/******************************************************* Here we have the 15 different components of h20 under Rosenhain transformations. Run the commands below to produce the output. > R:=PolynomialRing(Rationals(),3); > load "h20.txt"; Loading "h20.txt" > load "../fixedgroups.txt"; Loading "../fixedgroups.txt" > time H20:=humbertcomponentsfast(h20,20); computing 15 humbert components: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Time: 607.766 ********************************************************/ H20:= [ e1^16*e2^8*e3^8 - 8*e1^16*e2^8*e3^7 + 28*e1^16*e2^8*e3^6 - 56*e1^16*e2^8*e3^5 + 70*e1^16*e2^8*e3^4 - 56*e1^16*e2^8*e3^3 + 28*e1^16*e2^8*e3^2 - 8*e1^16*e2^8*e3 + e1^16*e2^8 - 8*e1^15*e2^9*e3^8 - 1472*e1^15*e2^9*e3^7 + 800*e1^15*e2^9*e3^6 + 10176*e1^15*e2^9*e3^5 - 18992*e1^15*e2^9*e3^4 + 10176*e1^15*e2^9*e3^3 + 800*e1^15*e2^9*e3^2 - 1472*e1^15*e2^9*e3 - 8*e1^15*e2^9 + 5120*e1^15*e2^8*e3^8 + 23552*e1^15*e2^8*e3^7 - 101376*e1^15*e2^8*e3^6 + 72704*e1^15*e2^8*e3^5 + 72704*e1^15*e2^8*e3^4 - 101376*e1^15*e2^8*e3^3 + 23552*e1^15*e2^8*e3^2 + 5120*e1^15*e2^8*e3 - 3592*e1^15*e2^7*e3^9 - 68032*e1^15*e2^7*e3^8 + 103200*e1^15*e2^7*e3^7 + 256960*e1^15*e2^7*e3^6 - 577072*e1^15*e2^7*e3^5 + 256960*e1^15*e2^7*e3^4 + 103200*e1^15*e2^7*e3^3 - 68032*e1^15*e2^7*e3^2 - 3592*e1^15*e2^7*e3 + 43520*e1^15*e2^6*e3^9 + 126464*e1^15*e2^6*e3^8 - 640512*e1^15*e2^6*e3^7 + 470528*e1^15*e2^6*e3^6 + 470528*e1^15*e2^6*e3^5 - 640512*e1^15*e2^6*e3^4 + 126464*e1^15*e2^6*e3^3 + 43520*e1^15*e2^6*e3^2 - 138240*e1^15*e2^5*e3^9 + 165888*e1^15*e2^5*e3^8 + 580608*e1^15*e2^5*e3^7 - 1216512*e1^15*e2^5*e3^6 + 580608*e1^15*e2^5*e3^5 + 165888*e1^15*e2^5*e3^4 - 138240*e1^15*e2^5*e3^3 + 163840*e1^15*e2^4*e3^9 - 491520*e1^15*e2^4*e3^8 + 327680*e1^15*e2^4*e3^7 + 327680*e1^15*e2^4*e3^6 - 491520*e1^15*e2^4*e3^5 + 163840*e1^15*e2^4*e3^4 - 65536*e1^15*e2^3*e3^9 + 262144*e1^15*e2^3*e3^8 - 393216*e1^15*e2^3*e3^7 + 262144*e1^15*e2^3*e3^6 - 65536*e1^15*e2^3*e3^5 + 28*e1^14*e2^10*e3^8 + 800*e1^14*e2^10*e3^7 + 633616*e1^14*e2^10*e3^6 + 3749344*e1^14*e2^10*e3^5 + 8009640*e1^14*e2^10*e3^4 + 3749344*e1^14*e2^10*e3^3 + 633616*e1^14*e2^10*e3^2 + 800*e1^14*e2^10*e3 + 28*e1^14*e2^10 + 23552*e1^14*e2^9*e3^8 - 1936384*e1^14*e2^9*e3^7 - 15303680*e1^14*e2^9*e3^6 - 49892352*e1^14*e2^9*e3^5 - 