## load package _wrnlvl := interface(warnlevel): interface(warnlevel=0): with(PolynomialIdeals): infolevel[GroebnerBasis] := 4: infolevel[TriangularSet] := 4: interface(warnlevel=_wrnlvl): _wrnlvl := '_wrnlvl': ## Some of my favorite examples from ## http://www2.math.uic.edu/~jan/demo.html ## http://www.symbolicdata.org/SD_HTML/Data/INTPS/ ## http://www-sop.inria.fr/saga/POL/ printf(%s,"\n"); printf(%s,"PolynomialIdeals test suite\n"); printf(%s,"---------------------------\n"); printf(%s,"\n"); printf(%s,"butcher caprasse cassou circles cyclic5 cyclic6\n"); printf(%s,"cyclohexane des18_3 des22_24 discriminant4 eco7\n"); printf(%s,"hairer1 katsura5 katsura6 kinema noon4 pavelle\n"); printf(%s,"rabmo reimer4 reimer5 rose S4 S6 schwarz7 schwarz8\n"); printf(%s,"sendra tangents trinks utbikker vermeer wang92c\n"); printf(%s,"wang92e weispfenning94 wright\n"); printf(%s,"\n"); # alex1 alex2 alex3 # butcher # caprasse # cassou # circles # cohn2 cohn3 # cpdm5 # cyclic4 cyclic5 cyclic6 cyclic7 # cyclohexane # des18_3 des22_24 # discriminant4 discriminant5 # eco5 eco6 eco7 eco8 # fateman # fee1 # filter9 # geneig # gerdt85 # gonnet83 # hairer1 hairer2 # katsura4 katsura5 katsura6 katsura7 # kinema # kotsireas # krider # ku10 # noon3 noon4 noon5 noon6 # pavelle # rabmo # random3 random4 # rbpl24 # redcyc5 redcyc6 redcyc7 # redeco5 redeco6 redeco7 redeco8 # reimer4 reimer5 # rose # S4 # S6 # schiele # schwarz7 schwarz8 schwarz9 # sendra # symmetric5 symmetric6 # tangents # trinks # utbikker # vermeer # virasoro # wang89 wang91 wang92a wang92c wang92e wang92f # weispfenning94 # wright alex1 := <3*x^2*t^4*y^3*z^2+9*z^8, 2*x^5*t^2*y^4+7*x*t*y^6+9*y^8+2*x^2*t^2*y*z^3, t^3*y^7*z^4+9*x^8+5*x^4*t^2*y^2+2*x*t^2*y^2*z^3>: alex2 := <3*t^6*x^2*y*z^2+9*t^3*y^2*z+2*x*y^3*z^2, 2*t^3*x^5*y^2*z+t^5*x^2*y+2*x^2*y, t^3*x^5*y^2*z^2+t*x^2*y^3+2*t^5*z>: alex3 := <7*x*y^6*z^2+4*t^6*x+9*t^3*y^2*z+6*x^2*y, 8*t*x^5*y^3+2*t^3*x^3*y^2+4*t^6*z+3*x, 5*t^3*x^8*y^2*z+t^5*x^2*y+2*x^2*y+5*t>: butcher := <2*z*u+2*y*v+2*t*w-2*w^2-w-1, 3*z*u^2+3*y*v^2-3*t*w^2+3*w^3+3*w^2-t+4*w, 6*x*z*v-6*t*w^2+6*w^3-3*t*w+6*w^2-t+4*w, 4*z*u^3+4*y*v^3+4*t*w^3-4*w^4-6*w^3+4*t*w-10*w^2-w-1, 8*x*z*u*v+8*t*w^3-8*w^4+4*t*w^2-12*w^3+4*t*w-14*w^2-3*w-1, 12*x*z*v^2+12*t*w^3-12*w^4+12*t*w^2-18*w^3+8*t*w-14*w^2-w-1, -24*t*w^3+24*w^4-24*t*w^2+36*w^3-8*t*w+26*w^2+7*w+1>: caprasse := : cassou := < 15*b^4*c*d^2+6*b^4*c^3+21*b^4*c^2*d-144*b^2*c-8*b^2*c^2*e -28*b^2*c*d*e-648*b^2*d+36*b^2*d^2*e+9*b^4*d^3-120, 30*c^3*b^4*d-32*d*e^2*c-720*d*b^2*c-24*c^3*b^2*e-432*c^2*b^2 +576*e*c-576*d*e+16*c*b^2*d^2*e+16*d^2*e^2+16*e^2*c^2 +9*c^4*b^4+5184+39*d^2*b^4*c^2+18*d^3*b^4*c-432*d^2*b^2 +24*d^3*b^2*e-16*c^2*b^2*d*e-240*c, 261+4*d*b^2*c-3*d^2*b^2-4*c^2*b^2+22*e*c-22*d*e, 216*d*b^2*c-162*d^2*b^2-81*c^2*b^2+5184+1008*e*c-1008*d*e +15*c^2*b^2*d*e-15*c^3*b^2*e-80*d*e^2*c+40*d^2*e^2+40*e^2*c^2>: circles := <(1-z)^2+(w+m-1)^2-m^2, x^2+y^2-m^2, (1-x-m)^2+w^2-m^2, (1-m-1/2*z)^2+(w-1/2-1/2*y-1/2*m)^2-m^2, 1/4*z^2+(1/2-1/2*y-1/2*m)^2-m^2>: cohn2 := : cohn3 := <-x^3*y^2+2*x^2*y^2*z-x^2*y*z^2-144*x^2*y^2-207*x^2*y*z +288*x*y^2*z+78*x*y*z^2+x*z^3-3456*x^2*y-5184*x*y^2-9504*x*y*z -432*x*z^2-248832*x*y+62208*x*z-2985984*x, -x^3*z*t^2+x^2*z^2*t^2-6*x^3*z*t+4*x^2*z^2*t+32*x^3*t^2 -72*x^2*z*t^2-87*x*z^2*t^2-z^3*t^2-8*x^3*z-432*x^2*z*t -414*x*z^2*t+2592*x*z*t^2+864*z^2*t^2-1728*x^2*z-20736*x*z*t +3456*z^2*t-186624*z*t^2-124416*x*z-1492992*z*t-2985984*z, x^2*y*t^3-2*x*y^2*t^3+y^3*t^3+8*x^2*y*t^2-12*x*y^2*t^2+4*y^3*t^2 -24*x*y*t^3+24*y^2*t^3+20*x^2*y*t-20*x*y^2*t-160*x*y*t^2+96*y^2*t^2 +128*x*t^3+16*x^2*y+96*x*y*t+2304*x*t^2+1152*x*y+13824*x*t+27648*x, y^3*t^3-y^2*z*t^3+4*y^3*t^2-2*y^2*z*t^2+72*y^2*t^3+71*y*z*t^3 +288*y^2*t^2+360*y*z*t^2+6*z^2*t^2+1728*y*t^3-464*z*t^3+432*y*z*t +8*z^2*t+6912*y*t^2-4320*z*t^2+13824*t^3+z^2-13824*z*t+55296*t^2-13824*z>: cpdm5 := <4*x1^3+3*x1^2*x2+3*x1^2*x3+3*x1^2*x4+3*x1^2*x5+3*x1*x2^2 +3*x1*x3^2+3*x1*x4^2+3*x1*x5^2+x2^3+x3^3+x4^3+x5^3+2*x1^2+3*x1*x2 +3*x1*x3+3*x1*x4+3*x1*x5-x2^2-x3^2-x4^2-x5^2-6*x1, x1^3+3*x1^2*x2+3*x1*x2^2+4*x2^3+3*x2^2*x3+3*x2^2*x4+3*x2^2*x5 +3*x2*x3^2+3*x2*x4^2+3*x2*x5^2+x3^3+x4^3+x5^3-x1^2+3*x1*x2+2*x2^2 +3*x2*x3+3*x2*x4+3*x2*x5-x3^2-x4^2-x5^2-6*x2, x1^3+3*x1^2*x3+3*x1*x3^2+x2^3+3*x2^2*x3+3*x2*x3^2+4*x3^3+3*x3^2*x4 +3*x3^2*x5+3*x3*x4^2+3*x3*x5^2+x4^3+x5^3-x1^2+3*x1*x3-x2^2+3*x2*x3 +2*x3^2+3*x3*x4+3*x3*x5-x4^2-x5^2-6*x3, x1^3+3*x1^2*x4+3*x1*x4^2+x2^3+3*x2^2*x4+3*x2*x4^2+x3^3+3*x3^2*x4 +3*x3*x4^2+4*x4^3+3*x4^2*x5+3*x4*x5^2+x5^3-x1^2+3*x1*x4-x2^2 +3*x2*x4-x3^2+3*x3*x4+2*x4^2+3*x4*x5-x5^2-6*x4, x1^3+3*x1^2*x5+3*x1*x5^2+x2^3+3*x2^2*x5+3*x2*x5^2+x3^3+3*x3^2*x5 +3*x3*x5^2+x4^3+3*x4^2*x5+3*x4*x5^2+4*x5^3-x1^2+3*x1*x5-x2^2 +3*x2*x5-x3^2+3*x3*x5-x4^2+3*x4*x5+2*x5^2-6*x5>: cyclic4 := : cyclic5 := : cyclic6 := : cyclic7 := : cyclohexane := <-5/3-34/9*z-23/9*z^2-34/9*x-20/9*z*x-23/9*x^2+z^2*x^2+2/3*z*x^2+2/3*z^2*x, -2+10/3*z*x*y+2/9*x-40/9*z-40/9*y+2*z*x^2*y-23/9*z^2+10/9*z*x+2/3*z^2*x+16/9*x^2+z^2*x^2 +10/3*z*x^2-23/9*y^2-32/9*y*z+10/9*x*y+2/3*x*y^2+x^2*y^2+10/3*x^2*y, -5/3-23/9*x^2-34/9*x-20/9*x*y-34/9*y-23/9*y^2+2/3*x^2*y+2/3*x*y^2+x^2*y^2, 40/3*z*x*y+50/9*x+2*x*y^2*z+2*x*y*z^2+20/3*z+50/9*y+2*z*x^2*y+7/3+4*z^2 +118/9*z*x+20/3*z^2*x+16/9*x^2+z^2*x^2+10/3*z*x^2+16/9*y^2+118/9*y*z+98/9*x*y +10/3*x*y^2+x^2*y^2+10/3*x^2*y+20/3*y*z^2+10/3*y^2*z+y^2*z^2, -2+10/3*z*x*y-40/9*x+2*x*y^2*z-40/9*z+2/9*y-23/9*z^2-32/9*z*x-23/9*x^2+16/9*y^2 +10/9*y*z+10/9*x*y+10/3*x*y^2+x^2*y^2+2/3*x^2*y+2/3*y*z^2+10/3*y^2*z+y^2*z^2, -5/3-23/9*y^2-20/9*y*z-34/9*y-23/9*z^2-34/9*z+y^2*z^2+2/3*y*z^2+2/3*y^2*z, 40/3*z*x*y+20/3*x+2*x*y^2*z+2*x*y*z^2+50/9*z+50/9*y+2*z*x^2*y+7/3+16/9*z^2 +118/9*z*x+10/3*z^2*x+4*x^2+z^2*x^2+20/3*z*x^2+16/9*y^2+98/9*y*z+118/9*x*y +10/3*x*y^2+x^2*y^2+20/3*x^2*y+10/3*y*z^2+10/3*y^2*z+y^2*z^2, -2+10/3*z*x*y-40/9*x+2*x*y*z^2+2/9*z-40/9*y+16/9*z^2+10/9*z*x+10/3*z^2*x-23/9*x^2 +z^2*x^2+2/3*z*x^2-23/9*y^2+10/9*y*z-32/9*x*y+10/3*y*z^2+2/3*y^2*z+y^2*z^2, 40/3*z*x*y+50/9*x+2*x*y^2*z+2*x*y*z^2+50/9*z+20/3*y+2*z*x^2*y+7/3+16/9*z^2 +98/9*z*x+10/3*z^2*x+16/9*x^2+z^2*x^2+10/3*z*x^2+4*y^2+118/9*y*z+118/9*x*y +20/3*x*y^2+x^2*y^2+10/3*x^2*y+10/3*y*z^2+20/3*y^2*z+y^2*z^2>: des18_3 := <11*a33*a10+56*a32+15*a31+13*a22*a33-176*a10-15*a21, 180*a33*a10-284*a22*a10-162*a10^2+60*a22*a32+50*a32*a10+70*a30 +55*a33*a21+260*a31-112*a20, 5*a33*a10*a21-54*a10^2*a22-104*a10*a20 +8*a10*a30+9*a31*a21+8*a32*a20+6*a22*a10*a32+10*a22*a30+28*a31*a10, 7*a22*a10*a33+48*a30+32*a32*a10+9*a31*a20+9*a33*a20-75*a10*a21 +10*a32*a21-162*a10^2+11*a22*a31, a33-1, -60*a10+105*a33-16*a22+28*a32, 4*a22*a10*a30+2*a32*a10*a20+6*a20*a30-162*a10^2*a20+3*a31*a21*a10, 3*a33*a10*a20+5*a22*a10*a31+4*a32*a10*a21-81*a10^2*a21 +8*a21*a30+7*a31*a20+24*a10*a30>: des22_24 := <9*a33*a20+10*a32*a21+11*a22*a31+12*a23*a30, -16*a23+36*a34+171*a35, 68*a23*a35-57*a22+76*a33+360*a34, 7*a31*a20+8*a21*a30, 8*a32*a20+9*a31*a21+10*a22*a30, a35-1, 11*a20*a35+12*a21*a34+13*a22*a33+14*a23*a32+16*a30+75*a31, 39*a21*a35+42*a22*a34+45*a23*a33-85*a20+51*a31+240*a32, 10*a20*a34+11*a33*a21+12*a22*a32+13*a23*a31+70*a30, 105*a22*a35+112*a23*a34-144*a21+126*a32+595*a33>: discriminant4 := : discriminant5 := <-6*y^3*z^2*w^2+2250*x^2*y*z^2-27*x^2*t^4*w^2-4*y^3*t^3*w^2 -900*x^2*z^3*w-4*y^2*z^3*w^3-1600*x^3*t*w^3-1600*x*y^3*z+16*x*z^4*w^3 +16*x*z^3*t^3-2500*x^3*y*w-3750*x^3*z*t-4*y^2*z^2*t^3-192*y^4*z*w -900*x^2*y*t^3-2050*x^2*y*z*t*w-128*x^2*z^2*w^4+2000*x^3*z*w^2 +144*y^3*z^2*t+18*x*y*z*t^3*w^2+256*x^3*w^5+144*y^4*t*w^2-50*x^2*y^2*w^2 -36*x*y^3*w^3+825*x^2*z^2*t^2-80*x*y*z^2*t*w^3-27*y^4*w^4+2000*x^2*y^2*t +2250*x^3*t^2*w+16*y^3*t^4+108*x^2*t^5-27*y^2*z^4+108*x*z^5-128*y^4*t^2 +y^2*z^2*t^2*w^2-4*x*z^3*t^2*w^2+18*y^3*z*t*w^3-6*x*y^2*t^2*w^3+256*y^5 +3125*x^4+144*x^2*z*t^2*w^3+144*x*y^2*z*w^4-192*x^2*y*t*w^4-72*x*y*z*t^4 +18*y^2*z^3*t*w-72*x*z^4*t*w-80*y^3*z*t^2*w+24*x*y^2*t^3*w-630*x^2*z*t^3*w +24*x*y*z^3*w^2+560*x^2*z^2*t*w^2+1020*x^2*y*t^2*w^2+160*x^2*y*z*w^3 -630*x*y*z^3*t+560*x*y^2*z*t^2+1020*x*y^2*z^2*w+160*x*y^3*t*w +356*x*y*z^2*t^2*w-746*x*y^2*z*t*w^2, -3*y^2*t^2*w^3-50*x*y^2*w^2+12*y*z^3*w^2+3375*x^2*t^2*w+3000*x^2*z*w^2 +80*y^3*t*w+12*y^2*t^3*w-900*x*z^3*w-5625*x^2*z*t+72*y^2*z*w^4-315*y*z^3*t -2400*x^2*t*w^3-36*z^4*t*w-36*y*z*t^4+280*y^2*z*t^2+825*x*z^2*t^2-900*x*y*t^3 +2250*x*y*z^2+2000*x*y^2*t-2*z^3*t^2*w^2-27*x*t^4*w^2+510*y^2*z^2*w -3750*x^2*y*w-128*x*z^2*w^4-800*y^3*z+6250*x^3+54*z^5-18*y^3*w^3+8*z^4*w^3 +8*z^3*t^3+108*x*t^5+9*y*z*t^3*w^2-40*y*z^2*t*w^3+144*x*z*t^2*w^3-192*x*y*t*w^4 +178*y*z^2*t^2*w-630*x*z*t^3*w-373*y^2*z*t*w^2+560*x*z^2*t*w^2+1020*x*y*t^2*w^2 +160*x*y*z*w^3+384*x^2*w^5-2050*x*y*z*t*w, -9*y^2*z^2*w^2-315*x*z^3*t-4*y*z^2*t^3-50*x^2*y*w^2-746*x*y*z*t*w^2-27*y*z^4 +288*y^3*t*w^2-384*y^3*z*w-4*y*z^3*w^3+216*y^2*z^2*t+1125*x^2*z^2-54*x*y^2*w^3 -96*x^2*t*w^4-6*y^2*t^3*w^2-36*x*z*t^4+12*x*z^3*w^2+510*x^2*t^2*w^2+560*x*y*z*t^2 -256*y^3*t^2-450*x^2*t^3+640*y^4-2400*x*y^2*z+2000*x^2*y*t+24*y^2*t^4-54*y^3*w^4 -1250*x^3*w+y*z^2*t^2*w^2+9*x*z*t^3*w^2+27*y^2*z*t*w^3-40*x*z^2*t*w^3-6*x*y*t^2*w^3 +144*x*y*z*w^4+18*y*z^3*t*w-120*y^2*z*t^2*w+178*x*z^2*t^2*w+24*x*y*t^3*w +1020*x*y*z^2*w+240*x*y^2*t*w-1025*x^2*z*t*w+80*x^2*z*w^3, -4*y^2*z*t^3+32*x*z^3*w^3-40*y^3*t^2*w-1350*x^2*z^2*w+280*x*y^2*t^2+9*y^3*t*w^3 -315*x^2*t^3*w+72*x*y^2*w^4-6*y^3*z*w^2-80*x*y*z*t*w^3-36*x*y*t^4+80*x^2*y*w^3 +72*x^2*t^2*w^3+24*x*z^2*t^3-6*y^2*z^2*w^3-128*x^2*z*w^4-945*x*y*z^2*t+270*x*z^4 +144*y^3*z*t-54*y^2*z^3+825*x^2*z*t^2-800*x*y^3-1875*x^3*t+1000*x^3*w^2-96*y^4*w +y^2*z*t^2*w^2-6*x*z^2*t^2*w^2+9*x*y*t^3*w^2+27*y^2*z^2*t*w-144*x*z^3*t*w +36*x*y*z^2*w^2-373*x*y^2*t*w^2+560*x^2*z*t*w^2+1020*x*y^2*z*w-1025*x^2*y*t*w +2250*x^2*y*z+356*x*y*z*t^2*w, -54*x^2*t^3*w^2-6*y^2*z^2*t^2+9*y^3*z*w^3-315*x*y*z^3+2250*x^3*t*w+825*x^2*z^2*t -96*x^2*y*w^4-6*y^3*t^2*w^2+9*y^2*z^3*w+24*x*z^3*t^2-144*x*y*z*t^3+270*x^2*t^4 +32*y^3*t^3+72*y^4*w^2-800*x^3*w^3+72*y^3*z^2-128*y^4*t+1000*x^2*y^2-1875*x^3*z +y^2*z^2*t*w^2-4*x*z^3*t*w^2-40*x*y*z^2*w^3-6*x*y^2*t*w^3+144*x^2*z*t*w^3 -80*y^3*z*t*w+36*x*y^2*t^2*w-945*x^2*z*t^2*w-373*x*y^2*z*w^2+1020*x^2*y*t*w^2 +560*x*y^2*z*t-1025*x^2*y*z*w-36*x*z^4*w+280*x^2*z^2*w^2-1350*x^2*y*t^2+80*x*y^3*w +27*x*y*z*t^2*w^2+356*x*y*z^2*t*w, -4*y^3*t^3*w-315*x^2*z*t^3+2000*x^3*z*w-40*y^3*z*t^2-54*x*y^3*w^2-256*x^2*z^2*w^3 +80*x*y^3*t+9*y^2*z^3*t+510*x*y^2*z^2-27*x^2*t^4*w-6*y^2*z^3*w^2-2400*x^3*t*w^2 -50*x^2*y^2*w-36*x*z^4*t+12*x*y^2*t^3-54*y^4*w^3+640*x^3*w^4-96*y^4*z-450*x^2*z^3 +1125*x^3*t^2-1250*x^3*y+y^2*z^2*t^2*w-4*x*z^3*t^2*w+27*y^3*z*t*w^2-9*x*y^2*t^2*w^2 +216*x^2*z*t^2*w^2+288*x*y^2*z*w^3-384*x^2*y*t*w^3+178*x*y*z^2*t^2+24*x*y*z^3*w +560*x^2*z^2*t*w+1020*x^2*y*t^2*w+240*x^2*y*z*w^2-1025*x^2*y*z*t+24*x*z^4*w^2 -6*y^3*z^2*w+144*y^4*t*w+18*x*y*z*t^3*w-120*x*y*z^2*t*w^2-746*x*y^2*z*t*w>: eco5 := : eco6 := : eco7 := : eco8 := : fateman := <2*p^3+2*q^3+2*r^3+s^3, 2*p^5+2*q^5+2*r^5+s^5, 6*p^4*q+4*p^3*q^2+2*p^2*q^3+4*p*q^4+6*p^4*r+8*p^3*q*r +4*p*q^3*r+6*q^4*r+4*p^3*r^2+4*q^3*r^2+2*p^2*r^3 +4*p*q*r^3+2*q^2*r^3+4*p*r^4+4*q*r^4+3*p^4*s+4*p^3*q*s +2*p*q^3*s+3*q^4*s+4*p^3*r*s+4*q^3*r*s+2*p*r^3*s+2*q*r^3*s +3*r^4*s+p^3*s^2+q^3*s^2+r^3*s^2+p^2*s^3+2*p*q*s^3+q^2*s^3 +2*p*r*s^3+2*q*r*s^3+r^2*s^3+p*s^4+q*s^4+r*s^4-s^5>: fee1 := <-2*q*p-2*p^2-2*q+8*p-2, -3*q*c*p+2*q*p*d+4*p^2*d+3*c*p+q*d-7*p*d, q^2*c^2-2*q^2*c*d-2*q*c*p*d+q^2*d^2+2*q*p*d^2+p^2*d^2-2*q*c^2+4*q*c*p+2*q*c*d +2*c*p*d-4*q*d^2-4*p*d^2+c^2+2*q*p+10*p^2-4*c*d+4*d^2-2*q-8*p+2, 3*q^2*c^2+12*q*c*p*d-3*q^2*d^2+6*q*p*d^2-3*p^2*d^2-6*q*c^2+12*q*c*d+12*c*p*d -4*q^2+3*c^2+5*p^2-12*c*d+12*d^2-6*p+5>: filter9 := : geneig := : gerdt85 := <2*v*x-u*x+2*t*x, -2*z*x^2+10*y*x^2-20*x^3+7*t*z -35*t*y+70*t*x, 2*v*x^2-2*u*x^2+6*t*x^2-7*v*t+7*u*t-21*t^2, 2*z*y*x-6*y^2*x-z*x^2+13*y*x^2-5*x^3+14*v*x-28*t*x, z^2*x-3*z*y*x+5*z*x^2+14*v*x-28*t*x, -2*u*z*x-2*t*z*x +4*v*y*x+6*u*y*x-2*t*y*x-16*v*x^2-10*u*x^2+22*t*x^2+42*w*x, 28*v*z*x+8*u*z*x-20*t*z*x-88*v*y*x-24*u*y*x+68*t*y*x +156*v*x^2+40*u*x^2-132*t*x^2-252*w*x, -4*v*u*x+10*v*t*x +8*u*t*x-20*t^2*x+12*w*z*x-30*w*y*x+15*w*x^2, -2*v^2*x +v*u*x+2*v*t*x-2*u*t*x+4*t^2*x-6*w*z*x+12*w*y*x-6*w*x^2, 8*w*v*x-4*w*u*x+8*w*t*x, -2*y^3+4*z*y*x+5*y^2*x-6*z*x^2 -7*y*x^2+15*x^3+42*v*y-14*u*y-63*v*x+21*u*x-42*t*x+147*w, -9*z*x^3+45*y*x^3-135*x^4+14*u*y^2-14*t*y^2-28*u*z*x+70*t*z*x -14*u*y*x-196*t*y*x+28*u*x^2+602*t*x^2-294*v*u+98*u^2+294*v*t -98*u*t-147*w*z+735*w*y-2205*w*x, 6*v*x^3-9*u*x^3+36*t*x^3 -14*w*y^2-28*v*t*x+42*u*t*x-168*t^2*x+28*w*z*x+14*w*y*x -28*w*x^2+392*w*v-245*w*u+588*w*t>: gonnet83 := : hairer1 := <3*c3^2*b3+3*c2^2*b2-1,6*c2*b3*a32-1, b3+b2+b1-1, c3-a32-a31, c2-a21, 2*c3*b3+2*c2*b2-1>: hairer2 := <8*c2*c3*b3*a32+8*c2*c4*b4*a42+8*c3*c4*b4*a43-1, 12*c2^2*b3*a32+12*c2^2*b4*a42+12*c3^2*b4*a43-1, c2-a21, 