072c -10980a-7952c
-5658a+286b+8690c 3719a+268b+2616c -4829a+1988b+8796c
-13233a+1716b+11854c -11654a+1608b-15708c 15806a+11928b+11062c
-7908a-5924b 13138a+7857b 9845a-5489b-c
-1855a+8295b 3349a-587b 979a+9879b
14886a 13268a 5238a+2b
143a 134a 994a-2c
a a 14a+4b
0 0 a
-----------------------------------------------------------------------
13944b+8113c -12487b-10199c 11493b-3230c
-15777b-3330c 11605b+15016c -6460b+10930c
-1665b-9464c 7508b-2013c 5465b+9843c
4115a+3655b-13627c -7029a+11202b-9870c 9017a-13905b-10840c
-449a-96b-10941c 8793a-4578b+5692c 12920a+12644b-2954c
3330a+1715b+9216c -15016a-1300b-13233c -10930a+10268b-5069c
15777a-4893b-7101c -11605a+12873b-5446c 6460a+8643b-9990c
6660a+169b+6374c 1971a+12819b-4774c 10143a+3510b+14230c
-13075a-15829b-1522c 4026a+3036b-13463c 12317a+13207b+10645c
-10965a-3751c -1603a+15007c 9712a-3181c
288a-2428c 13734a+7603c -5929a+4719c
-5145a-3628c 3900a-15438c 1199a-5707c
-8446a+3751b-10743c -9009a-15007b-13513c 6591a+3181b-7312c
313a+2428b+14400c 8473a-7603b+6775c -1668a-4719b+6030c
-12164a+3628b-8838c -1412a+15438b-12058c 7589a+5707b+3309c
-10700a+10743b -15665a+13513b -2033a+7312b
12881a-14400b 14322a-6775b -10687a-6030b
4566a+8838b 8386a+12058b 68a-3309b
15669a-7533c 1326a-581c 14909a+11467c
4795a+9884b-8050c -4631a+8146b+11934c -5256a+5134b+3257c
-8089a-4702b+15121c -12580a-15130b-8618c 9905a-1199b+11729c
14031a+8735b-16c -10726a+4564b-15c -3338a+10320b-13c
3203a+1761b -13550a-14767b -12060a+8545b
-14327a+32b -7887a+30b -6618a+26b
4942a-30c 4073a-28c 2567a-24c
98a+60b-c 85a+56b-c 61a+48b-c
16a+3b 15a+3b 13a+3b
-----------------------------------------------------------------------
-12152b+5475c -7500b-3750c 3601b-14201c
10950b-4201c -7500b-12651c 3601b-14201c
13901b+9024c 9676b+7975c 8901b+14976c
-7699a-11453b-530c 15000a-7001b-1228c -7202a+6075b+12181c
10103a-1952b-5791c 15000a+9022b-1078c -7202a-8095b-2134c
4201a+421b-6692c 12651a+13839b+2171c 14201a+11919b+9122c
-10950a-1868b-12264c 7500a+15989b-3786c -3601a+11500b-7098c
8402a+14108b-605c -6701a-10819b-13931c -3601a+11776b+12273c
13955a+10893b+6492c -15950a-3533b+171c 2051a-3357b-13273c
2356a-10975c -11000a+10754c 13778a-13697c
5856a+9441c 4937a-6991c -7718a+6289c
-1263a+9943c -9514a-7889c -3754a+14309c
7194a+10975b-15119c -12280a-10754b+15534c -7037a+13697b+1965c
7052a-9441b-3531c 3688a+6991b+2007c 3077a-6289b+8197c
-12603a-9943b+1032c 4086a+7889b-13825c 14708a-14309b-5059c
4789a+15119b 11358a-15534b -10709a-1965b
1815a+3531b 9790a-2007b -4816a-8197b
12527a-1032b -513a+13825b 7816a+5059b
-6702a-11912c -3671a-6136c 7595a-2632c
5653a+2978b+7658c 14319a+1534b-5087c 12202a+658b+8068c
-11206a-14135b-14437c 7926a+9204b-1781c -10219a+3948b+15442c
11355a-8660b-11c -11123a-15036b-9c -10603a-7682b-7c
7062a-3129b -4014a+3562b 15609a+1119b
-2064a+22b -4353a+18b 10118a+14b
1489a-20c 767a-16c 329a-12c
41a+40b-c 25a+32b-c 13a+24b-c
11a+3b 9a+3b 7a+3b
-----------------------------------------------------------------------
0 0 0 |
0 0 0 |
8901c 0 0 |
8901b+4661c 0 0 |
-4240b-8732c 0 0 |
2077b-12513c 0 0 |
-15682b+8520c 0 0 |
-2077b+3408c 0 0 |
14201a-7189b+1704c 0 0 |
5300a+639c 0 0 |
12720a-5184c 0 0 |
-6231a-8527c -748c 0 |
1060a-639b-13516c 0 0 |
424a+5184b-4170c -374c 0 |
-4900a+8527b-1337c 748b-187c 0 |
6443a+13516b 0 0 |
-10224a+4170b 374b 0 |
-5112a+1337b 187b 0 |
-852a-824c -136c 0 |
-14238a+206b+1696c 34b+184c 0 |
213a+1236b-10236c 204b-1116c 0 |
14782a+5133b-5c 1309a+561b-3c -c |
8340a-11531b 748a+2232b 0 |
2674a+10b 374a+6b 2b |
103a-8c 17a-4c -c |
5a+16b-c a+8b-c 2b-c |
5a+3b 3a+3b a+3b |
27 24
o28 : Matrix R <-- R
|
i29 : f3 = pieri({4,3,3},{3,3,3},R)
o29 = | -20c3 -15c3 0 |
| 60bc2 45bc2 0 |
| -60b2c -45b2c 0 |
| 20b3 15b3 0 |
| 20c3 20c3 0 |
| -48ac2-48bc2 -36ac2-48bc2 3c3 |
| 96abc+36b2c 72abc+36b2c -6bc2 |
| -48ab2-8b3 -36ab2-8b3 3b2c |
| 48ac2-12bc2 36ac2-12bc2 2c3 |
| -96abc+24b2c -72abc+24b2c -9bc2 |
| 48ab2-12b3 36ab2-12b3 12b2c |
| 0 0 -5b3 |
| 90ac2 90ac2 0 |
| 72a2c-108abc 54a2c-108abc 18ac2 |
| 24a2b+24ab2 18a2b+24ab2 -9abc |
| 288a2c-72abc 216a2c-72abc 27ac2 |
| -144a2b+36ab2 -108a2b+36ab2 -36abc |
| 0 0 15ab2 |
| 60a2c 60a2c 0 |
| 16a3-24a2b 12a3-24a2b 9a2c |
| 144a3-36a2b 108a3-36a2b 36a2c |
| 0 0 -15a2b |
| 5a3 5a3 0 |
| 0 0 5a3 |
24 3
o29 : Matrix R <-- R
|
i30 : f2 = map(source f1,,f2)
o30 = | 6986b+4510c -1451b-7220c 13064b+9527c
