| Quellcodebibliothek Statistik Leitseite products/sources/formale Sprachen/GAP/pkg/liepring/gap/evals/ (Algebra von RWTH Aachen Version 4.15.1©) Datei vom 11.5.2024 mit Größe 46 kB |
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BindGlobal( "ValsPreFunction28", function(P, case) local W, F, SQ, i, CU, x, y, z, t, u, v, k, ii, transversal3, sofar, transversal4, transversal5, transversal6, params, xrange, yrange, zrange, urange, vrange, mats, y5, y6, y3, y4, A, y1, y2, a, b, c, m, B, D, C, z3, z4, z5, z6, z1, z2, new, index, ind1, AS, stab1, stab2, half, bcrange, sol, expect, val, B1, C1, B2, C2, BB1, BB2, lns, x1, u1, range, k2, km2, wover2, bc, s, A1, A2, AS1, AS2; W:=PrimitiveRootMod(P); F:=GF(P); SQ:=Set(List([1..(P-1)/2], X -> (X^2) mod P)); for i in [2..P-1] do if not i in SQ then lns:=i; break; fi; od; CU:=[1]; for x in [2..P-1] do if (x^3) mod P = 1 then AddSet(CU,x); fi; od; ##If p=1 mod 3 compute a transversal for the cube roots of 1 transversal3:=[]; if P mod 3 = 1 then transversal3:=[]; sofar:=[]; for i in [1..P-1] do if i^3 mod P in sofar then continue; fi; Add(transversal3,i); AddSet(sofar,i^3 mod P); od; fi; ##If p=1 mod 4 then compute a transversal for the fourth roots of 1 transversal4:=[]; if P mod 4 = 1 then sofar:=[]; for i in [1..(P-1)/2] do if i^4 mod P in sofar then continue; fi; Add(transversal4,i); AddSet(sofar,i^4 mod P); od; fi; ##If p=1 mod 5 then compute a transversal for the fifth roots of 1 transversal5:=[]; if P mod 5 = 1 then sofar:=[]; for i in [1..P-1] do if i^5 mod P in sofar then continue; fi; Add(transversal5,i); AddSet(sofar,i^5 mod P); od; fi; ##If p=1 mod 3 then compute a transversal for the sixth roots of 1 transversal6:=[]; if P mod 3 = 1 then sofar:=[]; for i in [1..P-1] do if i^6 mod P in sofar then continue; fi; Add(transversal6,i); AddSet(sofar,i^6 mod P); od; fi; params := List([1..24], x -> []); ##Case 1: cb=caa=cab=cac=0 if case = true or case = 1 then Add(params[1],[0,0,0,0,0,0]); Add(params[1],[1,0,0,0,0,0]); Add(params[1],[0,1,0,0,0,0]); Add(params[1],[0,W,0,0,0,0]); Add(params[1],[0,0,1,0,0,0]); Add(params[1],[0,0,W,0,0,0]); Add(params[1],[0,1,1,0,0,0]); Add(params[1],[0,1,W,0,0,0]); Add(params[1],[0,W,1,0,0,0]); Add(params[1],[0,W,W,0,0,0]); for y in [0..P-1] do Add(params[1],[1,y,1,0,0,0]); Add(params[1],[1,y,W,0,0,0]); od; Add(params[1],[1,1,0,1,0,0]); Add(params[1],[1,W,0,1,0,0]); for x in [0..P-1] do