#Theorem39iveqs
#
# Here are the equations, as computed by SINGULAR
#
G[1]:=27*s^5*t*a^2-135*s^4*t^2*a^2+270*s^3*t^3*a^2-270*s^2*t^4*a^2+135*s*t^5*a^2-27*t^6*a^2+4*s^5*t*b^2-20*s^4*t^2*b^2+40*s^3*t^3*b^2-40*s^2*t^4*b^2+20*s*t^5*b^2-4*t^6*b^2-18*s^6*t*a+72*s^5*t^2*a-90*s^4*t^3*a+90*s^2*t^5*a-72*s*t^6*a+18*t^7*a-8*s^6*t*b+32*s^5*t^2*b-40*s^4*t^3*b+40*s^2*t^5*b-32*s*t^6*b+8*t^7*b+3*s^7*t+3*s^6*t^2-57*s^5*t^3+135*s^4*t^4-135*s^3*t^5+57*s^2*t^6-3*s*t^7-3*t^8
:G[2]:=27*s^5*a^2-135*s^4*t*a^2+270*s^3*t^2*a^2-270*s^2*t^3*a^2+135*s*t^4*a^2-27*t^5*a^2+4*s^5*b^2-20*s^4*t*b^2+40*s^3*t^2*b^2-40*s^2*t^3*b^2+20*s*t^4*b^2-4*t^5*b^2-18*s^6*a+72*s^5*t*a-90*s^4*t^2*a+90*s^2*t^4*a-72*s*t^5*a+18*t^6*a-8*s^6*b+32*s^5*t*b-40*s^4*t^2*b+40*s^2*t^4*b-32*s*t^5*b+8*t^6*b+3*s^7+3*s^6*t-57*s^5*t^2+135*s^4*t^3-135*s^3*t^4+57*s^2*t^5-3*s*t^6-3*t^7
:G[3]:=192*s^5*a*b^3-960*s^4*t*a*b^3+1920*s^3*t^2*a*b^3-1920*s^2*t^3*a*b^3+960*s*t^4*a*b^3-192*t^5*a*b^3-128*s^5*b^4+640*s^4*t*b^4-1280*s^3*t^2*b^4+1280*s^2*t^3*b^4-640*s*t^4*b^4+128*t^5*b^4-576*s^6*a*b^2+2304*s^5*t*a*b^2-2880*s^4*t^2*a*b^2+2880*s^2*t^4*a*b^2-2304*s*t^5*a*b^2+576*t^6*a*b^2+448*s^6*b^3-1792*s^5*t*b^3+2240*s^4*t^2*b^3-2240*s^2*t^4*b^3+1792*s*t^5*b^3-448*t^6*b^3+540*s^7*a*b-1512*s^6*t*a*b+3780*s^4*t^3*a*b-3780*s^3*t^4*a*b+1512*s*t^6*a*b-540*t^7*a*b-408*s^7*b^2+720*s^6*t*b^2+2112*s^5*t^2*b^2-7080*s^4*t^3*b^2+7080*s^3*t^4*b^2-2112*s^2*t^5*b^2-720*s*t^6*b^2+408*t^7*b^2-162*s^8*a+243*s^7*t*a+648*s^6*t^2*a-1377*s^5*t^3*a+1377*s^3*t^5*a-648*s^2*t^6*a-243*s*t^7*a+162*t^8*a+954*s^7*t*b-3816*s^6*t^2*b+4770*s^5*t^3*b-4770*s^3*t^5*b+3816*s^2*t^6*b-954*s*t^7*b+54*s^9-297*s^8*t+189*s^7*t^2+1593*s^6*t^3-4131*s^5*t^4+4131*s^4*t^5-1593*s^3*t^6-189*s^2*t^7+297*s*t^8-54*t^9