49892352*e1^14*e2^9*e3^4 - 15303680*e1^14*e2^9*e3^3 - 1936384*e1^14*e2^9*e3^2 + 23552*e1^14*e2^9*e3 - 68032*e1^14*e2^8*e3^9 + 2289152*e1^14*e2^8*e3^8 + 21769984*e1^14*e2^8*e3^7 + 117801472*e1^14*e2^8*e3^6 + 186176896*e1^14*e2^8*e3^5 + 117801472*e1^14*e2^8*e3^4 + 21769984*e1^14*e2^8*e3^3 + 2289152*e1^14*e2^8*e3^2 - 68032*e1^14*e2^8*e3 + 43520*e1^14*e2^7*e3^10 - 1126400*e1^14*e2^7*e3^9 - 13665792*e1^14*e2^7*e3^8 - 126743040*e1^14*e2^7*e3^7 - 328270336*e1^14*e2^7*e3^6 - 328270336*e1^14*e2^7*e3^5 - 126743040*e1^14*e2^7*e3^4 - 13665792*e1^14*e2^7*e3^3 - 1126400*e1^14*e2^7*e3^2 + 43520*e1^14*e2^7*e3 + 140316*e1^14*e2^6*e3^10 + 3744544*e1^14*e2^6*e3^9 + 61545232*e1^14*e2^6*e3^8 + 294589920*e1^14*e2^6*e3^7 + 454365096*e1^14*e2^6*e3^6 + 294589920*e1^14*e2^6*e3^5 + 61545232*e1^14*e2^6*e3^4 + 3744544*e1^14*e2^6*e3^3 + 140316*e1^14*e2^6*e3^2 - 294400*e1^14*e2^5*e3^10 - 10865152*e1^14*e2^5*e3^9 - 125021696*e1^14*e2^5*e3^8 - 333580800*e1^14*e2^5*e3^7 - 333580800*e1^14*e2^5*e3^6 - 125021696*e1^14*e2^5*e3^5 - 10865152*e1^14*e2^5*e3^4 - 294400*e1^14*e2^5*e3^3 + 143360*e1^14*e2^4*e3^10 + 18833408*e1^14*e2^4*e3^9 + 118411264*e1^14*e2^4*e3^8 + 194985984*e1^14*e2^4*e3^7 + 118411264*e1^14*e2^4*e3^6 + 18833408*e1^14*e2^4*e3^5 + 143360*e1^14*e2^4*e3^4 - 163840*e1^14*e2^3*e3^10 - 14188544*e1^14*e2^3*e3^9 - 52756480*e1^14*e2^3*e3^8 - 52756480*e1^14*e2^3*e3^7 - 14188544*e1^14*e2^3*e3^6 - 163840*e1^14*e2^3*e3^5 + 131072*e1^14*e2^2*e3^10 + 3670016*e1^14*e2^2*e3^9 + 9175040*e1^14*e2^2*e3^8 + 3670016*e1^14*e2^2*e3^7 + 131072*e1^14*e2^2*e3^6 - 56*e1^13*e2^11*e3^8 + 10176*e1^13*e2^11*e3^7 + 3749344*e1^13*e2^11*e3^6 - 6699456*e1^13*e2^11*e3^5 - 61228880*e1^13*e2^11*e3^4 - 6699456*e1^13*e2^11*e3^3 + 3749344*e1^13*e2^11*e3^2 + 10176*e1^13*e2^11*e3 - 56*e1^13*e2^11 - 101376*e1^13*e2^10*e3^8 - 15303680*e1^13*e2^10*e3^7 + 42324992*e1^13*e2^10*e3^6 + 174406656*e1^13*e2^10*e3^5 + 174406656*e1^13*e2^10*e3^4 + 42324992*e1^13*e2^10*e3^3 - 15303680*e1^13*e2^10*e3^2 - 101376*e1^13*e2^10*e3 + 103200*e1^13*e2^9*e3^9 + 21769984*e1^13*e2^9*e3^8 - 74684544*e1^13*e2^9*e3^7 - 221804288*e1^13*e2^9*e3^6 - 256075072*e1^13*e2^9*e3^5 - 221804288*e1^13*e2^9*e3^4 - 74684544*e1^13*e2^9*e3^3 + 21769984*e1^13*e2^9*e3^2 + 103200*e1^13*e2^9*e3 + 126464*e1^13*e2^8*e3^10 - 13665792*e1^13*e2^8*e3^9 + 57502720*e1^13*e2^8*e3^8 + 178754560*e1^13*e2^8*e3^7 - 222717952*e1^13*e2^8*e3^6 - 222717952*e1^13*e2^8*e3^5 + 178754560*e1^13*e2^8*e3^4 + 57502720*e1^13*e2^8*e3^3 - 13665792*e1^13*e2^8*e3^2 + 126464*e1^13*e2^8*e3 - 138240*e1^13*e2^7*e3^11 + 3744544*e1^13*e2^7*e3^10 - 22935808*e1^13*e2^7*e3^9 - 104632448*e1^13*e2^7*e3^8 + 698518784*e1^13*e2^7*e3^7 + 1669458624*e1^13*e2^7*e3^6 + 698518784*e1^13*e2^7*e3^5 - 104632448*e1^13*e2^7*e3^4 - 22935808*e1^13*e2^7*e3^3 + 3744544*e1^13*e2^7*e3^2 - 138240*e1^13*e2^7*e3 - 294400*e1^13*e2^6*e3^11 + 4069376*e1^13*e2^6*e3^10 + 47147520*e1^13*e2^6*e3^9 - 538305024*e1^13*e2^6*e3^8 - 2331189760*e1^13*e2^6*e3^7 - 2331189760*e1^13*e2^6*e3^6 - 538305024*e1^13*e2^6*e3^5 + 47147520*e1^13*e2^6*e3^4 + 4069376*e1^13*e2^6*e3^3 - 294400*e1^13*e2^6*e3^2 + 421320*e1^13*e2^5*e3^11 - 12891200*e1^13*e2^5*e3^10 + 166356448*e1^13*e2^5*e3^9 + 1394205248*e1^13*e2^5*e3^8 + 2540960944*e1^13*e2^5*e3^7 + 1394205248*e1^13*e2^5*e3^6 + 166356448*e1^13*e2^5*e3^5 - 12891200*e1^13*e2^5*e3^4 + 421320*e1^13*e2^5*e3^3 + 250880*e1^13*e2^4*e3^11 - 15475712*e1^13*e2^4*e3^10 - 368217088*e1^13*e2^4*e3^9 - 1227170816*e1^13*e2^4*e3^8 - 1227170816*e1^13*e2^4*e3^7 - 368217088*e1^13*e2^4*e3^6 - 15475712*e1^13*e2^4*e3^5 + 250880*e1^13*e2^4*e3^4 - 10240*e1^13*e2^3*e3^11 + 34353152*e1^13*e2^3*e3^10 + 244361216*e1^13*e2^3*e3^9 + 449224704*e1^13*e2^3*e3^8 + 244361216*e1^13*e2^3*e3^7 + 34353152*e1^13*e2^3*e3^6 - 10240*e1^13*e2^3*e3^5 - 163840*e1^13*e2^2*e3^11 - 14188544*e1^13*e2^2*e3^10 - 52756480*e1^13*e2^2*e3^9 - 52756480*e1^13*e2^2*e3^8 - 14188544*e1^13*e2^2*e3^7 - 163840*e1^13*e2^2*e3^6 - 65536*e1^13*e2*e3^11 + 262144*e1^13*e2*e3^10 - 393216*e1^13*e2*e3^9 + 262144*e1^13*e2*e3^8 - 65536*e1^13*e2*e3^7 + 70*e1^12*e2^12*e3^8 - 18992*e1^12*e2^12*e3^7 + 8009640*e1^12*e2^12*e3^6 - 61228880*e1^12*e2^12*e3^5 + 207139620*e1^12*e2^12*e3^4 - 61228880*e1^12*e2^12*e3^3 + 8009640*e1^12*e2^12*e3^2 - 18992*e1^12*e2^12*e3 + 70*e1^12*e2^12 + 72704*e1^12*e2^11*e3^8 - 49892352*e1^12*e2^11*e3^7 + 174406656*e1^12*e2^11*e3^6 - 258804736*e1^12*e2^11*e3^5 - 258804736*e1^12*e2^11*e3^4 + 174406656*e1^12*e2^11*e3^3 - 49892352*e1^12*e2^11*e3^2 + 72704*e1^12*e2^11*e3 + 256960*e1^12*e2^10*e3^9 + 117801472*e1^12*e2^10*e3^8 - 221804288*e1^12*e2^10*e3^7 - 