Add(params[1],[x,0,0,1,0,0]); od; Add(params[1],[0,0,0,0,1,0]); Add(params[1],[0,1,0,0,1,0]); Add(params[1],[0,W,0,0,1,0]); Add(params[1],[0,0,0,1,1,0]); Add(params[1],[0,1,0,1,1,0]); Add(params[1],[0,W,0,1,1,0]); Add(params[1],[1,0,0,0,0,1]); Add(params[1],[0,0,0,0,0,1]); Add(params[1],[0,0,1,0,0,1]); Add(params[1],[0,0,W,0,0,1]); if Length(params[1]) <> 3*P+22 then Error("params[1] wrong"); fi; if case = 1 then return params[1]; fi; fi; ##Case 2: caa=cab=cac=0, cb=baa if case = true or case = 2 then Add(params[2],[0,0,0,0,0,0]); Add(params[2],[1,0,0,0,0,0]); Add(params[2],[0,1,0,0,0,0]); Add(params[2],[0,W,0,0,0,0]); Add(params[2],[0,0,1,0,0,0]); Add(params[2],[0,0,W,0,0,0]); Add(params[2],[0,1,1,0,0,0]); Add(params[2],[0,1,W,0,0,0]); Add(params[2],[0,W,1,0,0,0]); Add(params[2],[0,W,W,0,0,0]); for y in [0..P-1] do Add(params[2],[1,y,1,0,0,0]); Add(params[2],[1,y,W,0,0,0]); od; Add(params[2],[1,1,0,1,0,0]); Add(params[2],[1,W,0,1,0,0]); for x in [0..P-1] do Add(params[2],[x,0,0,1,0,0]); od; for x in [0..P-1] do Add(params[2],[0,x,0,0,1,0]); Add(params[2],[0,x,0,1,1,0]); od; Add(params[2],[0,0,0,0,0,1]); Add(params[2],[1,0,0,0,0,1]); if P mod 3 = 1 then Add(params[2],[W,0,0,0,0,1]); Add(params[2],[W^2 mod P,0,0,0,0,1]); fi; Add(params[2],[0,0,1,0,0,1]); Add(params[2],[0,0,W,0,0,1]); if P mod 4 = 1 then Add(params[2],[0,0,W^2 mod P,0,0,1]); Add(params[2],[0,0,W^3 mod P,0,0,1]); fi; if Length(params[2])<>5*P+13+Gcd(P-1,3)+Gcd(P-1,4) then Error("params[2] wrong"); fi; if case = 2 then return params[2]; fi; fi; ##Case 3: cb=bab=bac=cac=0 if case = true or case = 3 then Add(params[3],[0,0,0,0,0,0]); Add(params[3],[1,0,0,0,0,0]); Add(params[3],[0,0,0,0,1,0]); Add(params[3],[0,1,0,0,1,0]); Add(params[3],[0,0,0,0,1,1]); Add(params[3],[1,0,0,0,1,1]); Add(params[3],[0,0,0,0,1,W]); Add(params[3],[1,0,0,0,1,W]); Add(params[3],[0,0,1,0,0,1]); Add(params[3],[0,0,W,0,0,W]); for i in [1..P-1] do Add(params[3],[0,0,0,i,1,1]); Add(params[3],[0,0,0,i,1,W]); od; Add(params[3],[0,0,0,1,1,0]); Add(params[3],[0,0,0,W,1,0]); if P mod 4 = 1 then Add(params[3],[0,0,0,W^2 mod P,1,0]); Add(params[3],[0,0,0,W^3 mod P,1,0]); fi; if Length(params[3]) <> 2*P+8+Gcd(P-1,4) then Error("params[3] wrong"); fi; if case = 3 then return params[3]; fi; fi; ##Case 4: bab=bac=cac=0, cb=baa if case = true or case = 4 then Add(params[4],[0,0,0,0,0,0]); Add(params[4],[1,0,0,0,0,0]); Add(params[4],[0,1,0,0,0,0]); if P mod 3 = 1 then Add(params[4],[0,W,0,0,0,0]); Add(params[4],[0,W^2 