4*c4^3*b4+4*c3^3*b3+4*c2^3*b2-1, c4-a41-a42-a43, c3-a31-a32, b4+b3+b2+b1-1, 2*c4*b4+2*c3*b3+2*c2*b2-1, 24*c2*b4*a32*a43-1, 3*c4^2*b4+3*c3^2*b3+3*c2^2*b2-1, 6*c2*b3*a32+6*c2*b4*a42+6*c3*b4*a43-1>: katsura4 := <2*x*t+2*u*y+2*z*t-y, 2*t*u+x*y+2*z*t+2*y*z-t, t^2+2*y*t+2*z*u+2*x*z-z, 2*t+u+2*x+2*y+2*z-1, 2*t^2+u^2+2*x^2+2*y^2+2*z^2-u>: katsura5 := <2*x^2+2*y^2+2*z^2+2*t^2+2*u^2+v^2-v, x*y+y*z+2*z*t+2*t*u+2*u*v-u, 2*x*z+2*y*t+2*z*u+u^2+2*t*v-t, 2*x*t+2*u*y+2*t*u+2*z*v-z, t^2+2*x*v+2*y*v+2*z*v-y, 2*x+2*y+2*z+2*t+2*u+v-1>: katsura6 := : katsura7 := <2*t*z+2*y*u+2*x*v+2*y*w+2*z*s-v, t^2+2*z*u+2*y*v+2*w*x+2*y*s-w, x+2*y+2*z+2*t+2*u+2*v+2*w+2*s-1, z^2+2*y*t+2*x*u+2*y*v+2*w*z+2*t*s-u, 2*y*z+2*t*x+2*y*u+2*v*z+2*t*w+2*u*s-t, y^2+2*x*z+2*y*t+2*z*u+2*t*v+2*u*w+2*v*s-z, 2*x*y+2*y*z+2*t*z+2*t*u+2*u*v+2*v*w+2*w*s-y, x^2+2*y^2+2*z^2+2*t^2+2*u^2+2*v^2+2*w^2+2*s^2-x>: kinema := : krider := <-6*c*g^2*u*v^5*p-12*c*g^2*u*v^3*w^2*p-2*c*g^2*u*v*w^4*p -12*c*f*g*u*v^3*w*p-4*c*f*g*u*v*w^3*p-2*c*f^2*u*v^3*p-4*c*d*g*u*v^3*p -2*c*f^2*u*v*w^2*p-4*c*d*g*u*v*w^2*p-2*b*g*u*v^3*p-4*c*d*f*u*v*w*p -2*b*g*u*v*w^2*p-2*c*d^2*u*v*p-2*c*u^3*v*p-2*b*f*u*v*w*p-2*b*d*u*v*p -2*a*u*v*p+2*u*v*w*p, -6*c*g^2*u*v^5*p-12*c*g^2*u*v^3*w^2*p-2*c*g^2*u*v*w^4*p-12*c*f*g*u*v^3*w*p -4*c*f*g*u*v*w^3*p-2*c*f^2*u*v^3*p-4*c*d*g*u*v^3*p-2*c*f^2*u*v*w^2*p -4*c*d*g*u*v*w^2*p-2*b*g*u*v^3*p-4*c*g*u*v^3*p-4*c*d*f*u*v*w*p -2*b*g*u*v*w^2*p-4*c*g*u*v*w^2*p-2*c*d^2*u*v*p-2*c*u^3*v*p-2*b*f*u*v*w*p -4*c*f*u*v*w*p-2*b*d*u*v*p-4*c*d*u*v*p-2*a*u*v*p-2*b*u*v*p+2*u*v*w*p, -30*c*g^2*u*v^5*w*p-20*c*g^2*u*v^3*w^3*p-2*c*g^2*u*v*w^5*p-12*c*f*g*u*v^5*p -24*c*f*g*u*v^3*w^2*p-4*c*f*g*u*v*w^4*p-6*c*f^2*u*v^3*w*p-12*c*d*g*u*v^3*w*p -2*c*f^2*u*v*w^3*p-4*c*d*g*u*v*w^3*p-4*c*d*f*u*v^3*p-6*b*g*u*v^3*w*p -12*c*g*u*v^3*w*p-4*c*d*f*u*v*w^2*p-2*b*g*u*v*w^3*p-4*c*g*u*v*w^3*p -2*b*f*u*v^3*p-4*c*f*u*v^3*p-2*c*d^2*u*v*w*p-2*c*u^3*v*w*p-2*b*f*u*v*w^2*p -4*c*f*u*v*w^2*p-2*b*d*u*v*w*p-4*c*d*u*v*w*p+2*u*v^3*p-2*a*u*v*w*p -2*b*u*v*w*p+2*u*v*w^2*p, -30*c*g^2*u*v^7*p-90*c*g^2*u*v^5*w^2*p-30*c*g^2*u*v^3*w^4*p-2*c*g^2*u*v*w^6*p -60*c*f*g*u*v^5*w*p-40*c*f*g*u*v^3*w^3*p-4*c*f*g*u*v*w^5*p-6*c*f^2*u*v^5*p -12*c*d*g*u*v^5*p-12*c*f^2*u*v^3*w^2*p-24*c*d*g*u*v^3*w^2*p-2*c*f^2*u*v*w^4*p -4*c*d*g*u*v*w^4*p-6*b*g*u*v^5*p-12*c*g*u*v^5*p-12*c*d*f*u*v^3*w*p -12*b*g*u*v^3*w^2*p-24*c*g*u*v^3*w^2*p-4*c*d*f*u*v*w^3*p-2*b*g*u*v*w^4*p -4*c*g*u*v*w^4*p-2*c*d^2*u*v^3*p-2*c*u^3*v^3*p-6*b*f*u*v^3*w*p-12*c*f*u*v^3*w*p -2*c*d^2*u*v*w^2*p-2*c*u^3*v*w^2*p-2*b*f*u*v*w^3*p-4*c*f*u*v*w^3*p-2*b*d*u*v^3*p -4*c*d*u*v^3*p-2*b*d*u*v*w^2*p-4*c*d*u*v*w^2*p-2*a*u*v^3*p-2*b*u*v^3*p+6*u*v^3*w*p -2*a*u*v*w^2*p-2*b*u*v*w^2*p+2*u*v*w^3*p, -30*c*g^3*u*v^7*p-90*c*g^3*u*v^5*w^2*p-30*c*g^3*u*v^3*w^4*p-2*c*g^3*u*v*w^6*p -90*c*f*g^2*u*v^5*w*p-60*c*f*g^2*u*v^3*w^3*p-6*c*f*g^2*u*v*w^5*p-18*c*f^2*g*u*v^5*p -18*c*d*g^2*u*v^5*p-36*c*f^2*g*u*v^3*w^2*p-36*c*d*g^2*u*v^3*w^2*p-6*c*f^2*g*u*v*w^4*p -6*c*d*g^2*u*v*w^4*p-6*b*g^2*u*v^5*p-6*c*f^3*u*v^3*w*p-36*c*d*f*g*u*v^3*w*p -12*b*g^2*u*v^3*w^2*p-2*c*f^3*u*v*w^3*p-12*c*d*f*g*u*v*w^3*p-2*b*g^2*u*v*w^4*p -6*c*d*f^2*u*v^3*p-6*c*d^2*g*u*v^3*p-6*c*g*u^3*v^3*p-12*b*f*g*u*v^3*w*p -6*c*d*f^2*u*v*w^2*p-6*c*d^2*g*u*v*w^2*p-6*c*g*u^3*v*w^2*p-4*b*f*g*u*v*w^3*p -2*b*f^2*u*v^3*p-4*b*d*g*u*v^3*p-6*c*d^2*f*u*v*w*p-6*c*f*u^3*v*w*p-2*b*f^2*u*v*w^2*p -4*b*d*g*u*v*w^2*p-2*c*d^3*u*v*p-6*c*d*u^3*v*p-2*a*g*u*v^3*p-4*b*d*f*u*v*w*p +6*g*u*v^3*w*p-2*a*g*u*v*w^2*p+2*g*u*v*w^3*p-2*b*d^2*u*v*p-2*b*u^3*v*p+2*f*u*v^3*p -2*a*f*u*v*w*p+2*f*u*v*w^2*p-2*a*d*u*v*p+2*d*u*v*w*p, -210*c*g^4*u*v^9*p-840*c*g^4*u*v^7*w^2*p-420*c*g^4*u*v^5*w^4*p-56*c*g^4*u*v^3*w^6*p -2*c*g^4*u*v*w^8*p-840*c*f*g^3*u*v^7*w*p-840*c*f*g^3*u*v^5*w^3*p-168*c*f*g^3*u*v^3*w^5*p -8*c*f*g^3*u*v*w^7*p-180*c*f^2*g^2*u*v^7*p-120*c*d*g^3*u*v^7*p-540*c*f^2*g^2*u*v^5*w^2*p -360*c*d*g^3*u*v^5*w^2*p-180*c*f^2*g^2*u*v^3*w^4*p-120*c*d*g^3*u*v^3*w^4*p -12*c*f^2*g^2*u*v*w^6*p-8*c*d*g^3*u*v*w^6*p-30*b*g^3*u*v^7*p-120*c*f^3*g*u*v^5*w*p -360*c*d*f*g^2*u*v^5*w*p-90*b*g^3*u*v^5*w^2*p-80*c*f^3*g*u*v^3*w^3*p -240*c*d*f*g^2*u*v^3*w^3*p-30*b*g^3*u*v^3*w^4*p-8*c*f^3*g*u*v*w^5*p-24*c*d*f*g^2*u*v*w^5*p -2*b*g^3*u*v*w^6*p-6*c*f^4*u*v^5*p-72*c*d*f^2*g*u*v^5*p-36*c*d^2*g^2*u*v^5*p-36*c*g^2*u^3*v^5*p -90*b*f*g^2*u*v^5*w*p-12*c*f^4*u*v^3*w^2*p-144*c*d*f^2*g*u*v^3*w^2*p-72*c*d^2*g^2*u*v^3*w^2*p -72*c*g^2*u^3*v^3*w^2*p-60*b*f*g^2*u*v^3*w^3*p-2*c*f^4*u*v*w^4*p-24*c*d*f^2*g*u*v*w^4*p -12*c*d^2*g^2*u*v*w^4*p-12*c*g^2*u^3*v*w^4*p-6*b*f*g^2*u*v*w^5*p-18*b*f^2*g*u*v^5*p -18*b*d*g^2*u*v^5*p-24*c*d*f^3*u*v^3*w*p-72*c*d^2*f*g*u*v^3*w*p-72*c*f*g*u^3*v^3*w*p -36*b*f^2*g*u*v^3*w^2*p-36*b*d*g^2*u*v^3*w^2*p-8*c*d*f^3*u*v*w^3*p-24*c*d^2*f*g*u*v*w^3*p -24*c*f*g*u^3*v*w^3*p-6*b*f^2*g*u*v*w^4*p-6*b*d*g^2*u*v*w^4*p-12*c*d^2*f^2*u*v^3*p -8*c*d^3*g*u*v^3*p-12*c*f^2*u^3*v^3*p-24*c*d*g*u^3*v^3*p-6*a*g^2*u*v^5*p-6*b*f^3*u*v^3*w*p -36*b*d*f*g*u*v^3*w*p+30*g^2*u*v^5*w*p-12*c*d^2*f^2*u*v*w^2*p-8*c*d^3*g*u*v*w^2*p -12*c*f^2*u^3*v*w^2*p-24*c*d*g*u^3*v*w^2*p-12*a*g^2*u*v^3*w^2*p-2*b*f^3*u*v*w^3*p -12*b*d*f*g*u*v*w^3*p+20*g^2*u*v^3*w^3*p-2*a*g^2*u*v*w^4*p+2*g^2*u*v*w^5*p-6*b*d*f^2*u*v^3*p -6*b*d^2*g*u*v^3*p-6*b*g*u^3*v^3*p+12*f*g*u*v^5*p-8*c*d^3*f*u*v*w*p-24*c*d*f*u^3*v*w*p -12*a*f*g*u*v^3*w*p-6*b*d*f^2*u*v*w^2*p-6*b*d^2*g*u*v*w^2*p-6*b*g*u^3*v*w^2*p +24*f*g*u*v^3*w^2*p-4*a*f*g*u*v*w^3*p+4*f*g*u*v*w^4*p-2*c*d^4*u*v*p-12*c*d^2*u^3*v*p -6*c*u^5*v*p-2*a*f^2*u*v^3*p-4*a*d*g*u*v^3*p-6*b*d^2*f*u*v*w*p-6*b*f*u^3*v*w*p +6*f^2*u*v^3*w*p+12*d*g*u*v^3*w*p-2*a*f^2*u*v*w^2*p-4*a*d*g*u*v*w^2*p+2*f^2*u*v*w^3*p +4*d*g*u*v*w^3*p-2*b*d^3*u*v*p-6*b*d*u^3*v*p+4*d*f*u*v^3*p-4*a*d*f*u*v*w*p+4*d*f*u*v*w^2*p -2*a*d^2*u*v*p-2*a*u^3*v*p+2*d^2*u*v*w*p+2*u^3*v*w*p>: kotsireas := <(t-u)*(x-y)-2*z+2, (t-u)*(x+y-2*z)-2*(x-y), (t-u)*(t-u)-2*t-2*u+v+1, x^2*t^3-1, y^2*u^3-1, z^2*v^3-1>: ku10 := <5*x1*x2+5*x1+3*x2+55, 7*x2*x3+9*x2+9*x3+19, 3*x3*x4+6*x3+5*x4-4, 6*x4*x5+6*x4+7*x5+118, x5*x6+3*x5+9*x6+27, 6*x6*x7+7*x6+x7+72, 9*x7*x8+7*x7+x8+35, 8*x9*x10+4*x9+3*x10-51, 3*x1*x10-6*x1+x10+5, 2*x8*x9+2*x8+3*x9+8>: noon3 := <10*x1*x2^2+10*x1*x3^2-11*x1+10, 10*x1^2*x2+10*x2*x3^2-11*x2+10, 10*x1^2*x3+10*x2^2*x3-11*x3+10>: noon4 := <10*x1*x2^2+10*x1*x3^2+10*x1*x4^2-11*x1+10, 10*x1^2*x2+10*x2*x3^2+10*x2*x4^2-11*x2+10, 10*x1^2*x3+10*x2^2*x3+10*x3*x4^2-11*x3+10, 10*x1^2*x4+10*x2^2*x4+10*x3^2*x4-11*x4+10>: noon5 := <10*x1*x2^2+10*x1*x3^2+10*x1*x4^2+10*x1*x5^2-11*x1+10, 10*x1^2*x2+10*x2*x3^2+10*x2*x4^2+10*x2*x5^2-11*x2+10, 