lib/dim6/gapdec4.3

#3p^2+13p+37+gcd(p-1,3)+gcd(p-1,4) algebras
Append( LIE_DATA[6], [
[6,3,3,"<a,b,c|ca,cb,pa,pb,pc,class=3>",[[],[4,1],[],[],[],[],[5,1],[6,1]],,,"6.118"],
[6,3,3,"<a,b,c|ca,cb,pa-bab,pb,pc,class=3>",[[6,1],[4,1],[],[],[],[],[5,1],[6,1]],,,"6.119"],
[6,3,3,"<a,b,c|ca,cb,pa-wbab,pb,pc,class=3>",[[6,w],[4,1],[],[],[],[],[5,1],[6,1]],,,"6.120"],
[6,3,3,"<a,b,c|ca,cb,pa-baa,pb,pc,class=3>",[[5,1],[4,1],[],[],[],[],[5,1],[6,1]],,,"6.121"],
[6,3,3,"<a,b,c|ca,cb,pa-baa,pb-xbab,pc,class=3>",[[5,1],[4,1],[6,x],[],[],[],[5,1],[6,1]],"x ne 0, x~x^-1",,"6.122"],
[6,3,3,"<a,b,c|ca,cb,pa-baa-bab,pb-bab,pc,class=3>",[[5,1,6,1],[4,1],[6,1],[],[],[],[5,1],[6,1]],,,"6.123"],
[6,3,3,"<a,b,c|ca,cb,pa-baa-wbab,pb-bab,pc,class=3>",[[5,1,6,w],[4,1],[6,1],[],[],[],[5,1],[6,1]],,,"6.124"],
[6,3,3,"<a,b,c|ca,cb,pa-wbab,pb-baa,pc,class=3>",[[6,w],[4,1],[5,1],[],[],[],[5,1],[6,1]],,,"6.125"],
[6,3,3,"<a,b,c|ca,cb,pa-xbab,pb-baa-bab,pc,class=3>",[[6,x],[4,1],[5,1,6,1],[],[],[],[5,1],[6,1]],"1+4x not a square mod p",,"6.126"],
[6,3,3,"<a,b,c|ca,cb,pa,pb,pc-bab,class=3>",[[],[4,1],[],[],[],[6,1],[5,1],[6,1]],,,"6.127"],
[6,3,3,"<a,b,c|ca,cb,pa-baa,pb,pc-bab,class=3>",[[5,1],[4,1],[],[],[],[6,1],[5,1],[6,1]],,,"6.128"],
[6,3,3,"<a,b,c|ca,cb,pa,pb-baa,pc-bab,class=3>",[[],[4,1],[5,1],[],[],[6,1],[5,1],[6,1]],,,"6.129"],
[6,3,3,"<a,b,c|ca,cb,pa,pb-wbaa,pc-bab,class=3>",[[],[4,1],[5,w],[],[],[6,1],[5,1],[6,1]],,,"6.130"],
[6,3,3,"<a,b,c|ca-bab,cb,pa,pb,pc,class=3>",[[],[4,1],[],[6,1],[],[],[5,1],[6,1]],,,"6.131"],
[6,3,3,"<a,b,c|ca-bab,cb,pa-bab,pb,pc,class=3>",[[6,1],[4,1],[],[6,1],[],[],[5,1],[6,1]],,,"6.132"],
[6,3,3,"<a,b,c|ca-bab,cb,pa-wbab,pb,pc,class=3>",[[6,w],[4,1],[],[6,1],[],[],[5,1],[6,1]],,,"6.133"],
[6,3,3,"<a,b,c|ca-bab,cb,pa-baa,pb,pc,class=3>",[[5,1],[4,1],[],[6,1],[],[],[5,1],[6,1]],,,"6.134"],
[6,3,3,"<a,b,c|ca-bab,cb,pa-xbaa,pb-bab,pc,class=3>",[[5,x],[4,1],[6,1],[6,1],[],[],[5,1],[6,1]],"all x",,"6.135"],
[6,3,3,"<a,b,c|ca-bab,cb,pa-baa-bab,pb-bab,pc,class=3>",[[5,1,6,1],[4,1],[6,1],[6,1],[],[],[5,1],[6,1]],,,"6.136"],
[6,3,3,"<a,b,c|ca-bab,cb,pa-baa-wbab,pb-bab,pc,class=3>",[[5,1,6,w],[4,1],[6,1],[6,1],[],[],[5,1],[6,1]],,,"6.137"],