| 9020b-10741c -14440b+3016c -12949b-15317c
| 10631b+2953c 1508b+10808c 8343b+684c
| -13972a+14166b+3105c 2902a-9397b-5451c 5875a-5254b+4348c
| 13963a+923b+2263c -3123a-12640b-10200c -6105a-4110b+15487c
| 10741a+10088b-320c -3016a+9732b+14476c 15317a-12189b+420c
| -9020a+11176b+3043c 14440a-8058b-7439c 12949a-14861b+15883c
| -10521a-8004b-15157c -6032a+14786b+14710c -1369a-8099b+10532c
| -5906a-3207b+8650c 10387a-12207b+8371c -1368a+7689b+1079c
| -10495a-11636c -3812a-11660c 15762a-3966c
| -2769a+2034c 5917a+2034c 12330a+1147c
| 1739a+15880c 2807a+15880c 4564a+13355c
| -10840a+11636b-13565c 8524a+11660b-13565c -464a+3966b+11577c
| -14780a-2034b+11327c -13758a-2034b+11327c 9839a-1147b-4667c
| 10581a-15880b-270c -6807a-15880b-270c 7676a-13355b-10233c
| -9129a+13565b -9686a+13565b -15646a-11577b
| 13468a-11327b -12127a-11327b 407a+4667b
| 6053a+270b 6890a+270b -3237a+10233b
| 4847a-24c 4879a-24c 5288a-1392c
| -7163a+6b+2034c -7163a+6b+2034c 11569a+348b-2296c
| -6907a+36b-12204c -6907a+36b-12204c 7702a+2088b+13764c
| 15134a+6102b 15134a+6102b 9647a-6879b
| 9349a-7595b 9349a-7595b 9334a+4475b
| 540a 540a -11537a
| 3a 3a 174a
| 0 0 a
| 0 0 0
-----------------------------------------------------------------------
-15183b-7919c 4969b-6623c 15163b-9429c
-15838b-4094c -13246b+10515c 13145b-2015c
-2047b-12069c -10744b-5499c 14994b+30c
-1637a+7830b-12120c -9938a+8975b+14045c 1677a-13275b-6277c
-327a-10408b+12432c -5511a+13349b+6604c 5713a+7996b-3832c
4094a+11292b-3503c -10515a+11413b+7642c 2015a+15497b+8124c
15838a+8628b-15635c 13246a+7935b-12479c -13145a-7455b+907c
8188a+10885b-5888c 10973a-8736b+10767c 4030a+4637b+4339c
-7865a+13337b+7255c 10998a+12255b+10478c -60a+7193b-12886c
8513a+14347c 5078a+11453c 7822a-12082c
-779a-299c -8044a-4319c 8015a-8243c
-1873a+13436c -2236a-2363c -14488a+13760c
10476a-14347b-648c -1934a-11453b+1094c 9193a+12082b-15937c
-5945a+299b+9117c 6396a+4319b+11574c -2415a+8243b+247c
2501a-13436b-10053c 4315a+2363b-9603c -13948a-13760b-9333c
14902a+648b 5434a-1094b -2721a+15937b
-14339a-9117b -298a-11574b -13017a-247b
10238a+10053b 569a+9603b 6655a+9333b
2206a-1376c -4603a-1336c -5226a-1312c
-15636a+344b-3652c -3539a+334b-7042c 4100a+328b-9076c
1595a+2064b-10103c 2131a+2004b+10237c 8114a+1968b-9562c
-11110a-10947b -14998a+10886b 1871a+4784b
13769a-11797b 8855a+11529b -494a-12879b
-11897a -12797a -13337a
172a 167a 164a
a a a
0 0 0
-----------------------------------------------------------------------
-15488b-2190c -6016b-15512c -10796b-3322c
-4380b+3603c 979b+8643c -6644b+13540c
-14200b+3911c -11680b+13264c 6770b+594c
-1027a+13161b+1107c 12032a+12462b+8085c -10411a-8151b+73c
8760a-6030b+5120c -1958a+13732b+1140c 13288a+11081b+15412c
-3603a+3224b-8085c -8643a+188b+1322c -13540a-146b+14592c
4380a-11259b+3888c -979a+4428b-194c 6644a+474b-7998c
-7206a+9104b+401c 14717a-1152b-7492c 4923a+303b+6218c
-7822a+12344b+6148c 5475a-6280b-1448c -1188a+13369b-8693c
-7480a-6710c -5383a-4866c -7550a-6982c
-13913a-13787c -9193a+11052c -1240a+2268c
-9672a-2120c -564a+14003c 438a-1877c
-1547a+6710b+241c -5536a+4866b-14378c -1641a+6982b+4212c
-10669a+13787b-11080c 36a-11052b+9596c -15142a-2268b-1731c
-12777a+2120b-9063c 14874a-14003b-8793c 12126a+1877b-8523c
-11664a-241b 582a+14378b -8009a-4212b
-1203a+11080b -9527a-9596b 13349a+1731b
13559a+9063b 4344a+8793b -5924a+8523b
-1721a-1288c 6488a-1264c -12026a-1240c
12147a+322b-11110c -11401a+316b-13144c -2538a+310b-15178c
13305a+1932b+2642c -14299a+1896b+14846c -10692a+1860b-4953c
-13263a-1318b 3606a-7420b -11528a-13522b
-9843a-5284b 12811a+2311b 3462a+9906b
-13877a -14417a -14957a
161a 158a 155a
a a a
0 0 0
-----------------------------------------------------------------------
-5877b-6258c -8813b-14176c 9247b+1060c
-12516b+12885c 3651b-8309c 2120b+10717c
-9559b+5151c 11847b-9902c -10643b+15903c
11754a-5269b-13526c -14377a+10506b-6944c 13509a+1070b-4108c
-6971a-4888b+6606c -7302a-12365b+14458c -4240a+14466b-7935c
-12885a-6457b+8767c 8309a+3644b+324c -10717a+5242b+6182c
12516a-12283b+15786c -3651a+11342b+59c -2120a-2088b-1550c
6233a+12052b+3081c -15385a-7052b+12629c 10569a+15319b+7046c
-10302a+5928b+11394c -12199a+1309b-9825c 197a-13808b+9463c
15807a-13490c 485a+7187c -3210a-5592c
14664a-8136c 5092a+11835c -11395a-9899c
-12632a+14246c -10932a-1634c -15726a+14484c
13421a+13490b-7995c -13194a-7187b+13013c -13415a+5592b+9233c