:G[4]:=324*s^4*a^3*b-648*s^3*t*a^3*b+648*s*t^3*a^3*b-324*t^4*a^3*b+48*s^4*a*b^3-96*s^3*t*a*b^3+96*s*t^3*a*b^3-48*t^4*a*b^3-1215*s^4*t*a^3+3645*s^3*t^2*a^3-3645*s^2*t^3*a^3+1215*s*t^4*a^3-1242*s^4*t*a^2*b+3726*s^3*t^2*a^2*b-3726*s^2*t^3*a^2*b+1242*s*t^4*a^2*b-96*s^5*a*b^2-84*s^4*t*a*b^2+732*s^3*t^2*a*b^2-732*s^2*t^3*a*b^2+84*s*t^4*a*b^2+96*t^5*a*b^2+32*s^5*b^3-216*s^4*t*b^3+488*s^3*t^2*b^3-488*s^2*t^3*b^3+216*s*t^4*b^3-32*t^5*b^3+3645*s^4*t^2*a^2-12150*s^3*t^3*a^2+14580*s^2*t^4*a^2-7290*s*t^5*a^2+1215*t^6*a^2-108*s^6*a*b+1332*s^5*t*a*b-2340*s^4*t^2*a*b+2340*s^2*t^4*a*b-1332*s*t^5*a*b+108*t^6*a*b-64*s^6*b^2+248*s^5*t*b^2+236*s^4*t^2*b^2-1800*s^3*t^3*b^2+2464*s^2*t^4*b^2-1328*s*t^5*b^2+244*t^6*b^2+405*s^6*t*a-3375*s^5*t^2*a+6480*s^4*t^3*a-2430*s^3*t^4*a-3915*s^2*t^5*a+3645*s*t^6*a-810*t^7*a+24*s^7*b+222*s^6*t*b-1902*s^5*t^2*b+3708*s^4*t^3*b-1908*s^3*t^4*b-1338*s^2*t^5*b+1578*s*t^6*b-384*t^7*b-90*s^7*t+45*s^6*t^2+2070*s^5*t^3-6075*s^4*t^4+6570*s^3*t^5-2745*s^2*t^6+90*s*t^7+135*t^8
:G[5]:=1296*s^3*a^3*b-3888*s^2*t*a^3*b+3888*s*t^2*a^3*b-1296*t^3*a^3*b+192*s^3*a*b^3-576*s^2*t*a*b^3+576*s*t^2*a*b^3-192*t^3*a*b^3-1215*s^4*a^3+2430*s^3*t*a^3-2430*s*t^3*a^3+1215*t^4*a^3-1242*s^4*a^2*b+2484*s^3*t*a^2*b-2484*s*t^3*a^2*b+1242*t^4*a^2*b-564*s^4*a*b^2+1128*s^3*t*a*b^2-1128*s*t^3*a*b^2+564*t^4*a*b^2-56*s^4*b^3+112*s^3*t*b^3-112*s*t^3*b^3+56*t^4*b^3+4860*s^4*t*a^2-14580*s^3*t^2*a^2+14580*s^2*t^3*a^2-4860*s*t^4*a^2+756*s^5*a*b-180*s^4*t*a*b-3240*s^3*t^2*a*b+3240*s^2*t^3*a*b+180*s*t^4*a*b-756*t^5*a*b-8*s^5*b^2+728*s^4*t*b^2-2144*s^3*t^2*b^2+2144*s^2*t^3*b^2-728*s*t^4*b^2+8*t^5*b^2+405*s^6*a-3780*s^5*t*a+6345*s^4*t^2*a-6345*s^2*t^4*a+3780*s*t^5*a-405*t^6*a+198*s^6*b-1608*s^5*t*b+2622*s^4*t^2*b-2622*s^2*t^4*b+1608*s*t^5*b-198*t^6*b-90*s^7+90*s^6*t+2250*s^5*t^2-6570*s^4*t^3+6570*s^3*t^4-2250*s^2*t^5-90*s*t^6+90*t^7