[6,3,3,"<a,b,c|ca-bab,cb,pa-baa-xbab,pb-baa,pc,class=3>",[[5,1,6,x],[4,1],[5,1],[6,1],[],[],[5,1],[6,1]],"all x",,"6.138"],
[6,3,3,"<a,b,c|ca-bab,cb,pa,pb-baa,pc,class=3>",[[],[4,1],[5,1],[6,1],[],[],[5,1],[6,1]],,,"6.139"],
[6,3,3,"<a,b,c|ca-bab,cb,pa-bab,pb-baa,pc,class=3>",[[6,1],[4,1],[5,1],[6,1],[],[],[5,1],[6,1]],,,"6.140"],
[6,3,3,"<a,b,c|ca-bab,cb,pa-wbab,pb-baa,pc,class=3>",[[6,w],[4,1],[5,1],[6,1],[],[],[5,1],[6,1]],,,"6.141"],
[6,3,3,"<a,b,c|ca-bab,cb,pa-baa-xbab,pb-wbaa,pc,class=3>",[[5,1,6,x],[4,1],[5,w],[6,1],[],[],[5,1],[6,1]],"all x",,"6.142"],
[6,3,3,"<a,b,c|ca-bab,cb,pa,pb-wbaa,pc,class=3>",[[],[4,1],[5,w],[6,1],[],[],[5,1],[6,1]],,,"6.143"],
[6,3,3,"<a,b,c|ca-bab,cb,pa-bab,pb-wbaa,pc,class=3>",[[6,1],[4,1],[5,w],[6,1],[],[],[5,1],[6,1]],,,"6.144"],
[6,3,3,"<a,b,c|ca-bab,cb,pa-wbab,pb-wbaa,pc,class=3>",[[6,w],[4,1],[5,w],[6,1],[],[],[5,1],[6,1]],,,"6.145"],
[6,3,3,"<a,b,c|ca-bab,cb,pa,pb-xbaa,pc-bab,class=3>",[[],[4,1],[5,x],[6,1],[],[6,1],[5,1],[6,1]],"all x",,"6.146"],
[6,3,3,"<a,b,c|ca-bab,cb,pa-baa,pb,pc-bab,class=3>",[[5,1],[4,1],[],[6,1],[],[6,1],[5,1],[6,1]],,,"6.147"],
[6,3,3,"<a,b,c|ca-bab,cb,pa-xbab,pb,pc-baa,class=3>",[[6,x],[4,1],[],[6,1],[],[5,1],[5,1],[6,1]],"x=0,1,w,w^2,w^3","p=1 mod 4","6.148"],
[6,3,3,"<a,b,c|ca-bab,cb,pa-xbab,pb,pc-baa,class=3>",[[6,x],[4,1],[],[6,1],[],[5,1],[5,1],[6,1]],"x=0,1,w","p=3 mod 4","6.148A"],
[6,3,3,"<a,b,c|ca-bab,cb,pa-xbab,pb-ybab,pc-baa,class=3>",[[6,x],[4,1],[6,y],[6,1],[],[5,1],[5,1],[6,1]],"y=1,w,w^2, all x, x~x' if x^3=x'^3 mod p","p=1 mod 3","6.149"],
[6,3,3,"<a,b,c|ca-bab,cb,pa-xbab,pb-bab,pc-baa,class=3>",[[6,x],[4,1],[6,1],[6,1],[],[5,1],[5,1],[6,1]],"all x","p=2 mod 3","6.149A"],
[6,3,3,"<a,b,c|ca-baa,cb,pa,pb,pc,class=3>",[[],[4,1],[],[5,1],[],[],[5,1],[6,1]],,,"6.150"],
[6,3,3,"<a,b,c|ca-baa,cb,pa-baa,pb,pc,class=3>",[[5,1],[4,1],[],[5,1],[],[],[5,1],[6,1]],,,"6.151"],
[6,3,3,"<a,b,c|ca-baa,cb,pa-bab,pb,pc,class=3>",[[6,1],[4,1],[],[5,1],[],[],[5,1],[6,1]],,,"6.152"],
[6,3,3,"<a,b,c|ca-baa,cb,pa-baa-bab,pb,pc,class=3>",[[5,1,6,1],[4,1],[],[5,1],[],[],[5,1],[6,1]],,,"6.153"],
[6,3,3,"<a,b,c|ca-baa,cb,pa-wbab,pb,pc,class=3>",[[6,w],[4,1],[],[5,1],[],[],[5,1],[6,1]],,,"6.154"],