8032a+8136b-13058c 9785a-11835b+7618c 9851a+9899b-3711c
-12082a-14246b-8253c -4899a+1634b-7983c -9125a-14484b-7713c
-15355a+7995b -177a-13013b 4650a-9233b
-9243a+13058b -5884a-7618b 10865a+3711b
-2179a+8253b -2528a+7983b 3614a+7713b
7319a-1216c 1085a-1192c 7456a-1168c
6733a+304b+14791c -15589a+298b+12757c -3462a+292b+10723c
-7877a+1824b+7251c -5858a+1788b-12548c -8567a+1752b-344c
5341a+12379b -9793a+6277b 7084a+175b
-5887a-14502b -15236a-6907b 7422a+688b
-15497a 15966a 15426a
152a 149a 146a
a a a
0 0 0
-----------------------------------------------------------------------
8346b+14184c -9595b+9348c -13631b+10629c
-3635b+3555c -13307b+15643c -10745b+3953c
-14224b+9547c -8180b+3540c -14025b-10748c
15311a+7734b-3965c -12813a+9990b-9574c -4741a+2846b+13893c
7270a-8118b+15295c -5389a-15886b+2496c -10513a+4749b+11970c
-3555a+11902b-6621c -15643a+1686b+83c -3953a+11113b-5917c
3635a-4247b+155c 13307a-4681b+2124c 10745a-4661b-15762c
-7110a+8819b-14645c 717a+5124b-523c -7906a+10735b+15973c
12909a-15674b-15693c -7080a+7567b+10712c -10507a-9064b+15358c
8801a-643c 2033a-10155c -8538a+8235c
-7649a-5644c 15655a+15019c -14247a-9613c
-3703a-1484c -5058a+13376c -1336a-1110c
-7367a+643b-6563c 10762a+10155b+14319c 4307a-8235b+12905c
-8336a+5644b-15074c 9143a-15019b+14327c -4109a+9613b+15512c
2879a+1484b-7443c 9053a-13376b-6634c 12940a+1110b-2619c
-465a+6563b -6372a-14319b 15283a-12905b
11932a+15074b 1569a-14327b -15916a-15512b
15076a+7443b -133a+6634b -14071a+2619b
11525a-1144c 13540a-1072c -10980a-7952c
-5658a+286b+8690c 3719a+268b+2616c -4829a+1988b+8796c
-13233a+1716b+11854c -11654a+1608b-15708c 15806a+11928b+11062c
-7908a-5924b 13138a+7857b 9845a-5489b-c
-1855a+8295b 3349a-587b 979a+9879b
14886a 13268a 5238a+2b
143a 134a 994a-2c
a a 14a+4b
0 0 a
-----------------------------------------------------------------------
13944b+8113c -12487b-10199c 11493b-3230c
-15777b-3330c 11605b+15016c -6460b+10930c
-1665b-9464c 7508b-2013c 5465b+9843c
4115a+3655b-13627c -7029a+11202b-9870c 9017a-13905b-10840c
-449a-96b-10941c 8793a-4578b+5692c 12920a+12644b-2954c
3330a+1715b+9216c -15016a-1300b-13233c -10930a+10268b-5069c
15777a-4893b-7101c -11605a+12873b-5446c 6460a+8643b-9990c
6660a+169b+6374c 1971a+12819b-4774c 10143a+3510b+14230c
-13075a-15829b-1522c 4026a+3036b-13463c 12317a+13207b+10645c
-10965a-3751c -1603a+15007c 9712a-3181c
288a-2428c 13734a+7603c -5929a+4719c
-5145a-3628c 3900a-15438c 1199a-5707c
-8446a+3751b-10743c -9009a-15007b-13513c 6591a+3181b-7312c
313a+2428b+14400c 8473a-7603b+6775c -1668a-4719b+6030c
-12164a+3628b-8838c -1412a+15438b-12058c 7589a+5707b+3309c
-10700a+10743b -15665a+13513b -2033a+7312b
12881a-14400b 14322a-6775b -10687a-6030b
4566a+8838b 8386a+12058b 68a-3309b
15669a-7533c 1326a-581c 14909a+11467c
4795a+9884b-8050c -4631a+8146b+11934c -5256a+5134b+3257c
-8089a-4702b+15121c -12580a-15130b-8618c 9905a-1199b+11729c
14031a+8735b-16c -10726a+4564b-15c -3338a+10320b-13c
3203a+1761b -13550a-14767b -12060a+8545b
-14327a+32b -7887a+30b -6618a+26b
4942a-30c 4073a-28c 2567a-24c
98a+60b-c 85a+56b-c 61a+48b-c
16a+3b 15a+3b 13a+3b
-----------------------------------------------------------------------
-12152b+5475c -7500b-3750c 3601b-14201c
10950b-4201c -7500b-12651c 3601b-14201c
13901b+9024c 9676b+7975c 8901b+14976c
-7699a-11453b-530c 15000a-7001b-1228c -7202a+6075b+12181c
10103a-1952b-5791c 15000a+9022b-1078c -7202a-8095b-2134c
4201a+421b-6692c 12651a+13839b+2171c 14201a+11919b+9122c
-10950a-1868b-12264c 7500a+15989b-3786c -3601a+11500b-7098c
8402a+14108b-605c -6701a-10819b-13931c -3601a+11776b+12273c
13955a+10893b+6492c -15950a-3533b+171c 2051a-3357b-13273c
2356a-10975c -11000a+10754c 13778a-13697c
5856a+9441c 4937a-6991c -7718a+6289c
-1263a+9943c -9514a-7889c -3754a+14309c
7194a+10975b-15119c -12280a-10754b+15534c -7037a+13697b+1965c
7052a-9441b-3531c 3688a+6991b+2007c 3077a-6289b+8197c
-12603a-9943b+1032c 4086a+7889b-13825c 14708a-14309b-5059c
4789a+15119b 11358a-15534b -10709a-1965b
1815a+3531b 9790a-2007b -4816a-8197b
12527a-1032b -513a+13825b 7816a+5059b
-6702a-11912c -3671a-6136c 7595a-2632c
5653a+2978b+7658c 14319a+1534b-5087c 12202a+658b+8068c
-11206a-14135b-14437c 7926a+9204b-1781c -10219a+3948b+15442c
11355a-8660b-11c -11123a-15036b-9c -10603a-7682b-7c
7062a-3129b -4014a+3562b 15609a+1119b
-2064a+22b -4353a+18b 10118a+14b
