| 1 | monitor(":w ResultGHB.txt","o"); |
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| 2 | ring r=5,(u223,u222,u12,u23,u1,u2,delta2v,deltav1,deltav2,deltav3,v11,v12,v13,v22,v23,v33,v1,v2,v3,v),wp(1024,1024,256,256,64,64,4,3,3,3,2,2,2,2,2,2,1,1,1,0); |
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| 3 | |
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| 4 | //i to je chto j// |
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| 5 | |
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| 6 | //Simplifying assumptions:// |
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| 7 | number u111=1; |
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| 8 | number u112=0; |
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| 9 | number u113=0; |
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| 10 | number u123=0; |
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| 11 | |
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| 12 | //extra// |
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| 13 | //number u222=1; |
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| 14 | number u122=-1; |
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| 15 | number u11=1; |
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| 16 | number u13=0; |
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| 17 | number u22=-1; |
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| 18 | //number u23=-1; |
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| 19 | //number u1=1; |
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| 20 | number u3=1; |
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| 21 | |
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| 22 | |
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| 23 | poly Rv=v-u1^2-u2^2-u3^2; |
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| 24 | poly Rv1=v1-2*(u11*u1+u12*u2+u13*u3); |
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| 25 | poly Rv2=v2-2*(u12*u1+u22*u2+u23*u3); |
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| 26 | poly Rv3=v3-2*(u13*u1+u23*u2+(-u11-u22)*u3); |
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| 27 | poly Rv11=v11-2*(u111*u1+u112*u2+u113*u3+u11*u11+u12*u12+u13*u13); |
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| 28 | poly Rv12=v12-2*(u112*u1+u122*u2+u123*u3+u11*u12+u12*u22+u13*u23); |
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| 29 | poly Rv13=v13-2*(u113*u1+u123*u2+(-u111-u122)*u3+u11*u13+u12*u23+u13*(-u11-u22)); |
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| 30 | poly Rv22=v22-2*(u122*u1+u222*u2+u223*u3+u12*u12+u22*u22+u23*u23); |
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| 31 | poly Rv23=v23-2*(u123*u1+u223*u2+(-u112-u222)*u3+u12*u13+u22*u23+u23*(-u11-u22)); |
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| 32 | poly Rv33=v33-2*((-u111-u122)*u1+(-u112-u222)*u2+(-u113-u223)*u3+u13*u13+u23*u23+(-u11-u22)*(-u11-u22)); |
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| 33 | |
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| 34 | poly Rdeltav1=deltav1-4*(u11*u111+2*u12*u112+2*u13*u113+u22*u122+2*u23*u123+(-u11-u22)*(-u111-u122)); |
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| 35 | poly Rdeltav2=deltav2-4*(u11*u112+2*u12*u122+2*u13*u123+u22*u222+2*u23*u223+(-u11-u22)*(-u112-u222)); |
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| 36 | poly Rdeltav3=deltav3-4*(u11*u113+2*u12*u123+2*u13*(-u111-u122)+u22*u223+2*u23*(-u112-u222)+(-u11-u22)*(-u113-u223)); |
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| 37 | |
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| 38 | //poly Rgradv2=gradv2-(v1^2+v2^2+v3^2); |
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| 39 | //poly Rdeltav=deltav-(v11+v22+v33); |
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| 40 | |
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| 41 | //poly RD2vgradvgradv=D2vgradvgradv-(v11*v1*v1+2*v12*v1*v2+2*v13*v1*v3+v22*v2*v2+2*v23*v2*v3+v33*v3*v3); |
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| 42 | |
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| 43 | //poly RD2vgradvgraddeltav=D2vgradvgraddeltav-(v11*v1*deltav1+v12*v1*deltav2+v12*v2*deltav1+v13*v1*deltav3+v13*v3*deltav1+v22*v2*deltav2+v23*v2*deltav3+v23*v3*deltav2+v33*v3*deltav3); |
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| 44 | |
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| 45 | //poly RdetD2v=detD2v-(v11*v22*v33+2*v12*v23*v13-v13*v22*v13-v12*v12*v13-v11*v23*v23); |
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| 46 | |
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| 47 | //poly RD2vHS=D2vHS-(v11^2+2*v12^2+2*v13^2+v22^2+2*v23^2+v33^2); |
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| 48 | |
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| 49 | //poly Rgradvgraddeltav=v1*deltav1+v2*deltav2+v3*deltav3; |
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| 50 | |
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| 51 | //poly Rgraddeltav2=graddeltav2-(deltav1^2+deltav2^2+deltav3^2); |
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| 52 | |
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| 53 | poly Rdelta2v=delta2v-4*(u111^2+3*u112^2+3*u113^2+3*u122^2+6*u123^2+3*(-u111-u122)^2+u222^2+3*u223^2+3*(-u112-u222)^2+(-u113-u223)^2); |
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| 54 | |
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| 55 | ideal I=Rdelta2v,Rdeltav1,Rdeltav2,Rdeltav3,Rv11,Rv12,Rv13,Rv22,Rv23,Rv33,Rv1,Rv2,Rv3,Rv; |
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| 56 | |
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| 57 | |
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| 58 | option(prot); |
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| 59 | groebner(I); |
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| 60 | monitor(""); |
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| 61 | |
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