source:
git/Tst/Manual/centralizeSet.tst
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1 | LIB "tst.lib"; tst_init(); |
2 | LIB "central.lib"; |
3 | ring A = 0,(e(1..4)),dp; |
4 | matrix D[4][4]=0; |
5 | D[2,4] = -e(1); |
6 | D[3,4] = -e(2); |
7 | // This is A_4_1 - the first real Lie algebra of dimension 4. |
8 | def A_4_1 = nc_algebra(1,D); setring A_4_1; |
9 | ideal F = variablesSorted(); F; |
10 | // the center of A_4_1 is generated by |
11 | // e(1) and -1/2*e(2)^2+e(1)*e(3) |
12 | // therefore one may consider computing it in the following way: |
13 | // 1. Compute a PBW basis consisting of |
14 | // monomials with exponent <= (1,2,1,0) |
15 | ideal V = PBW_maxMonom( e(1) * e(2)^ 2 * e(3) ); |
16 | // 2. Compute the centralizer of F within the vector space |
17 | // spanned by these monomials: |
18 | ideal C = centralizeSet( F, V ); C; |
19 | inCenter(C); // check the result |
20 | tst_status(1);$ |
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