1489a-20c 767a-16c 329a-12c
41a+40b-c 25a+32b-c 13a+24b-c
11a+3b 9a+3b 7a+3b
-----------------------------------------------------------------------
0 0 0 |
0 0 0 |
8901c 0 0 |
8901b+4661c 0 0 |
-4240b-8732c 0 0 |
2077b-12513c 0 0 |
-15682b+8520c 0 0 |
-2077b+3408c 0 0 |
14201a-7189b+1704c 0 0 |
5300a+639c 0 0 |
12720a-5184c 0 0 |
-6231a-8527c -748c 0 |
1060a-639b-13516c 0 0 |
424a+5184b-4170c -374c 0 |
-4900a+8527b-1337c 748b-187c 0 |
6443a+13516b 0 0 |
-10224a+4170b 374b 0 |
-5112a+1337b 187b 0 |
-852a-824c -136c 0 |
-14238a+206b+1696c 34b+184c 0 |
213a+1236b-10236c 204b-1116c 0 |
14782a+5133b-5c 1309a+561b-3c -c |
8340a-11531b 748a+2232b 0 |
2674a+10b 374a+6b 2b |
103a-8c 17a-4c -c |
5a+16b-c a+8b-c 2b-c |
5a+3b 3a+3b a+3b |
27 24
o30 : Matrix R <-- R
|
i31 : f3 = map(source f2,,f3)
o31 = {1} | -20c3 -15c3 0 |
{1} | 60bc2 45bc2 0 |
{1} | -60b2c -45b2c 0 |
{1} | 20b3 15b3 0 |
{1} | 20c3 20c3 0 |
{1} | -48ac2-48bc2 -36ac2-48bc2 3c3 |
{1} | 96abc+36b2c 72abc+36b2c -6bc2 |
{1} | -48ab2-8b3 -36ab2-8b3 3b2c |
{1} | 48ac2-12bc2 36ac2-12bc2 2c3 |
{1} | -96abc+24b2c -72abc+24b2c -9bc2 |
{1} | 48ab2-12b3 36ab2-12b3 12b2c |
{1} | 0 0 -5b3 |
{1} | 90ac2 90ac2 0 |
{1} | 72a2c-108abc 54a2c-108abc 18ac2 |
{1} | 24a2b+24ab2 18a2b+24ab2 -9abc |
{1} | 288a2c-72abc 216a2c-72abc 27ac2 |
{1} | -144a2b+36ab2 -108a2b+36ab2 -36abc |
{1} | 0 0 15ab2 |
{1} | 60a2c 60a2c 0 |
{1} | 16a3-24a2b 12a3-24a2b 9a2c |
{1} | 144a3-36a2b 108a3-36a2b 36a2c |
{1} | 0 0 -15a2b |
{1} | 5a3 5a3 0 |
{1} | 0 0 5a3 |
24 3
o31 : Matrix R <-- R
|
i32 : f1 * f2
o32 = | 3253a3+5047a2b-1601ab2-12426b3+6717a2c+6959abc-4464b2c-5683ac2-3930bc
| 267a3+9095a2b-93ab2-14086b3-11447a2c-14714abc-2149b2c-10471ac2+11716b
| 11576a3-10838a2b-12579ab2+2734b3-10134a2c+10361abc+8410b2c-4926ac2+11
| 5577a3+971a2b-1520ab2-8124b3-4824a2c-9075abc-15841b2c+11537ac2-12867b
| -299a3+4752a2b+10383ab2+11115b3+4920a2c-2145abc-1583b2c+212ac2-5152bc
| 6023a3-1770a2b-15405ab2+9867b3+15602a2c+5903abc-1371b2c+12587ac2+6444
-----------------------------------------------------------------------
2-6379c3 -10844a3+10340a2b+4202ab2+15438b3+4976a2c-2293abc-13300b2c
c2+12911c3 -8459a3-14651a2b-7616ab2+7859b3+2835a2c+9117abc+3093b2c-15
220bc2-826c3 6483a3-6927a2b+8397ab2+10240b3+8686a2c+4987abc+13256b2c+58
c2-8831c3 15419a3+15273a2b+7039ab2-3395b3+5236a2c+15383abc-4577b2c+4
2+3108c3 -1568a3+13761a2b-5619ab2-7923b3-14571a2c-7211abc+13872b2c+
bc2+863c3 11655a3-12102a2b-7669ab2+10011b3+6370a2c-15951abc-1371b2c+
-----------------------------------------------------------------------
-11659ac2+15014bc2+4334c3
798ac2-9663bc2+15851c3
24ac2+12168bc2+11899c3
216ac2+6510bc2+3985c3
3274ac2-14865bc2+14248c3
2941ac2+6444bc2+863c3
-----------------------------------------------------------------------
-12893a3+11254a2b+9293ab2
-13273a3-9154a2b-2421ab2-
-8742a3-10835a2b-12394ab2
1057a3+15620a2b+10655ab2-
-2510a3+12559a2b-8149ab2+
9381a3-10179a2b+11313ab2-
-----------------------------------------------------------------------
+6315b3+6513a2c+8291abc+5745b2c+1999ac2+7067bc2-15927c3
11012b3-11023a2c-1747abc+4939b2c-1254ac2+2368bc2-15065c3
+14008b3+7277a2c+15288abc-15126b2c-14357ac2-11433bc2-14903c3
12440b3-12125a2c-8473abc-13417b2c+10782ac2-10863bc2+7756c3
2209b3-7337a2c-15633abc+13837b2c+7241ac2-11889bc2-12698c3
8922b3+4063a2c+13041abc-6571b2c+15768ac2-13383bc2-4824c3
-----------------------------------------------------------------------
10432a3-6305a2b-8548ab2-683b3+8196a2c-2128abc-8250b2c+12467ac2-6360bc2+
13831a3+7064a2b-11476ab2-11340b3+1496a2c-11410abc-307b2c+14972ac2+7752b
7519a3+11323a2b+8321ab2-13808b3+15193a2c-443abc-14102b2c+15854ac2-15195
-7764a3+15894a2b+2935ab2-11060b3+9707a2c-2953abc+15212b2c-3471ac2-3332b
11581a3-708a2b+8334ab2-4803b3+7982a2c+15687abc-243b2c-5403ac2-9747bc2+6
-5351a3+544a2b-10469ab2+5548b3-3586a2c+15343abc-4634b2c-1317ac2+14347bc
-----------------------------------------------------------------------
11673c3 14229a3-5657a2b
c2+13183c3 8899a3-7400a2b+
bc2+12224c3 2407a3-6580a2b+
c2-15634c3 4425a3-11834a2b
7c3 9232a3-15000a2b
2+15936c3 7646a3+11764a2b
-----------------------------------------------------------------------
-731ab2-11568b3-7671a2c-13273abc-8756b2c+1366ac2-5118bc2-1302c3
1534ab2-4742b3+537a2c+8801abc-3226b2c+9844ac2+3689bc2-6585c3
568ab2-5261b3-5882a2c-15147abc-6891b2c+5926ac2+3281bc2+6489c3