mod P,0,0,0,0]); fi; Add(params[4],[0,0,0,0,1,0]); Add(params[4],[0,1,0,0,1,0]); if P mod 3 = 1 then Add(params[4],[0,W,0,0,1,0]); Add(params[4],[0,W^2 mod P,0,0,1,0]); fi; Add(params[4],[0,0,0,0,0,1]); Add(params[4],[1,0,0,0,0,1]); Add(params[4],[0,0,0,0,0,W]); Add(params[4],[1,0,0,0,0,W]); for y in [0..P-1] do Add(params[4],[0,0,1,0,0,y]); Add(params[4],[0,0,W,0,0,y]); od; Add(params[4],[0,0,1,0,1,1]); Add(params[4],[0,0,W,0,1,W]); for z in [1..(P-1)/2] do Add(params[4],[0,z,1,0,0,0]); Add(params[4],[0,z,W,0,0,0]); od; Add(params[4],[0,0,0,1,0,0]); Add(params[4],[1,0,0,1,0,0]); if P mod 5 = 1 then Add(params[4],[W,0,0,1,0,0]); Add(params[4],[W^2 mod P,0,0,1,0,0]); Add(params[4],[W^3 mod P,0,0,1,0,0]); Add(params[4],[W^4 mod P,0,0,1,0,0]); fi; Add(params[4],[0,0,0,1,1,0]); Add(params[4],[0,0,0,1,W,0]); if P mod 4 = 1 then Add(params[4],[0,0,0,1,W^2 mod P,0]); Add(params[4],[0,0,0,1,W^3 mod P,0]); fi; for x in [0..P-1] do Add(params[4],[0,0,0,1,x,1]); Add(params[4],[0,0,0,1,x,W]); od; for z in [1..(P-1)/2] do Add(params[4],[z,0,0,1,0,1]); Add(params[4],[z,0,0,1,0,W]); od; if Length(params[4]) <> 6*P+8+2*Gcd(P-1,3)+Gcd(P-1,4)+Gcd(P-1,5) then Error("params[4] wrong"); fi; if case = 4 then return params[4]; fi; fi; ##Case 5: cb=bac=cac=0, caa=bab if case = true or case = 5 then Add(params[5],[0,0,0,0,0,0]); Add(params[5],[1,0,0,0,0,0]); Add(params[5],[0,1,0,0,0,0]); Add(params[5],[0,W,0,0,0,0]); Add(params[5],[0,0,1,0,0,0]); Add(params[5],[0,0,W,0,0,0]); Add(params[5],[0,1,1,0,0,0]); Add(params[5],[0,1,W,0,0,0]); Add(params[5],[0,W,1,0,0,0]); Add(params[5],[0,W,W,0,0,0]); for x in [0..P-1] do Add(params[5],[x,0,0,1,0,0]); od; Add(params[5],[0,0,0,0,1,0]); Add(params[5],[0,1,0,0,1,0]); Add(params[5],[0,W,0,0,1,0]); if P mod 3 = 1 then Add(params[5],[0,W^2 mod P,0,0,1,0]); Add(params[5],[0,W^3 mod P,0,0,1,0]); Add(params[5],[0,W^4 mod P,0,0,1,0]); Add(params[5],[0,W^5 mod P,0,0,1,0]); fi; if P mod 4 = 1 then for x in [0..(P-1)/2] do Add(params[5],[0,x,0,1,1,0]); Add(params[5],[0,x,0,W,1,0]); Add(params[5],[0,x,0,W^2 mod P,1,0]); Add(params[5],[0,x,0,W^3 mod P,1,0]); od; fi; if P mod 4 = 3 then for x in [0..P-1] do Add(params[5],[0,x,0,1,1,0]); Add(params[5],[0,x,0,W,1,0]); od; fi; for x in [0..P-1] do Add(params[5],[0,0,x,0,0,1]); Add(params[5],[0,0,x,0,0,W]); od; Add(params[5],[1,0,0,0,0,1]); Add(params[5],[1,0,0,0,0,W]); Add(params[5],[1,0,1,0,0,1]); Add(params[5],[1,0,W,0,0,W]); if Length(params[5]) <> 