:G[6]:=256*s^5*b^5-1280*s^4*t*b^5+2560*s^3*t^2*b^5-2560*s^2*t^3*b^5+1280*s*t^4*b^5-256*t^5*b^5-1280*s^6*b^4+5120*s^5*t*b^4-6400*s^4*t^2*b^4+6400*s^2*t^4*b^4-5120*s*t^5*b^4+1280*t^6*b^4-324*s^7*a*b^2+1944*s^6*t*a*b^2-5184*s^5*t^2*a*b^2+8100*s^4*t^3*a*b^2-8100*s^3*t^4*a*b^2+5184*s^2*t^5*a*b^2-1944*s*t^6*a*b^2+324*t^7*a*b^2+2232*s^7*b^3-5712*s^6*t*b^3-2688*s^5*t^2*b^3+21000*s^4*t^3*b^3-21000*s^3*t^4*b^3+2688*s^2*t^5*b^3+5712*s*t^6*b^3-2232*t^7*b^3+648*s^8*a*b-3240*s^7*t*a*b+6480*s^6*t^2*a*b-5832*s^5*t^3*a*b+5832*s^3*t^5*a*b-6480*s^2*t^6*a*b+3240*s*t^7*a*b-648*t^8*a*b-1476*s^8*b^2-288*s^7*t*b^2+15912*s^6*t^2*b^2-25056*s^5*t^3*b^2+25056*s^3*t^5*b^2-15912*s^2*t^6*b^2+288*s*t^7*b^2+1476*t^8*b^2-243*s^9*a+729*s^8*t*a+243*s^7*t^2*a-4131*s^6*t^3*a+8262*s^5*t^4*a-8262*s^4*t^5*a+4131*s^3*t^6*a-243*s^2*t^7*a-729*s*t^8*a+243*t^9*a+162*s^9*b+2970*s^8*t*b-9450*s^7*t^2*b+810*s^6*t^3*b+22572*s^5*t^4*b-22572*s^4*t^5*b-810*s^3*t^6*b+9450*s^2*t^7*b-2970*s*t^8*b-162*t^9*b+81*s^10-729*s^9*t+243*s^8*t^2+4698*s^7*t^3-7614*s^6*t^4+7614*s^4*t^6-4698*s^3*t^7-243*s^2*t^8+729*s*t^9-81*t^10
:G[7]:=1536*s^3*a*b^4-4608*s^2*t*a*b^4+4608*s*t^2*a*b^4-1536*t^3*a*b^4-1296*s^4*a^2*b^2+2592*s^3*t*a^2*b^2-2592*s*t^3*a^2*b^2+1296*t^4*a^2*b^2-6528*s^4*a*b^3+13056*s^3*t*a*b^3-13056*s*t^3*a*b^3+6528*t^4*a*b^3-448*s^4*b^4+896*s^3*t*b^4-896*s*t^3*b^4+448*t^4*b^4+11340*s^4*t*a^2*b-34020*s^3*t^2*a^2*b+34020*s^2*t^3*a^2*b-11340*s*t^4*a^2*b+9648*s^5*a*b^2-4896*s^4*t*a*b^2-33552*s^3*t^2*a*b^2+33552*s^2*t^3*a*b^2+4896*s*t^4*a*b^2-9648*t^5*a*b^2+1568*s^5*b^3+16*s^4*t*b^3-7888*s^3*t^2*b^3+7888*s^2*t^3*b^3-16*s*t^4*b^3-1568*t^5*b^3-18225*s^4*t^2*a^2+60750*s^3*t^3*a^2-72900*s^2*t^4*a^2+36450*s*t^5*a^2-6075*t^6*a^2-4104*s^6*a*b-17064*s^5*t*a*b+46440*s^4*t^2*a*b-46440*s^2*t^4*a*b+17064*s*t^5*a*b+4104*t^6*a*b-1968*s^6*b^2-4224*s^5*t*b^2+11652*s^4*t^2*b^2+9000*s^3*t^3*b^2-25152*s^2*t^4*b^2+9624*s*t^5*b^2+1068*t^6*b^2+648*s^7*a+3402*s^6*t*a+10368*s^5*t^2*a-44550*s^4*t^3*a+24300*s^3*t^4*a+26082*s^2*t^5*a-23652*s*t^6*a+3402*t^7*a+1080*s^7*b+3384*s^6*t*b+4680*s^5*t^2*b-34920*s^4*t^3*b+25920*s^3*t^4*b+11520*s^2*t^5*b-12384*s*t^6*b+720*t^7*b-216*s^8-918*s^7*t-1593*s^6*t^2-2646*s^5*t^3+30375*s^4*t^4-40554*s^3*t^5+15093*s^2*t^6+918*s*t^7-459*t^8