-10836ab2+10920b3-6937a2c-2897abc-7641b2c+14895ac2-7544bc2-12339c3
-14636ab2+6196b3+16a2c-5212abc+9336b2c+3599ac2-4423bc2+15238c3
+10992ab2+9435b3-11569a2c-143abc+4812b2c+9342ac2+3768bc2+3830c3
-----------------------------------------------------------------------
7671a3+4827a2b+879ab2-14812b3+14268a2c+11388abc+6628b2c-10653ac2+9294bc
1163a3-14544a2b-925ab2-12106b3+11335a2c+15325abc-14257b2c-8917ac2-14630
-2226a3+4183a2b+10664ab2-9775b3+6707a2c-1362abc-7235b2c-15270ac2-11936b
-6935a3+8207a2b-5528ab2+1688b3+2610a2c+15332abc+14151b2c+11188ac2+2890b
15556a3-11286a2b+7548ab2-3982b3-367a2c-2865abc+4109b2c+1307ac2-14871bc2
14355a3+9489a2b-985ab2-1570b3-8034a2c+8065abc-4337b2c-1728ac2-2193bc2+2
-----------------------------------------------------------------------
2-7463c3 12906a3+12736a2b+7065ab2
bc2+5399c3 -4058a3-9133a2b+7088ab2-
c2+3947c3 -10475a3+6079a2b-6788ab2
c2+7298c3 -13796a3-9895a2b-9911ab2
-9516c3 13371a3+9285a2b-2923ab2-
967c3 7519a3-12292a2b-12788ab2
-----------------------------------------------------------------------
+15342b3+11045a2c-14954abc-8387b2c-355ac2-3169bc2-9756c3
7990b3-10773a2c+1218abc+6606b2c+2722ac2+7937bc2+7435c3
-15739b3-2385a2c+2010abc+11769b2c+4234ac2-3177bc2-5692c3
+10102b3-11040a2c+9420abc-135b2c-1329ac2-15303bc2-8515c3
1106b3-2079a2c-9751abc-12049b2c+5151ac2-14552bc2-10484c3
-11267b3-10778a2c-15745abc+4928b2c+4703ac2-7740bc2+2104c3
-----------------------------------------------------------------------
5650a3+5484a2b-7668ab2+10288b3+3029a2c+670abc-11707b2c+14062ac2+4403bc2
-1210a3-2881a2b+3550ab2+12803b3+945a2c+11551abc+12875b2c-1289ac2+3636bc
10599a3-12691a2b-8232ab2+14005b3+3182a2c-14925abc+15614b2c-4736ac2-1463
4235a3-6922a2b+6616ab2+10735b3-3296a2c+3614abc-2633b2c-3554ac2-7006bc2+
-15506a3-11539a2b+4278ab2+15942b3+2475a2c-11680abc+7820b2c-14465ac2-734
-8649a3-14167a2b-2321ab2+14939b3+8326a2c-15416abc+604b2c+15028ac2-12873
-----------------------------------------------------------------------
+13213c3 -2353a3-15525a2b+13178ab2+8936b3+5483a2c-12960abc-11958b2c+
2-1472c3 5807a3+487a2b-7366ab2-8686b3-1836a2c-4182abc-9678b2c+4991ac
4bc2-7958c3 -9966a3+2858a2b-4076ab2-2761b3-4878a2c-12583abc+5833b2c-255
2873c3 8957a3+11679a2b-15648ab2-2245b3+3892a2c-14493abc+8661b2c-66
7bc2+1602c3 -15113a3+3397a2b+8533ab2+11354b3+11895a2c+2805abc-5733b2c+5
bc2+1241c3 -13746a3+3192a2b-13762ab2+15634b3-12432a2c-8571abc+14694b2c
-----------------------------------------------------------------------
12671ac2+15570bc2+2596c3
2+12477bc2-9719c3
0ac2-9414bc2+14942c3
22ac2+20bc2+10764c3
237ac2+7282bc2+5180c3
-15517ac2+14411bc2+378c3
-----------------------------------------------------------------------
-13868a3-4297a2b+2974ab2-6824b3-6079a2c-9352abc-9913b2c+49ac2+12922bc2+
15301a3+12293a2b-14636ab2-12572b3+14418a2c+9548abc+14285b2c+7799ac2+271
-15968a3+5103a2b-15086ab2-14693b3-8694a2c+5856abc+10687b2c+8471ac2+1079
-9344a3+15556a2b+7793ab2+6852b3-8467a2c+10046abc-2755b2c+12556ac2+13704
241a3+10771a2b-4401ab2+4454b3+8570a2c-14136abc-1276b2c-4367ac2-7818bc2-
-15064a3-9475a2b-15076ab2-6590b3+12675a2c-6167abc+15195b2c+11304ac2+101
-----------------------------------------------------------------------
10004c3 -3290a3-13425a2b-4342ab2+7276b3-6779a2c+
4bc2+13919c3 6190a3-5185a2b+7550ab2+12249b3+11643a2c-
7bc2+12958c3 -14630a3+63a2b-10355ab2+12513b3-1086a2c-
bc2-5092c3 11510a3-1757a2b-13134ab2-2031b3-6080a2c-
9127c3 -6042a3-9830a2b+6158ab2-3094b3-14827a2c+
06bc2-485c3 -9123a3+191a2b-11126ab2-15398b3-14699a2c
-----------------------------------------------------------------------
2901abc-6364b2c+8832ac2-10473bc2-10420c3
12201abc-10924b2c-4203ac2+15873bc2+3674c3
15127abc+3205b2c-2029ac2+5637bc2+13024c3
80abc-2931b2c+1075ac2+2276bc2-12480c3
11833abc+9897b2c+5373ac2-5717bc2+14146c3
-9472abc+2197b2c+3717ac2+6217bc2-1348c3
-----------------------------------------------------------------------
-8012a3+4342a2b-3093ab2-1300b3-7823a2c-8326abc+5125b2c-7611ac2-3781bc2-
2144a3-10955a2b+8130ab2+14568b3-10249a2c-9343abc-10688b2c+3489ac2-1212b
-3559a3+14046a2b+15269ab2+7582b3+10327a2c+11878abc-6114b2c+12224ac2-614
9309a3-4576a2b+298ab2-4786b3-13038a2c-6878abc-14214b2c-14461ac2-117bc2+
-12075a3-5922a2b+6244ab2-4842b3-12375a2c-4435abc+3871b2c-5036ac2-2895bc
1423a3-5688a2b+12657ab2-15545b3-8719a2c-3591abc+2186b2c+9826ac2+4768bc2
-----------------------------------------------------------------------