5*P+13+2*Gcd(P-1,3)+Gcd(P-1,4) then Error("params[5] wrong"); fi; if case = 5 then return params[5]; fi; fi; ##Case 6: bac=cac=0, caa=bab, cb=baa if case = true or case = 6 then Add(params[6],[0,0,0,0,0,0]); Add(params[6],[1,0,0,0,0,0]); if P mod 5 = 1 then Add(params[6],[W,0,0,0,0,0]); Add(params[6],[W^2 mod P,0,0,0,0,0]); Add(params[6],[W^3 mod P,0,0,0,0,0]); Add(params[6],[W^4 mod P,0,0,0,0,0]); fi; Add(params[6],[0,1,0,0,0,0]); Add(params[6],[0,W,0,0,0,0]); if P mod 3 = 1 then Add(params[6],[0,W^2 mod P,0,0,0,0]); Add(params[6],[0,W^3 mod P,0,0,0,0]); Add(params[6],[0,W^4 mod P,0,0,0,0]); Add(params[6],[0,W^5 mod P,0,0,0,0]); fi; if P mod 4 = 3 then for x in [0..P-1] do Add(params[6],[0,x,1,0,0,0]); Add(params[6],[0,x,W,0,0,0]); od; fi; if P mod 4 = 1 then for x in [0..(P-1)/2] do Add(params[6],[0,x,1,0,0,0]); Add(params[6],[0,x,W,0,0,0]); Add(params[6],[0,x,W^2 mod P,0,0,0]); Add(params[6],[0,x,W^3 mod P,0,0,0]); od; fi; for x in [0..P-1] do Add(params[6],[x,0,0,1,0,0]); if P mod 5 = 1 then Add(params[6],[x,0,0,W,0,0]); Add(params[6],[x,0,0,W^2 mod P,0,0]); Add(params[6],[x,0,0,W^3 mod P,0,0]); Add(params[6],[x,0,0,W^4 mod P,0,0]); fi; od; if P mod 3 = 2 then for x in [0..P-1] do for y in [0..P-1] do Add(params[6],[0,y,0,x,1,0]); od; od; fi; if P mod 3 = 1 then xrange:=ShallowCopy(transversal3); Add(xrange,0); for x in xrange do for y in [0..P-1] do Add(params[6],[0,y,0,x,1,0]); Add(params[6],[0,y,0,x,W,0]); Add(params[6],[0,y,0,x,W^2 mod P,0]); od; od; fi; if P mod 4 = 3 then for y in [0..(P-1)/2] do Add(params[6],[y,0,0,0,0,1]); Add(params[6],[y,0,0,0,0,W]); od; for x in [1..P-1] do Add(params[6],[0,0,x,0,0,1]); Add(params[6],[0,0,x,0,0,W]); od; for y in [1..(P-1)/2] do Add(params[6],[y,0,1,0,0,1]); Add(params[6],[y,0,W,0,0,W]); od; fi; if P mod 4 = 1 then yrange:=ShallowCopy(transversal4); Add(yrange,0); for y in yrange do Add(params[6],[y,0,0,0,0,1]); Add(params[6],[y,0,0,0,0,W]); Add(params[6],[y,0,0,0,0,W^2 mod P]); Add(params[6],[y,0,0,0,0,W^3 mod P]); od; for x in [1..P-1] do Add(params[6],[0,0,x,0,0,1]); Add(params[6],[0,0,x,0,0,W]); Add(params[6],[0,0,x,0,0,W^2 mod P]); Add(params[6],[0,0,x,0,0,W^3 mod P]); od; for y in transversal4 do Add(params[6],[y,0,1,0,0,1]); Add(params[6],[y,0,W,0,0,W]); Add(params[6],[y,0,W^2 mod P,0,0,W^2 mod P]); Add(params[6],[y,0,W^3 mod P,0,0,W^3 mod P]); od; fi; if Length(params[6])<>P^2+3*P-3+(P+2)*Gcd(P-1,3)+(P+1)*Gcd(P-1,4)+(P+1)*Gcd(P-1,5) then