10*x1^2*x3+10*x2^2*x3+10*x3*x4^2+10*x3*x5^2-11*x3+10, 10*x1^2*x4+10*x2^2*x4+10*x3^2*x4+10*x4*x5^2-11*x4+10, 10*x1^2*x5+10*x2^2*x5+10*x3^2*x5+10*x4^2*x5-11*x5+10>: noon6 := <10*x1^2*x6+10*x2^2*x6+10*x3^2*x6+10*x4^2*x6+10*x5^2*x6-11*x6+10, 10*x1^2*x5+10*x2^2*x5+10*x3^2*x5+10*x4^2*x5+10*x5*x6^2-11*x5+10, 10*x1^2*x4+10*x2^2*x4+10*x3^2*x4+10*x4*x5^2+10*x4*x6^2-11*x4+10, 10*x1^2*x3+10*x2^2*x3+10*x3*x4^2+10*x3*x5^2+10*x3*x6^2-11*x3+10, 10*x1*x2^2+10*x1*x3^2+10*x1*x4^2+10*x1*x5^2+10*x1*x6^2-11*x1+10, 10*x1^2*x2+10*x2*x3^2+10*x2*x4^2+10*x2*x5^2+10*x2*x6^2-11*x2+10>: pavelle := : rabmo := : random3 := <77*y*z^2+66*x^3*y+54*x*y*z^2-5*x*z^3+99*y^2*z^2-61*x*z^4, 79*y+56*x^2*z^2+49*x*y^2*z+63*y^2*z^2+57*x^3*y^2-59*x^2*y^3, x*z-47*x*y*z-91*x*z^3-47*y*z^3-61*x^4*z+41*x*y^3*z>: random4 := <76*y^2*z-68*y^2*x^2+67*y^4-38*y^2*z*w+23*y*w*z^3+14*z^5, -19*x*y*w-4*x^3*z+38*y^2*z*w-61*x^5-58*x^2*z*w^2-91*y^2*z^2*w, 81*z*x*w+63*x^3*z-85*y*w^3-36*x^3*z^2-35*w^2*x^3+11*x^2*w^3>: rbpl24 := <62500*x1^2+62500*y1^2+62500*z1^2-74529, 625*x2^2+625*y2^2+625*z2^2-1250*x2-2624, 3200*x2+1271, 12500*x3^2+12500*y3^2+12500*z3^2+2500*x3-44975*y3-10982, 400000*x1*x2+400000*y1*y2+400000*z1*z2-400000*x2+178837, 1000000*x1*x3+1000000*y1*y3+1000000*z1*z3+100000*x3-1799000*y3-805427, 2000000*x2*x3+2000000*y2*y3+2000000*z2*z3-2000000*x2+200000*x3-3598000*y3-1403, 113800000000000*x3*y2*z1-113800000000000*x2*y3*z1-113800000000000*x3*y1*z2 +113800000000000*x1*y3*z2+113800000000000*x2*y1*z3-113800000000000*x1*y2*z3 -206888400000000*x2*y1+206888400000000*x3*y1+206888400000000*x1*y2 -206888400000000*x3*y2-206888400000000*x1*y3+206888400000000*x2*y3 -2014260000000*x2*z1+2014260000000*x3*z1-61907200000000*y2*z1 +61907200000000*y3*z1+2014260000000*x1*z2-2014260000000*x3*z2 +61907200000000*y1*z2-61907200000000*y3*z2-2014260000000*x1*z3 +2014260000000*x2*z3-61907200000000*y1*z3+61907200000000*y2*z3 -362960716800000*x1+38025201600000*x2+292548849600000*x3+11809567440000*y1 +1475978220000*y2-825269402280000*y3-1212982689600000*z1-151600474800000*z2 +825859951200000*z3-19295432410527, -777600000000*x3*y2*z1+777600000000*x2*y3*z1+ 777600000000*x3*y1*z2-777600000000*x1*y3*z2-777600000000*x2*y1*z3+ 777600000000*x1*y2*z3-1409011200000*x2*y1+1409011200000*x3*y1+ 1409011200000*x1*y2-1409011200000*x3*y2-1409011200000*x1*y3+ 1409011200000*x2*y3-1065312000000*x2*z1+1065312000000*x3*z1 -805593600000*y2*z1+805593600000*y3*z1+1065312000000*x1*z2 -1065312000000*x3*z2+805593600000*y1*z2-805593600000*y3*z2 -1065312000000*x1*z3+1065312000000*x2*z3-805593600000*y1*z3+ 805593600000*y2*z3+235685027200*x1+398417510400*x2+ 158626915200*x3-311668424000*y1-268090368000*y2+72704002800*y3+ 412221302400*z1+354583756800*z2+307085438400*z3+282499646407>: redcyc5 := : redcyc6 := <1+y1+y2+y3+y4+y5, y1+y1*y2+y2*y3+y3*y4+y4*y5+y5, y1*y2*y3+y1*y2*y3*y4+y2*y3*y4*y5+y3*y4*y5+y4*y5*y1+y5*y1*y2, y1*y2+y1*y2*y3+y2*y3*y4+y3*y4*y5+y4*y5+y5*y1, z0^6*y1*y2*y3*y4*y5-1, y1*y2*y3*y4+y1*y2*y3*y4*y5+y2*y3*y4*y5+y3*y4*y5*y1+y4*y5*y1*y2+y5*y1*y2*y3>: redcyc7 := : redeco5 := : redeco6 := : redeco7 := : redeco8 := : reimer4 := <2*x^2-2*y^2+2*z^2-2*t^2-1, 2*x^3-2*y^3+2*z^3-2*t^3-1, 