15124c3 -12193a3+8854a2b+2142ab2+14078b3+2728a2c-9601abc-12831b2c+2
c2+6997c3 -323a3-7291a2b-13103ab2+12554b3+5771a2c+7057abc+15111b2c-56
7bc2+9397c3 8094a3-3742a2b-13325ab2-2931b3-14207a2c+15902abc+3966b2c-11
10903c3 -1435a3+9142a2b+10638ab2-3574b3+13837a2c+12959abc+10780b2c+
2-9339c3 -9513a3+4720a2b-6329ab2+1728b3+13726a2c-6042abc+12552b2c-74
-2213c3 4047a3-6300a2b-2637ab2+3796b3+997a2c+4811abc+5169b2c-10303a
-----------------------------------------------------------------------
514ac2-3367bc2-4049c3
22ac2-13413bc2-4512c3
733ac2+9698bc2+9857c3
13503ac2-3238bc2-3017c3
40ac2-14165bc2-2035c3
c2-11575bc2-3117c3
-----------------------------------------------------------------------
13323a3-1873a2b+5179ab2+15531b3-2685a2c-549abc+3779b2c+5846ac2+14768bc2
11894a3+12256a2b-4976ab2+15861b3-4991a2c+2617abc-10062b2c+9698ac2+4312b
-1179a3+13369a2b+6846ab2+1067b3+4241a2c+14428abc+8485b2c+10751ac2-2797b
2277a3+387a2b-2835ab2+4249b3+7407a2c-12988abc-14540b2c-11889ac2-5823bc2
-991a3+15960a2b+4943ab2+2131b3-14798a2c-11947abc-13658b2c+15863ac2-7111
291a3+12162a2b-13458ab2+124b3-9892a2c+8079abc-4451b2c-15530ac2+8043bc2-
-----------------------------------------------------------------------
-8771c3 13479a3-2673a2b+8186ab2-7869b3-6472a2c+4045abc+9313b2c-10778
c2+348c3 1191a3+14474a2b+3119ab2+3625b3-2603a2c+4966abc+11921b2c+1251
c2-7585c3 -14967a3-4339a2b+9699ab2-2730b3+2157a2c-13109abc+11927b2c+40
-1840c3 -6819a3+12142a2b-2172ab2+3448b3-2571a2c-2685abc+13957b2c-151
bc2-6084c3 -5032a3+5168a2b+3912ab2+4394b3-4291a2c-2358abc-388b2c-3471ac
6471c3 -12663a3+10566a2b+8887ab2+10773b3-975a2c-1605abc+6359b2c-102
-----------------------------------------------------------------------
ac2-9874bc2+14937c3
9ac2-14658bc2-1402c3
85ac2+12262bc2-15188c3
88ac2+2238bc2-3094c3
2-13714bc2-4572c3
98ac2+686bc2-7207c3
-----------------------------------------------------------------------
13168a3+786a2b+13215ab2+5939b3+8856a2c-12310abc-9093b2c-4497ac2+15683bc
805a3-14218a2b+11609ab2-403b3-9697a2c+4951abc-1903b2c+15458ac2-4805bc2-
1194a3+5762a2b+12765ab2+3415b3+2489a2c+4864abc+2150b2c-9933ac2-1342bc2-
3864a3+2859a2b+11409ab2-12452b3-731a2c-10818abc+14326b2c-7744ac2+14185b
-3087a3+14005a2b-8485ab2-4328b3+1747a2c-2169abc-12619b2c-6276ac2+2294bc
13527a3+14393a2b-10837ab2-3763b3+7557a2c+3547abc+13651b2c+11653ac2+3742
-----------------------------------------------------------------------
2-9242c3 2206a3+5191a2b+3792ab2+12204b3-2642a2c-11609abc-3522b2c+6597
6518c3 -15326a3-3718a2b+14495ab2+15256b3-7099a2c-4043abc-13729b2c-6
7123c3 7514a3+436a2b-14241ab2+14798b3+6510a2c-12122abc-2128b2c+1247
c2-6792c3 13822a3-7511a2b+3419ab2-13285b3+2645a2c+2104abc-2951b2c+443a
2-2364c3 10294a3-11777a2b-691ab2+12756b3+14535a2c-14905abc-10428b2c+3
bc2+5053c3 -13160a3+13348a2b-11663ab2+6603b3+5647a2c+1762abc-351b2c-497
-----------------------------------------------------------------------
ac2-8682bc2-7612c3
174ac2-11643bc2-12072c3
8ac2-6741bc2-9805c3
c2+11334bc2-12747c3
316ac2+12116bc2+12228c3
1ac2+3851bc2-2592c3
-----------------------------------------------------------------------
1490a3-7028a2b-867ab2+15524b3-15341a2c
-1064a3+9823a2b-5852ab2-8089b3+8359a2c
6548a3-6654a2b-5503ab2+15986b3+136a2c-
-7792a3-11541a2b+437ab2+2978b3-7578a2c
15813a3-9657a2b-6303ab2-6330b3+9805a2c
1953a3+858a2b+15816ab2+4986b3+9192a2c-
-----------------------------------------------------------------------
+10883abc+5463b2c-810ac2+10379bc2+7684c3
+10828abc+10341b2c-10325ac2-12190bc2-15790c3
14927abc+4275b2c+8500ac2-5614bc2-13485c3
+3393abc-8394b2c+12776ac2-4378bc2-11814c3
+14185abc-5099b2c+2659ac2-714bc2+13689c3
5886abc-7448b2c+5621ac2-4641bc2+3751c3
-----------------------------------------------------------------------
-14618a3+5980a2b-8488ab2+9007b3+7300a2c-4212abc-679b2c-10439ac2+13602bc
-10529a3-12894a2b+1116ab2-7308b3+13622a2c+15225abc+11997b2c+11361ac2+12
-13229a3+9124a2b-2252ab2-9649b3-12812a2c+12094abc+4646b2c+10714ac2+7719
15887a3+14099a2b+6519ab2+14350b3-6307a2c-13167abc+4278b2c+2762ac2+7172b
-4201a3-15945a2b+9210ab2+2519b3-15231a2c-14362abc-2581b2c+14925ac2-6448
2504a3-160a2b-487ab2-615b3+940a2c+11163abc+1273b2c+8254ac2+10632bc2+107
-----------------------------------------------------------------------
2+10226c3 10049a3-14286a2b
823bc2-12909c3 -5069a3+5393a2b-
bc2+11052c3 14871a3+4636a2b-