636383744*e1^12*e2^10*e3^6 + 473626240*e1^12*e2^10*e3^5 - 636383744*e1^12*e2^10*e3^4 - 221804288*e1^12*e2^10*e3^3 + 117801472*e1^12*e2^10*e3^2 + 256960*e1^12*e2^10*e3 - 640512*e1^12*e2^9*e3^10 - 126743040*e1^12*e2^9*e3^9 + 178754560*e1^12*e2^9*e3^8 + 1872669696*e1^12*e2^9*e3^7 + 894531584*e1^12*e2^9*e3^6 + 894531584*e1^12*e2^9*e3^5 + 1872669696*e1^12*e2^9*e3^4 + 178754560*e1^12*e2^9*e3^3 - 126743040*e1^12*e2^9*e3^2 - 640512*e1^12*e2^9*e3 + 165888*e1^12*e2^8*e3^11 + 61545232*e1^12*e2^8*e3^10 - 104632448*e1^12*e2^8*e3^9 - 2175224384*e1^12*e2^8*e3^8 - 2679290752*e1^12*e2^8*e3^7 - 70130080*e1^12*e2^8*e3^6 - 2679290752*e1^12*e2^8*e3^5 - 2175224384*e1^12*e2^8*e3^4 - 104632448*e1^12*e2^8*e3^3 + 61545232*e1^12*e2^8*e3^2 + 165888*e1^12*e2^8*e3 + 163840*e1^12*e2^7*e3^12 - 10865152*e1^12*e2^7*e3^11 + 47147520*e1^12*e2^7*e3^10 + 1428030464*e1^12*e2^7*e3^9 + 2805849088*e1^12*e2^7*e3^8 - 1451753472*e1^12*e2^7*e3^7 - 1451753472*e1^12*e2^7*e3^6 + 2805849088*e1^12*e2^7*e3^5 + 1428030464*e1^12*e2^7*e3^4 + 47147520*e1^12*e2^7*e3^3 - 10865152*e1^12*e2^7*e3^2 + 163840*e1^12*e2^7*e3 + 143360*e1^12*e2^6*e3^12 - 12891200*e1^12*e2^6*e3^11 - 515153408*e1^12*e2^6*e3^10 - 1629624064*e1^12*e2^6*e3^9 + 1756790272*e1^12*e2^6*e3^8 + 6438614656*e1^12*e2^6*e3^7 + 1756790272*e1^12*e2^6*e3^6 - 1629624064*e1^12*e2^6*e3^5 - 515153408*e1^12*e2^6*e3^4 - 12891200*e1^12*e2^6*e3^3 + 143360*e1^12*e2^6*e3^2 + 250880*e1^12*e2^5*e3^12 + 78840832*e1^12*e2^5*e3^11 + 512802816*e1^12*e2^5*e3^10 - 803905536*e1^12*e2^5*e3^9 - 5827786752*e1^12*e2^5*e3^8 - 5827786752*e1^12*e2^5*e3^7 - 803905536*e1^12*e2^5*e3^6 + 512802816*e1^12*e2^5*e3^5 + 78840832*e1^12*e2^5*e3^4 + 250880*e1^12*e2^5*e3^3 - 1116090*e1^12*e2^4*e3^12 - 58116656*e1^12*e2^4*e3^11 + 143775656*e1^12*e2^4*e3^10 + 2268477616*e1^12*e2^4*e3^9 + 4252992292*e1^12*e2^4*e3^8 + 2268477616*e1^12*e2^4*e3^7 + 143775656*e1^12*e2^4*e3^6 - 58116656*e1^12*e2^4*e3^5 - 1116090*e1^12*e2^4*e3^4 + 250880*e1^12*e2^3*e3^12 - 15475712*e1^12*e2^3*e3^11 - 368217088*e1^12*e2^3*e3^10 - 1227170816*e1^12*e2^3*e3^9 - 1227170816*e1^12*e2^3*e3^8 - 368217088*e1^12*e2^3*e3^7 - 15475712*e1^12*e2^3*e3^6 + 250880*e1^12*e2^3*e3^5 + 143360*e1^12*e2^2*e3^12 + 18833408*e1^12*e2^2*e3^11 + 118411264*e1^12*e2^2*e3^10 + 194985984*e1^12*e2^2*e3^9 + 118411264*e1^12*e2^2*e3^8 + 18833408*e1^12*e2^2*e3^7 + 143360*e1^12*e2^2*e3^6 + 163840*e1^12*e2*e3^12 - 491520*e1^12*e2*e3^11 + 327680*e1^12*e2*e3^10 + 327680*e1^12*e2*e3^9 - 491520*e1^12*e2*e3^8 + 163840*e1^12*e2*e3^7 - 56*e1^11*e2^13*e3^8 + 10176*e1^11*e2^13*e3^7 + 3749344*e1^11*e2^13*e3^6 - 6699456*e1^11*e2^13*e3^5 - 61228880*e1^11*e2^13*e3^4 - 6699456*e1^11*e2^13*e3^3 + 3749344*e1^11*e2^13*e3^2 + 10176*e1^11*e2^13*e3 - 56*e1^11*e2^13 + 72704*e1^11*e2^12*e3^8 - 49892352*e1^11*e2^12*e3^7 + 174406656*e1^11*e2^12*e3^6 - 258804736*e1^11*e2^12*e3^5 - 258804736*e1^11*e2^12*e3^4 + 174406656*e1^11*e2^12*e3^3 - 49892352*e1^11*e2^12*e3^2 + 72704*e1^11*e2^12*e3 - 577072*e1^11*e2^11*e3^9 + 186176896*e1^11*e2^11*e3^8 - 256075072*e1^11*e2^11*e3^7 + 473626240*e1^11*e2^11*e3^6 + 1878052576*e1^11*e2^11*e3^5 + 473626240*e1^11*e2^11*e3^4 - 256075072*e1^11*e2^11*e3^3 + 186176896*e1^11*e2^11*e3^2 - 577072*e1^11*e2^11*e3 + 470528*e1^11*e2^10*e3^10 - 328270336*e1^11*e2^10*e3^9 - 222717952*e1^11*e2^10*e3^8 + 894531584*e1^11*e2^10*e3^7 - 2692824064*e1^11*e2^10*e3^6 - 2692824064*e1^11*e2^10*e3^5 + 894531584*e1^11*e2^10*e3^4 - 222717952*e1^11*e2^10*e3^3 - 328270336*e1^11*e2^10*e3^2 + 470528*e1^11*e2^10*e3 + 580608*e1^11*e2^9*e3^11 + 294589920*e1^11*e2^9*e3^10 + 698518784*e1^11*e2^9*e3^9 - 2679290752*e1^11*e2^9*e3^8 - 2004541696*e1^11*e2^9*e3^7 + 2682665792*e1^11*e2^9*e3^6 - 2004541696*e1^11*e2^9*e3^5 - 2679290752*e1^11*e2^9*e3^4 + 698518784*e1^11*e2^9*e3^3 + 294589920*e1^11*e2^9*e3^2 + 580608*e1^11*e2^9*e3 - 491520*e1^11*e2^8*e3^12 - 125021696*e1^11*e2^8*e3^11 - 538305024*e1^11*e2^8*e3^10 + 2805849088*e1^11*e2^8*e3^9 + 8650687488*e1^11*e2^8*e3^8 + 2360619008*e1^11*e2^8*e3^7 + 2360619008*e1^11*e2^8*e3^6 + 8650687488*e1^11*e2^8*e3^5 + 2805849088*e1^11*e2^8*e3^4 - 538305024*e1^11*e2^8*e3^3 - 125021696*e1^11*e2^8*e3^2 - 491520*e1^11*e2^8*e3 - 65536*e1^11*e2^7*e3^13 + 18833408*e1^11*e2^7*e3^12 + 166356448*e1^11*e2^7*e3^11 - 1629624064*e1^11*e2^7*e3^10 - 9215617920*e1^11*e2^7*e3^9 - 7532134656*e1^11*e2^7*e3^8 + 682588992*e1^11*e2^7*e3^7 - 7532134656*e1^11*e2^7*e3^6 - 9215617920*e1^11*e2^7*e3^5 - 1629624064*e1^11*e2^7*e3^4 + 166356448*e1^11*e2^7*e3^3 + 18833408*e1^11*e2^7*e3^2 - 65536*e1^11*e2^7*e3 - 163840*e1^11*e2^6*e3^13 - 15475712*e1^11*e2^6*e3^12 + 512802816*e1^11*e2^6*e3^11 + 4679932928*e1^11*e2^6*e3^10 + 7092835328*e1^11*e2^6*e3^9 - 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163840*e1*e2^7*e3^12 + 138240*e1*e2^7*e3^11 - 43520*e1*e2^7*e3^10 + 3592*e1*e2^7*e3^9 - 8*e1*e2^7*e3^8 + e2^16*e3^8 - 8*e2^15*e3^8 + 28*e2^14*e3^8 - 56*e2^13*e3^8 + 70*e2^12*e3^8 - 56*e2^11*e3^8 + 28*e2^10*e3^8 - 8*e2^9*e3^8 + e2^8*e3^8, e1^16*e2^8*e3^8 - 8*e1^16*e2^8*e3^7 + 28*e1^16*e2^8*e3^6 - 56*e1^16*e2^8*e3^5 + 70*e1^16*e2^8*e3^4 - 56*e1^16*e2^8*e3^3 + 28*e1^16*e2^8*e3^2 - 8*e1^16*e2^8*e3 + e1^16*e2^8 + 3592*e1^15*e2^9*e3^7 + 18376*e1^15*e2^9*e3^6 - 47448*e1^15*e2^9*e3^5 - 280*e1^15*e2^9*e3^4 + 47896*e1^15*e2^9*e3^3 - 18600*e1^15*e2^9*e3^2 - 3528*e1^15*e2^9*e3 - 8*e1^15*e2^9 - 8*e1^15*e2^8*e3^9 - 5064*e1^15*e2^8*e3^8 - 59560*e1^15*e2^8*e3^7 + 41240*e1^15*e2^8*e3^6 + 209640*e1^15*e2^8*e3^5 - 209752*e1^15*e2^8*e3^4 - 41016*e1^15*e2^8*e3^3 + 59400*e1^15*e2^8*e3^2 + 5120*e1^15*e2^8*e3 + 1536*e1^15*e2^7*e3^9 + 50688*e1^15*e2^7*e3^8 + 109568*e1^15*e2^7*e3^7 - 377344*e1^15*e2^7*e3^6 + 377344*e1^15*e2^7*e3^4 - 109568*e1^15*e2^7*e3^3 - 50688*e1^15*e2^7*e3^2 - 1536*e1^15*e2^7*e3 - 9728*e1^15*e2^6*e3^9 - 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119296*e1*e2^13*e3^10 + 109568*e1*e2^13*e3^9 + 41240*e1*e2^13*e3^8 - 47448*e1*e2^13*e3^7 - 8192*e1*e2^12*e3^12 + 98304*e1*e2^12*e3^11 + 77312*e1*e2^12*e3^10 - 377344*e1*e2^12*e3^9 + 209640*e1*e2^12*e3^8 - 280*e1*e2^12*e3^7 - 24576*e1*e2^11*e3^12 - 245760*e1*e2^11*e3^11 + 432640*e1*e2^11*e3^10 - 209752*e1*e2^11*e3^8 + 47896*e1*e2^11*e3^7 + 114688*e1*e2^10*e3^12 - 432640*e1*e2^10*e3^10 + 377344*e1*e2^10*e3^9 - 41016*e1*e2^10*e3^8 - 18600*e1*e2^10*e3^7 - 114688*e1*e2^9*e3^12 + 245760*e1*e2^9*e3^11 - 77312*e1*e2^9*e3^10 - 109568*e1*e2^9*e3^9 + 59400*e1*e2^9*e3^8 - 3528*e1*e2^9*e3^7 + 24576*e1*e2^8*e3^12 - 98304*e1*e2^8*e3^11 + 119296*e1*e2^8*e3^10 - 50688*e1*e2^8*e3^9 + 5120*e1*e2^8*e3^8 - 8*e1*e2^8*e3^7 + 8192*e1*e2^7*e3^12 - 16384*e1*e2^7*e3^11 + 9728*e1*e2^7*e3^10 - 1536*e1*e2^7*e3^9 + e2^16*e3^8 - 8*e2^15*e3^8 + 28*e2^14*e3^8 - 56*e2^13*e3^8 + 70*e2^12*e3^8 - 56*e2^11*e3^8 + 28*e2^10*e3^8 - 8*e2^9*e3^8 + e2^8*e3^8, e1^16*e2^8*e3^8 - 8*e1^16*e2^7*e3^8 + 28*e1^16*e2^6*e3^8 - 56*e1^16*e2^5*e3^8 + 70*e1^16*e2^4*e3^8 - 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