2*x^4-2*y^4+2*z^4-2*t^4-1, 2*x^5-2*y^5+2*z^5-2*t^5-1>: reimer5 := <-1+2*x^2-2*y^2+2*z^2-2*t^2+2*u^2, -1+2*x^3-2*y^3+2*z^3-2*t^3+2*u^3, -1+2*x^4-2*y^4+2*z^4-2*t^4+2*u^4, -1+2*x^5-2*y^5+2*z^5-2*t^5+2*u^5, -1+2*x^6-2*y^6+2*z^6-2*t^6+2*u^6>: rose := <7*y^4-20*x^2, 2160*x^2*z^4+1512*x*z^4+315*z^4-4000*x^2-2800*x-490, 40320000*x^6*y^2*z+67200000*x^5*y^3+28800000*x^5*y^2*z+94080000*x^4*y^3 -23520000*x^4*y*z^2-10080000*x^4*z^3+40924800*x^3*y^3+21168000*x^3*y^2*z -41395200*x^3*y*z^2-28224000*x^3*z^3+2634240*x^2*y^3+4939200*x^2*y^2*z -26726560*x^2*y*z^2-15288000*x^2*z^3-2300844*x*y^3+347508*x*y^2*z -7727104*x*y*z^2-1978032*x*z^3-432180*y^3-852355*y*z^2-180075*z^3>: S4 := <-2*p^3+2*p^3*phi^3-4*phi^3*s*p^2+5*phi^3*s^3*p-phi^3*s^5, -2*s*p^3-2*phi^3*s^2+phi^3*s^4-3*phi^3*s^2*p+2*phi^3*p,-2*s^2+s^4-4*s^2*p+phi^2+1+4*p>: S6 := <2*x6*x3+2*x4*x5+2*x1*x2+x2, 2*x5*x6+2*x1*x4+x4+2*x2*x3, 2*x1*x6+x6+2*x2*x5+2*x3*x4, 2*x6*x2+2*x3*x5+x4^2+x1^2+x1, 2*x6*x4+x5^2+2*x1*x3+x3+x2^2, x6^2+2*x1*x5+x5+2*x2*x4+x3^2>: schiele := : schwarz7 := : schwarz8 := <2*x4*x5+2*x3*x6+2*x2*x7+2*x1*x8+x8, x4^2+2*x3*x5+2*x2*x6+2*x1*x7+x8^2+x7, 2*x3*x4+2*x2*x5+2*x1*x6+2*x7*x8+x6, x3^2+2*x2*x4+2*x1*x5+x7^2+2*x6*x8+x5, 2*x2*x3+2*x1*x4+2*x6*x7+2*x5*x8+x4, x2^2+2*x1*x3+x6^2+2*x5*x7+2*x4*x8+x3, 2*x1*x2+2*x5*x6+2*x4*x7+2*x3*x8+x2, x1^2+x5^2+2*x4*x6+2*x3*x7+2*x2*x8+x1>: schwarz9 := : sendra := <-270*x^4*y^3-314*x*y^4-689*x*y^3+1428, 36*x^7+417*y*x^6-422*x^5*y^2-270*x^4*y^3+1428*x^3*y^4-1475*x^2*y^5 +510*x*y^6-200*x^6-174*x^5*y-966*x^4*y^2+529*x^3*y^3+269*x^2*y^4 +49*x*y^5-267*y^6+529*x^4*y+1303*x^2*y^3-314*x*y^4+262*y^5+36*x^4 -788*x^2*y^2-689*x*y^3+177*y^4>: symmetric5 := : symmetric6 := : tangents := : trinks := <-9*w+15*p*t+20*z*s, 99*w-11*s*b+3*b^2, w*p+2*z*t-11*b^3, 45*p+35*s-165*b-36, 35*p+40*z+25*t-27*s, 15*w+25*p*s+30*z-18*t-165*b^2>: utbikker := : vermeer := : virasoro := <-6*x4*x5+6*x4*x8+6*x5*x8-6*x6*x7+6*x6*x8+6*x7*x8+8*x8^2-x8, 8*x1^2+8*x1*x2+8*x1*x3+2*x1*x4+2*x1*x5+2*x1*x6+2*x1*x7-8*x2*x3-2*x4*x7-2*x5*x6-x1, 8*x1*x2-8*x1*x3+8*x2^2+8*x2*x3+2*x2*x4+2*x2*x5+2*x2*x6+2*x2*x7-2*x4*x6-2*x5*x7-x2, -8*x1*x2+8*x1*x3+8*x2*x3+8*x3^2+2*x3*x4+2*x3*x5+2*x3*x6+2*x3*x7-2*x4*x5-2*x6*x7-x3, 2*x1*x4-2*x1*x7+2*x2*x4-2*x2*x6+2*x3*x4-2*x3*x5 +8*x4^2+8*x4*x5+2*x4*x6+2*x4*x7+6*x4*x8-6*x5*x8-x4, 2*x1*x5-2*x1*x6+2*x2*x5-2*x2*x7-2*x3*x4+2*x3*x5 +8*x4*x5-6*x4*x8+8*x5^2+2*x5*x6+2*x5*x7+6*x5*x8-x5, -2*x1*x5+2*x1*x6-2*x2*x4+2*x2*x6+2*x3*x6-2*x3*x7 +2*x4*x6+2*x5*x6+8*x6^2+8*x6*x7+6*x6*x8-6*x7*x8-x6, -2*x1*x4+2*x1*x7-2*x2*x5+2*x2*x7-2*x3*x6+2*x3*x7 +2*x4*x7+2*x5*x7+8*x6*x7-6*x6*x8+8*x7^2+6*x7*x8-x7>: wang89 := : wang91 := <3*x2*x1*a+3*x0^2, 3*x2*x1*b+3*x3^2, 3*x3*x1*b+3*x1*x0*a+3*x2^2, 3*x3*x2*b+3*x2*x0*a+3*x1^2>: wang92a := : wang92c := <-3*d*c+b^2-2*a+2, -3*d*c^2+c*b^2-d*a+b, -3*d*a^2-4*c*b+2*b^2-6*c*a+3*b*a>: wang92e := : wang92f := <4*x12-3*x10-u4, 4*x13-3*x11-u5, 4*x14-u6, 2*x15-u1, 2*x7*u1-u4*u1-u2*u1, 2*x8*u3-u5*u3+2*x7*u2-u4*u2-2*x7*u1+u4*u1, -2*x10*u3+2*x11*u2-x11*u1+u3*u1, -x10*u3+x11*u2-2*x11*u1+u3*u1, 2*x16*u3-u3^2+2*x15*u2-u2^2, 2*x17*u6-u6^2+2*x16*u5-u5^2+2*x15*u4-u4^2, 2*x9*u6+2*x8*u5+2*x7*u4-2*x8*u3-2*x7*u2-u4*u1+u2*u1>: weispfenning94 := : wright := :