| 1 | LIB "tst.lib"; |
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| 2 | tst_init(); |
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| 3 | ring r1=(0,Q),(x,y,z),Dp; |
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| 4 | minpoly=Q^4+Q^2+1; |
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| 5 | matrix C[3][3]; |
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| 6 | matrix D[3][3]; |
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| 7 | C[1,2]=Q2; |
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| 8 | C[1,3]=1/Q2; |
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| 9 | C[2,3]=Q2; |
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| 10 | D[1,2]=-Q*z; |
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| 11 | D[1,3]=1/Q*y; |
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| 12 | D[2,3]=-Q*x; |
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| 13 | def S=nc_algebra(C,D);setring S; |
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| 14 | // it is quantum deformation U'_q(so_3) |
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| 15 | // where q=Q^2 specialized at the 3rd root of unity |
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| 16 | S; |
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| 17 | kill r1,S; |
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| 18 | ring r2=0,(Xa,Xb,Xc,Ya,Yb,Yc,Ha,Hb),dp; |
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| 19 | matrix d[8][8]; |
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| 20 | d[1,2]=-Xc; d[1,4]=-Ha; d[1,6]=Yb; |
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| 21 | d[1,7]=2*Xa; d[1,8]=-Xa; d[2,5]=-Hb; |
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| 22 | d[2,6]=-Ya; d[2,7]=-Xb; d[2,8]=2*Xb; |
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| 23 | d[3,4]=Xb; d[3,5]=-Xa; d[3,6]=-Ha-Hb; |
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| 24 | d[3,7]=Xc; d[3,8]=Xc; d[4,5]=Yc; |
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| 25 | d[4,7]=-2*Ya; d[4,8]=Ya; d[5,7]=Yb; |
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| 26 | d[5,8]=-2*Yb; d[6,7]=-Yc; d[6,8]=-Yc; |
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| 27 | def S2=nc_algebra(1,d);setring S2; |
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| 28 | // it is U(sl_3) |
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| 29 | S2; |
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| 30 | kill r2,S2; |
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| 31 | ring r3=0,(a,b,c,d),lp; |
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| 32 | matrix c[4][4]; |
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| 33 | c[1,2]=1; c[1,3]=3; c[1,4]=-2; |
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| 34 | c[2,3]=-1; c[2,4]=-3; c[3,4]=1; |
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| 35 | def S3=nc_algebra(c,0);setring S3; |
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| 36 | // it is some quasi--commutative algebra |
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| 37 | S3; |
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| 38 | kill r3,S3; |
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| 39 | ring r4=0,(t,u,v,w),dp; |
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| 40 | def S4=nc_algebra(-1,0); setring S4; |
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| 41 | // it is anticommutative algebra |
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| 42 | S4; |
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| 43 | kill r4,S4; |
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| 44 | tst_status(1);$ |
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