| 1 | LIB "tst.lib"; tst_init(); |
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| 2 | LIB "nctools.lib"; |
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| 3 | // ------- first example: C, D are matrices -------- |
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| 4 | ring r1 = (0,Q),(x,y,z),Dp; |
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| 5 | minpoly = rootofUnity(6); |
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| 6 | matrix C[3][3]; |
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| 7 | matrix D[3][3]; |
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| 8 | C[1,2]=Q2; C[1,3]=1/Q2; C[2,3]=Q2; |
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| 9 | D[1,2]=-Q*z; D[1,3]=1/Q*y; D[2,3]=-Q*x; |
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| 10 | def S=nc_algebra(C,D); |
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| 11 | // this algebra is a quantum deformation U'_q(so_3), |
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| 12 | // where Q is a 6th root of unity |
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| 13 | setring S;S; |
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| 14 | kill r1,S; |
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| 15 | // ----- second example: number n=1, D is a matrix |
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| 16 | ring r2=0,(Xa,Xb,Xc,Ya,Yb,Yc,Ha,Hb),dp; |
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| 17 | matrix d[8][8]; |
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| 18 | d[1,2]=-Xc; d[1,4]=-Ha; d[1,6]=Yb; d[1,7]=2*Xa; |
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| 19 | d[1,8]=-Xa; d[2,5]=-Hb; d[2,6]=-Ya; d[2,7]=-Xb; |
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| 20 | d[2,8]=2*Xb; d[3,4]=Xb; d[3,5]=-Xa; d[3,6]=-Ha-Hb; |
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| 21 | d[3,7]=Xc; d[3,8]=Xc; d[4,5]=Yc; d[4,7]=-2*Ya; |
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| 22 | d[4,8]=Ya; d[5,7]=Yb; d[5,8]=-2*Yb; |
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| 23 | d[6,7]=-Yc; d[6,8]=-Yc; |
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| 24 | def S=nc_algebra(1,d); // this algebra is U(sl_3) |
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| 25 | setring S;S; |
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| 26 | kill r2,S; |
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| 27 | // ---- third example: C is a matrix, p=0 is a poly |
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| 28 | ring r3=0,(a,b,c,d),lp; |
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| 29 | matrix c[4][4]; |
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| 30 | c[1,2]=1; c[1,3]=3; c[1,4]=-2; |
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| 31 | c[2,3]=-1; c[2,4]=-3; c[3,4]=1; |
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| 32 | def S=nc_algebra(c,0); // it is a quasi--commutative algebra |
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| 33 | setring S;S; |
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| 34 | kill r3,S; |
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| 35 | // -- fourth example : number n = -1, poly p = 3w |
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| 36 | ring r4=0,(u,v,w),dp; |
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| 37 | def S=nc_algebra(-1,3w); |
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| 38 | setring S;S; |
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| 39 | kill r4,S; |
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| 40 | tst_status(1);$ |
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