[6,3,3,"<a,b,c|ca-baa,cb,pa-baa-wbab,pb,pc,class=3>",[[5,1,6,w],[4,1],[],[5,1],[],[],[5,1],[6,1]],,,"6.155"],
[6,3,3,"<a,b,c|ca-baa,cb,pa-bab,pb-baa,pc,class=3>",[[6,1],[4,1],[5,1],[5,1],[],[],[5,1],[6,1]],,"p=1 mod 4","6.156"],
[6,3,3,"<a,b,c|ca-baa,cb,pa-bab,pb-wbaa,pc,class=3>",[[6,1],[4,1],[5,w],[5,1],[],[],[5,1],[6,1]],,"p=1 mod 4","6.157"],
[6,3,3,"<a,b,c|ca-baa,cb,pa-wbab,pb-wbaa,pc,class=3>",[[6,w],[4,1],[5,w],[5,1],[],[],[5,1],[6,1]],,"p=1 mod 4","6.158"],
[6,3,3,"<a,b,c|ca-baa,cb,pa-bab,pb-baa,pc,class=3>",[[6,1],[4,1],[5,1],[5,1],[],[],[5,1],[6,1]],,"p=3 mod 4","6.156A"],
[6,3,3,"<a,b,c|ca-baa,cb,pa-bab,pb-wbaa,pc,class=3>",[[6,1],[4,1],[5,w],[5,1],[],[],[5,1],[6,1]],,"p=3 mod 4","6.157A"],
[6,3,3,"<a,b,c|ca-baa,cb,pa-wbab,pb-baa,pc,class=3>",[[6,w],[4,1],[5,1],[5,1],[],[],[5,1],[6,1]],,"p=3 mod 4","6.158A"],
[6,3,3,"<a,b,c|ca-baa,cb,pa-baa-xbab,pb-baa,pc,class=3>",[[5,1,6,x],[4,1],[5,1],[5,1],[],[],[5,1],[6,1]],"all x",,"6.159"],
[6,3,3,"<a,b,c|ca-baa,cb,pa-baa-xbab,pb-wbaa,pc,class=3>",[[5,1,6,x],[4,1],[5,w],[5,1],[],[],[5,1],[6,1]],"all x",,"6.160"],
[6,3,3,"<a,b,c|ca-baa,cb,pa-baa,pb-xbab,pc,class=3>",[[5,1],[4,1],[6,x],[5,1],[],[],[5,1],[6,1]],"x ne 0, x~x^-1",,"6.160A"],
[6,3,3,"<a,b,c|ca-baa,cb,pa-baa-bab,pb-xbab,pc,class=3>",[[5,1,6,1],[4,1],[6,x],[5,1],[],[],[5,1],[6,1]],"x ne 0",,"6.161"],
[6,3,3,"<a,b,c|ca-baa,cb,pa-baa-wbab,pb-xbab,pc,class=3>",[[5,1,6,w],[4,1],[6,x],[5,1],[],[],[5,1],[6,1]],"x ne 0",,"6.162"],
[6,3,3,"<a,b,c|ca-baa,cb,pa-baa-bab,pb-xbaa-ybab,pc,class=3>",[[5,1,6,1],[4,1],[5,x,6,y],[5,1],[],[],[5,1],[6,1]],"x ne 0, y ne 0,1,-1, y~y^-1",,"6.163"],
[6,3,3,"<a,b,c|ca-baa,cb,pa-baa-wbab,pb-xbaa-ybab,pc,class=3>",[[5,1,6,w],[4,1],[5,x,6,y],[5,1],[],[],[5,1],[6,1]],"x ne 0, y ne 0,1,-1, y~y^-1",,"6.164"],
[6,3,3,"<a,b,c|ca-baa,cb,pa-baa-bab,pb-x^2baa+bab,pc,class=3>",[[5,1,6,1],[4,1],[5,x^2,6,-1],[5,1],[],[],[5,1],[6,1]],"x ne 0, x~-x",,"6.165"],
[6,3,3,"<a,b,c|ca-baa,cb,pa-baa-bab,pb-x^2baa-bab,pc,class=3>",[[5,1,6,1],[4,1],[5,x^2,6,1],[5,1],[],[],[5,1],[6,1]],"x ne 0, x~-x",,"6.165"],
[6,3,3,"<a,b,c|ca-baa,cb,pa-baa-bab,pb-(x^2*w)baa+bab,pc,class=3>",[[5,1,6,1],[4,1],[5,w*x^2,6,-1],[5,1],[],[],[5,1],[6,1]],"x ne 0, x~-x",,"6.166"],