:G[8]:=768*s^3*a^2*b^3-2304*s^2*t*a^2*b^3+2304*s*t^2*a^2*b^3-768*t^3*a^2*b^3-2304*s^4*a^2*b^2+4608*s^3*t*a^2*b^2-4608*s*t^3*a^2*b^2+2304*t^4*a^2*b^2-512*s^4*a*b^3+1024*s^3*t*a*b^3-1024*s*t^3*a*b^3+512*t^4*a*b^3+8964*s^4*t*a^2*b-26892*s^3*t^2*a^2*b+26892*s^2*t^3*a^2*b-8964*s*t^4*a^2*b+1680*s^5*a*b^2-2112*s^4*t*a*b^2-2064*s^3*t^2*a*b^2+2064*s^2*t^3*a*b^2+2112*s*t^4*a*b^2-1680*t^5*a*b^2-224*s^5*b^3+1456*s^4*t*b^3-3248*s^3*t^2*b^3+3248*s^2*t^3*b^3-1456*s*t^4*b^3+224*t^5*b^3-8505*s^4*t^2*a^2+28350*s^3*t^3*a^2-34020*s^2*t^4*a^2+17010*s*t^5*a^2-2835*t^6*a^2-288*s^6*a*b-5112*s^5*t*a*b+11088*s^4*t^2*a*b-11088*s^2*t^4*a*b+5112*s*t^5*a*b+288*t^6*a*b+400*s^6*b^2-2240*s^5*t*b^2+2020*s^4*t^2*b^2+4200*s^3*t^3*b^2-8320*s^2*t^4*b^2+4760*s*t^5*b^2-820*t^6*b^2+108*s^7*a-108*s^6*t*a+5238*s^5*t^2*a-12150*s^4*t^3*a+2700*s^3*t^4*a+11772*s^2*t^5*a-9342*s*t^6*a+1782*t^7*a-72*s^7*b-468*s^6*t*b+6852*s^5*t^2*b-16032*s^4*t^3*b+11832*s^3*t^4*b+708*s^2*t^5*b-3732*s*t^6*b+912*t^7*b-36*s^8+252*s^7*t-513*s^6*t^2-3996*s^5*t^3+14175*s^4*t^4-16164*s^3*t^5+6813*s^2*t^6-252*s*t^7-279*t^8
:G[9]:=3*s^5*f-15*s^4*t*f+30*s^3*t^2*f-30*s^2*t^3*f+15*s*t^4*f-3*t^5*f-36*s^5*a*b+180*s^4*t*a*b-360*s^3*t^2*a*b+360*s^2*t^3*a*b-180*s*t^4*a*b+36*t^5*a*b-8*s^5*b^2+40*s^4*t*b^2-80*s^3*t^2*b^2+80*s^2*t^3*b^2-40*s*t^4*b^2+8*t^5*b^2+54*s^6*a-216*s^5*t*a+270*s^4*t^2*a-270*s^2*t^4*a+216*s*t^5*a-54*t^6*a+36*s^6*b-144*s^5*t*b+180*s^4*t^2*b-180*s^2*t^4*b+144*s*t^5*b-36*t^6*b-36*s^7+99*s^6*t+9*s^5*t^2-270*s^4*t^3+270*s^3*t^4-9*s^2*t^5-99*s*t^6+36*t^7
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