c2-11151c3 12876a3-4698a2b-
bc2-15150c3 -11577a3-5736a2b
81c3 10625a3-14342a2b
-----------------------------------------------------------------------
+11005ab2-13930b3-1058a2c+9559abc-3698b2c+8326ac2-5257bc2-7889c3
8502ab2-1087b3-3595a2c+2865abc+4407b2c+4457ac2-15699bc2+15492c3
11213ab2-8339b3+10251a2c+14831abc+13739b2c+6731ac2+15350bc2+298c3
13580ab2-9883b3-2577a2c-35abc+1265b2c+13376ac2-2844bc2+9988c3
-9028ab2+1370b3+12545a2c+14902abc-2735b2c-13701ac2+11920bc2-10797c3
+2064ab2-11826b3-5008a2c+1660abc-14605b2c+4693ac2+11824bc2+7155c3
-----------------------------------------------------------------------
-13610a3+4417a2b-5385ab2-1174b3-7698a2c+5290abc-8615b2c-3373ac2-178bc2-
6546a3-10112a2b+4114ab2+9977b3-3918a2c-5632abc+5684b2c-13949ac2+6130bc2
-10040a3-13438a2b-1613ab2-7103b3+8760a2c-5258abc-11467b2c+10352ac2+926b
7298a3+13745a2b+474ab2-7454b3+13945a2c+8819abc-2848b2c+2002ac2-14025bc2
13822a3+10660a2b+1494ab2+4950b3+1046a2c-3780abc+3631b2c-9126ac2-14046bc
-14049a3+2458a2b-15382ab2+2871b3+15070a2c+10050abc+8655b2c+6431ac2+1235
-----------------------------------------------------------------------
10789c3 2535a3-473a2b+9322ab2+7574b3+1243a2c-3242abc-3058b2c+4676ac
+6655c3 9239a3-14867a2b-11414ab2+3128b3+15678a2c+1410abc-330b2c-731
c2-15613c3 7124a3-13944a2b-7560ab2+2728b3-6872a2c+14114abc-7155b2c+142
-2394c3 -4869a3-2380a2b+15526ab2+4547b3-9399a2c+9740abc+10443b2c+14
2+1470c3 -2959a3+10334a2b+14997ab2+11856b3+416a2c-777abc-12168b2c+64
4bc2-8007c3 -9794a3-14999a2b+230ab2-2656b3+1294a2c+11721abc-14178b2c+52
-----------------------------------------------------------------------
2-12956bc2+9434c3
4ac2-1741bc2-15645c3
90ac2+6585bc2+14317c3
865ac2-8765bc2-2036c3
00ac2-11550bc2+4668c3
83ac2+10044bc2-14885c3
-----------------------------------------------------------------------
14677a3+1508a2b-5369ab2+15800b3-5266a2c-6770abc-
6816a3-3106a2b+14665ab2-14894b3-7378a2c+2323abc+
12892a3+11448a2b+1861ab2-3997b3+3432a2c-8070abc+
-2857a3+14361a2b+3505ab2+5812b3+3174a2c+4496abc+
-4180a3-1058a2b+3822ab2-14641b3+15496a2c+3527abc
-13752a3-7719a2b-2773ab2+13012b3+5821a2c+5315abc
-----------------------------------------------------------------------
6318b2c-10093ac2-4920bc2+15992c3
4675b2c+15268ac2-10292bc2+8404c3
6380b2c-102ac2-14388bc2-13468c3
14777b2c-9399ac2-7061bc2+3990c3
-12509b2c-5926ac2-3472bc2+2266c3
-7909b2c+11529ac2-7783bc2-1637c3
-----------------------------------------------------------------------
6487a2b+6487ab2+7698b3+2422a2c+3657abc+2707b2c-11250ac2-12515bc2+5297c3
8933a2b+6349ab2-6721b3-4365a2c-12064abc+11162b2c+836ac2-4416bc2+3297c3
-11352a2b-14353ab2-2032b3-5655a2c+11413abc+6542b2c+13931ac2+8078bc2+424
3879a2b-10172ab2+8007b3-985a2c+11878abc-893b2c+3038ac2+2170bc2-6584c3
-4062a2b+2410ab2+852b3+6984a2c-3105abc+4412b2c-650ac2-4214bc2+8925c3
13212a2b+5008ab2+1283b3-13919a2c+47abc-977b2c-191ac2-48bc2-3c3
-----------------------------------------------------------------------
|
|
2c3 |
|
|
|
6 24
o32 : Matrix R <-- R
|
i33 : f2 * f3
o33 = | 14508a3b-14796a2b2-14848ab3+10239b4+7254a3c-7562a2bc-10217ab2c-2502b3
| 14508a3b+9541a2b2+129ab3+15632b4-7150a3c+15121a2bc+7611ab2c+11536b3c+
| -3575a3b+13774a2b2+6885ab3+6345b4+11931a3c-4949a2bc+11480ab2c+2274b3c
| 2987a4-7699a3b+2383a2b2+5177ab3-5162b4-1084a3c-13260a2bc-7417ab2c-921
| 2987a4+15689a3b+15764a2b2+9374ab3-9621b4-11663a3c-9755a2bc-5526ab2c+1
| 7150a4-9968a3b-1048a2b2-10926ab3-11410b4-7027a3c+11968a2bc+7672ab2c-1
| -14508a4+14106a3b-11183a2b2-4259ab3+1032b4-14162a3c-11707a2bc+11066ab
| 14300a4-4594a3b+12052a2b2-5495ab3-8490b4-14138a3c-3732a2bc+13017ab2c-
| 8141a4-6785a3b+3472a2b2+9302ab3+13245b4-2135a3c-11369a2bc+5459ab2c+15
| 15864a4-14070a3b-12959a2b2+15486ab3+1950a3c-1690a2bc+759ab2c+15603b3c
| -8304a4+15940a3b+6098a2b2-3140ab3-12998a3c-14486a2bc-8077ab2c-12395b3
| 11266a4-6163a3b-5292a2b2+2227ab3+8816a3c-780a2bc+14029ab2c-15714b3c+1
| 6306a4+4669a3b-12276a2b2-8216ab3-15603b4+9626a3c-13344a2bc-9366ab2c-1
| -9952a4-7556a3b+10336a2b2+2842ab3+12395b4+13948a3c+4029a2bc+1158ab2c+
| 7124a4+3996a3b+220a2b2+10677ab3+15714b4-13801a3c-145a2bc-2138ab2c-112
| 15761a4-4227a3b+2576a2b2-10434ab3-9914b4+11262a3c+14621a2bc+4624ab2c+
| 7187a4-4198a3b+6927a2b2+10863ab3-14156b4-4773a3c-11433a2bc-7530ab2c-1
| -2809a4+360a3b+7156a2b2-13655ab3+2917b4+8860a3c-2858a2bc-4940ab2c+636
| 10848a4+280a3b+4917a2b2+11199ab3-864a3c+4816a2bc+4151ab2c-3104b3c-103