[6,3,3,"<a,b,c|ca-baa,cb,pa-baa-bab,pb-(x^2*w)baa-bab,pc,class=3>",[[5,1,6,1],[4,1],[5,w*x^2,6,1],[5,1],[],[],[5,1],[6,1]],"x ne 0, x~-x",,"6.166"],
[6,3,3,"<a,b,c|ca-baa,cb,pa-baa-wbab,pb-(x^2*w)baa+bab,pc,class=3>",[[5,1,6,w],[4,1],[5,w*x^2,6,-1],[5,1],[],[],[5,1],[6,1]],"x ne 0, x~-x","p=1 mod 4","6.167"],
[6,3,3,"<a,b,c|ca-baa,cb,pa-baa-wbab,pb-(x^2*w)baa-bab,pc,class=3>",[[5,1,6,w],[4,1],[5,w*x^2,6,1],[5,1],[],[],[5,1],[6,1]],"x ne 0, x~-x","p=1 mod 4","6.167"],
[6,3,3,"<a,b,c|ca-baa,cb,pa-baa-wbab,pb-x^2baa+bab,pc,class=3>",[[5,1,6,w],[4,1],[5,x^2,6,-1],[5,1],[],[],[5,1],[6,1]],"x ne 0, x~-x","p=3 mod 4","6.167A"],
[6,3,3,"<a,b,c|ca-baa,cb,pa-baa-wbab,pb-x^2baa-bab,pc,class=3>",[[5,1,6,w],[4,1],[5,x^2,6,1],[5,1],[],[],[5,1],[6,1]],"x ne 0, x~-x","p=3 mod 4","6.167A"],
[6,3,3,"<a,b,c|ca-baa,cb,pa,pb,pc-baa,class=3>",[[],[4,1],[],[5,1],[],[5,1],[5,1],[6,1]],,,"6.168"],
[6,3,3,"<a,b,c|ca-baa,cb,pa-bab,pb,pc-baa,class=3>",[[6,1],[4,1],[],[5,1],[],[5,1],[5,1],[6,1]],,,"6.169"],
[6,3,3,"<a,b,c|ca-baa,cb,pa-wbab,pb,pc-baa,class=3>",[[6,w],[4,1],[],[5,1],[],[5,1],[5,1],[6,1]],,,"6.170"],
[6,3,3,"<a,b,c|ca-baa,cb,pa-xbab,pb-bab,pc-baa,class=3>",[[6,x],[4,1],[6,1],[5,1],[],[5,1],[5,1],[6,1]],"all x",,"6.171"],
[6,3,3,"<a,b,c|ca-baa,cb,pa-xbab,pb-ybab,pc-baa-bab,class=3>",[[6,x],[4,1],[6,y],[5,1],[],[5,1,6,1],[5,1],[6,1]],"all x,y, [x,y]~[y,x]",,"6.172"],
[6,3,3,"<a,b,c|ca-bab,cb-wbaa,pa,pb,pc,class=3>",[[],[4,1],[],[6,1],[5,w],[],[5,1],[6,1]],,,"6.173"],
[6,3,3,"<a,b,c|ca-bab,cb-wbaa,pa-xbaa-bab,pb,pc,class=3>",[[5,x,6,1],[4,1],[],[6,1],[5,w],[],[5,1],[6,1]],"all x, x~-x",,"6.174"],
[6,3,3,"<a,b,c|ca-bab,cb-wbaa,pa-xbaa-wbab,pb,pc,class=3>",[[5,x,6,w],[4,1],[],[6,1],[5,w],[],[5,1],[6,1]],"all x, x~-x",,"6.175"],
[6,3,3,"<a,b,c|ca-bab,cb-wbaa,pa-baa,pb,pc,class=3>",[[5,1],[4,1],[],[6,1],[5,w],[],[5,1],[6,1]],,,"6.176"],
[6,3,3,"<a,b,c|ca-bab,cb-wbaa,pa-wbaa,pb,pc,class=3>",[[5,w],[4,1],[],[6,1],[5,w],[],[5,1],[6,1]],,"p=1 mod 4","6.177"],
[6,3,3,"<a,b,c|ca-bab,cb-wbaa,pa-tbaa-xbab,pb-ybaa-zbab,pc,class=3>",[[5,t,6,x],[4,1],[5,y,6,z],[6,1],[5,w],[],[5,1],[6,1]],"See note6.178",,"6.178"],
[6,3,3,"<a,b,c|ca-bab,cb-wbaa,pa-xbaa,pb-ybaa,pc-bab,class=3>",[[5,x],[4,1],[5,y],[6,1],[5,w],[6,1],[5,1],[6,1]],"all x,y, x~-x",,"6.179"]
]);