不妨设x≥y≥z≥w
记x=w+t+v+u，y=w+t+v，z=w+t代入得
864*t^8 + 1776*t^7*u + 4992*t^7*v + 6912*t^7*w + 2108*t^6*u^2 + 10376*t^6*u*v + 11928*t^6*u*w + 13112*t^6*v^2 + 35664*t^6*v*w + 22896*t^6*w^2 + 1792*t^5*u^3 + 11784*t^5*u^2*v + 13236*t^5*u^2*w + 26616*t^5*u*v^2 + 64248*t^5*u*v*w + 31860*t^5*u*w^2 + 20360*t^5*v^3 + 83112*t^5*v^2*w + 103896*t^5*v*w^2 + 40176*t^5*w^3 + 945*t^4*u^4 + 8278*t^4*u^3*v + 10596*t^4*u^3*w + 26738*t^4*u^2*v^2 + 66084*t^4*u^2*v*w + 34227*t^4*u^2*w^2 + 38072*t^4*u*v^3 + 146052*t^4*u*v^2*w + 159858*t^4*u*v*w^2 + 42282*t^4*u*w^3 + 20224*t^4*v^4 + 112032*t^4*v^3*w + 211698*t^4*v^2*w^2 + 157140*t^4*v*w^3 + 39366*t^4*w^4 + 262*t^3*u^5 + 3238*t^3*u^4*v + 4812*t^3*u^4*w + 14656*t^3*u^3*v^2 + 40104*t^3*u^3*v*w + 25614*t^3*u^3*w^2 + 31358*t^3*u^2*v^3 + 125184*t^3*u^2*v^2*w + 148428*t^3*u^2*v*w^2 + 47628*t^3*u^2*w^3 + 32336*t^3*u*v^4 + 175092*t^3*u*v^3*w + 315576*t^3*u*v^2*w^2 + 204120*t^3*u*v*w^3 + 27864*t^3*u*w^4 + 12992*t^3*v^5 + 92640*t^3*v^4*w + 241110*t^3*v^3*w^2 + 275076*t^3*v^2*w^3 + 129114*t^3*v*w^4 + 20412*t^3*w^5 + 29*t^2*u^6 + 606*t^2*u^5*v + 1038*t^2*u^5*w + 4040*t^2*u^4*v^2 + 12288*t^2*u^4*v*w + 9414*t^2*u^4*w^2 + 12512*t^2*u^3*v^3 + 53952*t^2*u^3*v^2*w + 74016*t^2*u^3*v*w^2 + 32076*t^2*u^3*w^3 + 20042*t^2*u^2*v^4 + 113112*t^2*u^2*v^3*w + 220644*t^2*u^2*v^2*w^2 + 169128*t^2*u^2*v*w^3 + 39123*t^2*u^2*w^4 + 16176*t^2*u*v^5 + 115356*t^2*u*v^4*w + 300006*t^2*u*v^3*w^2 + 337284*t^2*u*v^2*w^3 + 141912*t^2*u*v*w^4 + 7290*t^2*u*w^5 + 5212*t^2*v^6 + 46200*t^2*v^5*w + 157131*t^2*v^4*w^2 + 253368*t^2*v^3*w^3 + 190269*t^2*v^2*w^4 + 53946*t^2*v*w^5 + 4374*t^2*w^6 + 38*t*u^6*v + 78*t*u^6*w + 468*t*u^5*v^2 + 1560*t*u^5*v*w + 1404*t*u^5*w^2 + 2192*t*u^4*v^3 + 10152*t*u^4*v^2*w + 15840*t*u^4*v*w^2 + 8424*t*u^4*w^3 + 5180*t*u^3*v^4 + 30936*t*u^3*v^3*w + 66960*t*u^3*v^2*w^2 + 62208*t*u^3*v*w^3 + 21060*t*u^3*w^4 + 6630*t*u^2*v^5 + 49056*t*u^2*v^4*w + 136494*t*u^2*v^3*w^2 + 174960*t*u^2*v^2*w^3 + 99630*t*u^2*v*w^4 + 18954*t*u^2*w^5 + 4396*t*u*v^6 + 39420*t*u*v^5*w + 136782*t*u*v^4*w^2 + 228096*t*u*v^3*w^3 + 180306*t*u*v^2*w^4 + 52488*t*u*v*w^5 + 1184*t*v^7 + 12708*t*v^6*w + 54378*t*v^5*w^2 + 117126*t*v^4*w^3 + 130086*t*v^3*w^4 + 65610*t*v^2*w^5 + 8748*t*v*w^6 + 14*u^6*v^2 + 48*u^6*v*w + 54*u^6*w^2 + 122*u^5*v^3 + 588*u^5*v^2*w + 1026*u^5*v*w^2 + 648*u^5*w^3 + 439*u^4*v^4 + 2736*u^4*v^3*w + 6471*u^4*v^2*w^2 + 6966*u^4*v*w^3 + 2916*u^4*w^4 + 836*u^3*v^5 + 6432*u^3*v^4*w + 19278*u^3*v^3*w^2 + 28188*u^3*v^2*w^3 + 20250*u^3*v*w^4 + 5832*u^3*w^5 + 889*u^2*v^6 + 8214*u^2*v^5*w + 30096*u^2*v^4*w^2 + 55404*u^2*v^3*w^3 + 53217*u^2*v^2*w^4 + 24786*u^2*v*w^5 + 4374*u^2*w^6 + 500*u*v^7 + 5454*u*v^6*w + 23976*u*v^5*w^2 + 54108*u*v^4*w^3 + 65448*u*v^3*w^4 + 39366*u*v^2*w^5 + 8748*u*v*w^6 + 116*v^8 + 1476*v^7*w + 7713*v^6*w^2 + 21222*v^5*w^3 + 32481*v^4*w^4 + 26244*v^3*w^5 + 8748*v^2*w^6≥0
记x=w+t+v+u，y=w+t+v，z=w+t代入得
864*t^8 + 1776*t^7*u + 4992*t^7*v + 6912*t^7*w + 2108*t^6*u^2 + 10376*t^6*u*v + 11928*t^6*u*w + 13112*t^6*v^2 + 35664*t^6*v*w + 22896*t^6*w^2 + 1792*t^5*u^3 + 11784*t^5*u^2*v + 13236*t^5*u^2*w + 26616*t^5*u*v^2 + 64248*t^5*u*v*w + 31860*t^5*u*w^2 + 20360*t^5*v^3 + 83112*t^5*v^2*w + 103896*t^5*v*w^2 + 40176*t^5*w^3 + 945*t^4*u^4 + 8278*t^4*u^3*v + 10596*t^4*u^3*w + 26738*t^4*u^2*v^2 + 66084*t^4*u^2*v*w + 34227*t^4*u^2*w^2 + 38072*t^4*u*v^3 + 146052*t^4*u*v^2*w + 159858*t^4*u*v*w^2 + 42282*t^4*u*w^3 + 20224*t^4*v^4 + 112032*t^4*v^3*w + 211698*t^4*v^2*w^2 + 157140*t^4*v*w^3 + 39366*t^4*w^4 + 262*t^3*u^5 + 3238*t^3*u^4*v + 4812*t^3*u^4*w + 14656*t^3*u^3*v^2 + 40104*t^3*u^3*v*w + 25614*t^3*u^3*w^2 + 31358*t^3*u^2*v^3 + 125184*t^3*u^2*v^2*w + 148428*t^3*u^2*v*w^2 + 47628*t^3*u^2*w^3 + 32336*t^3*u*v^4 + 175092*t^3*u*v^3*w + 315576*t^3*u*v^2*w^2 + 204120*t^3*u*v*w^3 + 27864*t^3*u*w^4 + 12992*t^3*v^5 + 92640*t^3*v^4*w + 241110*t^3*v^3*w^2 + 275076*t^3*v^2*w^3 + 129114*t^3*v*w^4 + 20412*t^3*w^5 + 29*t^2*u^6 + 606*t^2*u^5*v + 1038*t^2*u^5*w + 4040*t^2*u^4*v^2 + 12288*t^2*u^4*v*w + 9414*t^2*u^4*w^2 + 12512*t^2*u^3*v^3 + 53952*t^2*u^3*v^2*w + 74016*t^2*u^3*v*w^2 + 32076*t^2*u^3*w^3 + 20042*t^2*u^2*v^4 + 113112*t^2*u^2*v^3*w + 220644*t^2*u^2*v^2*w^2 + 169128*t^2*u^2*v*w^3 + 39123*t^2*u^2*w^4 + 16176*t^2*u*v^5 + 115356*t^2*u*v^4*w + 300006*t^2*u*v^3*w^2 + 337284*t^2*u*v^2*w^3 + 141912*t^2*u*v*w^4 + 7290*t^2*u*w^5 + 5212*t^2*v^6 + 46200*t^2*v^5*w + 157131*t^2*v^4*w^2 + 253368*t^2*v^3*w^3 + 190269*t^2*v^2*w^4 + 53946*t^2*v*w^5 + 4374*t^2*w^6 + 38*t*u^6*v + 78*t*u^6*w + 468*t*u^5*v^2 + 1560*t*u^5*v*w + 1404*t*u^5*w^2 + 2192*t*u^4*v^3 + 10152*t*u^4*v^2*w + 15840*t*u^4*v*w^2 + 8424*t*u^4*w^3 + 5180*t*u^3*v^4 + 30936*t*u^3*v^3*w + 66960*t*u^3*v^2*w^2 + 62208*t*u^3*v*w^3 + 21060*t*u^3*w^4 + 6630*t*u^2*v^5 + 49056*t*u^2*v^4*w + 136494*t*u^2*v^3*w^2 + 174960*t*u^2*v^2*w^3 + 99630*t*u^2*v*w^4 + 18954*t*u^2*w^5 + 4396*t*u*v^6 + 39420*t*u*v^5*w + 136782*t*u*v^4*w^2 + 228096*t*u*v^3*w^3 + 180306*t*u*v^2*w^4 + 52488*t*u*v*w^5 + 1184*t*v^7 + 12708*t*v^6*w + 54378*t*v^5*w^2 + 117126*t*v^4*w^3 + 130086*t*v^3*w^4 + 65610*t*v^2*w^5 + 8748*t*v*w^6 + 14*u^6*v^2 + 48*u^6*v*w + 54*u^6*w^2 + 122*u^5*v^3 + 588*u^5*v^2*w + 1026*u^5*v*w^2 + 648*u^5*w^3 + 439*u^4*v^4 + 2736*u^4*v^3*w + 6471*u^4*v^2*w^2 + 6966*u^4*v*w^3 + 2916*u^4*w^4 + 836*u^3*v^5 + 6432*u^3*v^4*w + 19278*u^3*v^3*w^2 + 28188*u^3*v^2*w^3 + 20250*u^3*v*w^4 + 5832*u^3*w^5 + 889*u^2*v^6 + 8214*u^2*v^5*w + 30096*u^2*v^4*w^2 + 55404*u^2*v^3*w^3 + 53217*u^2*v^2*w^4 + 24786*u^2*v*w^5 + 4374*u^2*w^6 + 500*u*v^7 + 5454*u*v^6*w + 23976*u*v^5*w^2 + 54108*u*v^4*w^3 + 65448*u*v^3*w^4 + 39366*u*v^2*w^5 + 8748*u*v*w^6 + 116*v^8 + 1476*v^7*w + 7713*v^6*w^2 + 21222*v^5*w^3 + 32481*v^4*w^4 + 26244*v^3*w^5 + 8748*v^2*w^6≥0