| 2006a4+15518a3b-5296a2b2-14370ab3+776b4-3060a3c-10440a2bc-6243ab2c+50
| -594a4+13032a3b+1372a2b2-15001ab3+4656b4+12648a3c-2937a2bc-12486ab2c+
| -2096a4-2597a3b+15546a2b2+12441ab3-10883b4+2466a3c+13424a2bc-8708ab2c
| 11008a4+10234a3b+11173a2b2+2780ab3-11529b4-12838a3c+9146a2bc-10123ab2
| 13085a4+11905a3b+14836a2b2+6962ab3+1589a3c-11323a2bc+10434ab2c+13863a
| -4273a4+15149a3b+10037a2b2+388ab3-15864a3c-12599a2bc-2052ab2c+2598a2c
| 2277a4-8964a3b-6204a2b2+2112ab3-1412a3c+12720a2bc-4356ab2c-258a2c2+12
| 1167a4-2109a3b-48a2b2+108ab3+5268a3c-108a2bc-216ab2c
-----------------------------------------------------------------------
c+9788a2c2-1925abc2-13846b2c2+1549ac3-13087bc3+1361c4
11205a2c2-1439abc2+4342b2c2+10491ac3-10090bc3+9081c4
-9132a2c2+9277abc2-7047b2c2-9782ac3-11609bc3-9025c4
4b3c-7578a2c2+4043abc2+9576b2c2-3373ac3-2448bc3-5221c4
0235b3c+3360a2c2+4006abc2-5362b2c2-9398ac3-12455bc3-9189c4
45b3c+7963a2c2-4997abc2-8012b2c2-6480ac3+9974bc3-775c4
2c+7700b3c-6852a2c2+11615abc2+10578b2c2-173ac3-10678bc3+9590c4
2524b3c+12612a2c2+15584abc2-10604b2c2+2097ac3+9018bc3+6432c4
864b3c+5943a2c2-8595abc2-7993b2c2-8945ac3-1800bc3+4557c4
-15489a2c2-25abc2-7330b2c2-13658ac3-3877bc3+13738c4
c+7932a2c2+11637abc2+7656b2c2-12923ac3+10443bc3+952c4
882a2c2-7763abc2+8335b2c2-3546ac3-5186bc3-12827c4
4759b3c+7172a2c2-15356abc2-9866b2c2+10551ac3+14806bc3+5153c4
6500b3c-10591a2c2-6379abc2+5347b2c2-3988ac3+15521bc3+4940c4
52b3c-10275a2c2+2543abc2-1183b2c2+11762ac3+2836bc3+5358c4
13743b3c-7647a2c2+5143abc2+3459b2c2+3233ac3-5153bc3
5790b3c+3229a2c2+4501abc2+15530b2c2+12707ac3-4940bc3
9b3c-15024a2c2-4037abc2+9991b2c2-13671ac3-5358bc3
48a2c2-4986abc2+7968b2c2-477ac3+12410bc3+5763c4
48b3c-2178a2c2-8414abc2+9674b2c2-14370ac3+10315bc3+10498c4
9814b3c+7970a2c2-9011abc2+735b2c2-3286ac3-14453bc3+778c4
-9675b3c+15989a2c2-6086abc2+10725b2c2+5417ac3-329bc3
c-6697b3c-9065a2c2+15116abc2+11617b2c2-9880ac3-1556bc3
2c2-12021abc2-10716ac3
2-7392abc2+3280ac3
abc2+20ac3
-----------------------------------------------------------------------
10881a3b+1494a2b2-13287ab3-9855b4-10561a3c+10362a2bc+12397ab2c+9032b3c-
10881a3b+11746a2b2+68ab3-1187b4+10639a3c-12731a2bc+15771ab2c-2214b3c+13
-10682a3b-15824a2b2+12588ab3-15423b4-15054a3c-1833a2bc-15183ab2c-4254b3
10241a4-6954a3b+1421a2b2+4831ab3-12309b4+11714a3c-12120a2bc+10754ab2c+4
10241a4+10587a3b+14602a2b2+4143ab3+10416b4+6785a3c+6650a2bc-5488ab2c+14
-10639a4+12830a3b+2080a2b2-8862ab3-3864b4-14262a3c-5439a2bc-14944ab2c-5
-10881a4+13990a3b+227a2b2-6402ab3-10105b4+1145a3c+6579a2bc-14329ab2c-90
10725a4-10838a3b+2278a2b2-7638ab3+1091b4+3416a3c+10708a2bc+13800ab2c+14
-1895a4-15856a3b-4796a2b2-10438ab3+10566b4+7705a3c+3744a2bc-4515ab2c-10
11898a4+11453a3b+12634a2b2+4924ab3-11202a3c-8059a2bc-3456ab2c+7874b3c+1
-6228a4-12211a3b-5307a2b2+755ab3-1916a3c+10655a2bc+7462ab2c-10900b3c-85
-7552a4+14241a3b-8888a2b2+11592ab3-13268a3c-12871a2bc+14109ab2c+13115b3
-11272a4+4502a3b+4817a2b2-11969ab3-7874b4+3119a3c+1191a2bc+9720ab2c+159
-7464a4+8518a3b+10004a2b2+9960ab3+10900b4+3763a3c-4859a2bc+4852ab2c+771
5343a4+7059a3b-13471a2b2+2546ab3-13115b4+8390a3c-6248a2bc-1475ab2c-1297
3820a4-14941a3b-472a2b2-12276ab3-13154b4+274a3c-13663a2bc-399ab2c+103b3
13391a4+13926a3b+4401a2b2-5184ab3-574b4-357a3c+2191a2bc+14044ab2c-9791b
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-----------------------------------------------------------------------
279ac3-2650bc3-2928c4 |
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c-15798a2c2-1168abc2+15358b2c2-8022ac3-7293bc3-7384c4 |
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22a2c2-11801abc2-6681b2c2+8406ac3-4880bc3-13042c4 |
443a2c2-15526abc2-6503b2c2+7822ac3+7384bc3 |
8007a2c2-12230abc2+8016b2c2-12353ac3+2721bc3 |
24a2c2+8268abc2-643b2c2+8117ac3+13042bc3 |
36abc2+13907b2c2-6393ac3-13331bc3-6416c4 |
970a2c2+13461abc2+12975b2c2-3023ac3-849bc3+6422c4 |
699a2c2+7734abc2-6034b2c2+469ac3-7481bc3-6589c4 |
2c2-6710abc2-7494b2c2+14128ac3-12692bc3 |
252a2c2-10993abc2+2207b2c2+5442ac3+13178bc3 |
2-5919ac3 |
ac3 |
|
|
27 3
o33 : Matrix R <-- R
|
i34 : ker f1 == image f2
o34 = false
|
i35 : ker f2 == image f3
o35 = false
|
These do not piece together well. The reason is that
pieri changes the bases of the free modules in a way which is not invertible (over ZZ) when the ground field has positive characteristic.