Error("params[6] wrong"); fi; if case = 6 then return params[6]; fi; fi; ##Case 7: cb=baa=bac=cac=0 if case = true or case = 7 then for u in [0,1,W] do for t in [0,1] do for x in [0,1] do Add(params[7],[u,0,t,x,0,0]); od; od; od; for u in [0,1,W] do for x in [0,1] do Add(params[7],[u,1,0,x,0,0]); od; od; for x in [0,1,W] do Add(params[7],[0,1,1,x,0,0]); od; for u in [1,W] do for x in [0..P-1] do Add(params[7],[u,1,1,x,0,0]); od; od; for u in [0,1,W] do for x in [0,1] do for z in [1,W] do Add(params[7],[u,0,0,x,0,z]); od; od; od; for u in [0..P-1] do for x in [0,1] do for z in [1,W] do Add(params[7],[u,0,1,x,0,z]); od; od; od; for v in [0,1,W] do for z in [0,1,W] do Add(params[7],[0,v,0,0,1,z]); od; od; vrange:=[0,1,W]; if P mod 4 = 1 then vrange:=[0,1,W,W^2 mod P,W^3 mod P]; fi; for v in vrange do Add(params[7],[0,v,0,1,1,0]); od; for v in [0..P-1] do for z in [1,W] do Add(params[7],[0,v,0,1,1,z]); od; od; for v in [0..P-1] do for z in [0,1,W] do Add(params[7],[0,v,1,0,1,z]); od; od; for v in [0..P-1] do for x in [1,W] do for z in [0..P-1] do Add(params[7],[0,v,1,x,1,z]); od; od; od; if Length(params[7]) <> 2*P^2+11*P+43+Gcd(P-1,4) then Error("params[7] wrong"); fi; if case = 7 then return params[7]; fi; fi; ##Case 8: cb=caa, baa=bac=cac=0 if case = true or case = 8 then urange:=[0,1,W]; if P mod 4 = 1 then urange:=[0,1,W,W^2 mod P,W^3 mod P]; fi; for u in urange do Add(params[8],[u,0,0,0,0,0]); Add(params[8],[u,0,0,1,0,0]); Add(params[8],[u,1,0,0,0,0]); od; if P mod 3 = 1 then urange:=ShallowCopy(transversal3); Add(urange,0); else; urange:=[0..P-1]; fi; for u in urange do Add(params[8],[u,0,1,0,0,0]); Add(params[8],[u,0,1,1,0,0]); Add(params[8],[u,1,1,0,0,0]); if P mod 3 = 1 then Add(params[8],[u,0,W,0,0,0]); Add(params[8],[u,0,W,1,0,0]); Add(params[8],[u,1,W,0,0,0]); Add(params[8],[u,0,W^2 mod P,0,0,0]); Add(params[8],[u,0,W^2 mod P,1,0,0]); Add(params[8],[u,1,W^2 mod P,0,0,0]); fi; od; for u in [0..P-1] do for t in [0..P-1] do Add(params[8],[u,1,t,1,0,0]); od; od; for u in [0..P-1] do for t in [0..(P-1)/2] do for x in [0,1] do for z in [1,W] do Add(params[8],[u,0,t,x,0,z]); od; od; od; od; vrange:=[0,1,W]; if P mod 3 = 1 then vrange:=[0,1,W,W^2,W^3,W^4,W^5] mod P; fi; for v in vrange do Add(params[8],[0,v,0,0,1,0]); od; if P mod 5 <> 1 then for v in [0..P-1] do Add(params[8],[0,v,0,1,1,0]); od; fi; if P mod 5 = 1 then vrange:=ShallowCopy(transversal5); Add(vrange,0); for v in vrange do for x in ([1,W,W^2,W^3,W^4] mod P) do Add(params[8],[0,v,0,x,1,0]); od; od; fi; if P mod 3 = 2 then for v in [0..P-1] do for x in [0..P-1] do Add(params[8],[0,v,1,x,1,0]); od; od; fi; if P mod 3 = 1 then xrange:=ShallowCopy(transversal3); Add(xrange,0); for v in [0..P-1] do for x in xrange do Add(params[8],[0,v,1,x,1,0]); Add(params[8],[0,v,W,x,1,0]); Add(params[8],[0,v,W^2 mod P,x,1,0]); od; od; fi; for v in [0..P-1] do for x in [0..(P-1)/2] do for z in [1,W] do Add(params[8],[0,v,0,x,1,z]); od; od; od; for v in [0..P-1] do for t in [1..(P-1)/2] do for x in [0..P-1] do for z in [1,W] do Add(params[8],[0,v,t,x,1,z]); od; od; od; od; if Length(params[8]) <> P^3+4*P^2+6*P+(P+5)*Gcd(P-1,3)+3*Gcd(P-1,4)+Gcd(P-1,5) then Error("params[8] wrong"); fi; if case = 8 then return params[8]; fi; fi; #Cases 9 & 10: cb=bac=caa=0, cac=kbab (k=1,W) if case = true or case = 9 or case = 10 then Add(params[9],[0,0,0,0,0,0]); Add(params[9],[1,0,0,0,0,0]); Add(params[9],[0,1,0,0,0,0]); Add(params[9],[0,W,0,0,0,0]); for y in [0,1,W] do Add(params[9],[0,y,0,0,1,0]); if P mod 4 = 1 then Add(params[9],[0,y,0,0,W,0]); fi; od; yrange:=[0..P-1]; if P mod 4 = 1 then yrange:=[0..(P-1)/2]; fi; for y in yrange do Add(params[9],[1,y,0,0,1,0]); if P mod 4 = 1 then Add(params[9],[1,y,0,0,W,0]); fi; od; for x in [0..(P-1)/2] do Add(params[9],[x,0,0,0,0,1]); od; Add(params[9],[0,1,0,0,0,1]); Add(params[9],[0,W,0,0,0,1]); for y in [0,1,W] do for z in [0..(P-1)/2] do Add(params[9],[0,y,1,0,z,0]); Add(params[9],[0,y,W,0,z,0]); od; od; for y in [0..P-1] do for z in [0..(P-1)/2] do Add(params[9],[0,y,1,0,z,1]); Add(params[9],[0,y,W,0,z,1]); od; od; for y in [0..P-1] do for t in [0..(P-1)/2] do Add(params[9],[1,y,1,0,0,t]); Add(params[9],[1,y,W,0,0,t]); od; od; for y in [0..P-1] do for z in [1..(P-1)/2] do for t in [0..P-1] do Add(params[9],[1,y,1,0,z,t]); Add(params[9],[1,y,W,0,z,t]); od; od; od; for x in [0..(P-1)/2] do for y in [0..P-1] do Add(params[9],[y,0,0,1,0,x]); od; od; for x in [0..(P-1)/2] do Add(params[9],[1,1,0,1,0,x]); Add(params[9],[1,W,0,1,0,x]); od; if P mod 4 = 1 then for x in [0..P-1] do for y in [0..(P-1)/2] do Add(params[9],[x,y,0,1,1,0]); Add(params[9],[x,y,0,1,W,0]); od; od; fi; if P mod 4 = 3 then for x in [0..P-1] do for y in [0..P-1] do Add(params[9],[x,y,0,1,1,0]); od; od; fi; if Length(params[9]) <> P^3+5*P^2/2+7*P+19/2+(P+4)*Gcd(P-1,4)/2 then Error("params[9] wrong"); fi; if case = 9 then return params[9]; fi; if case = 10 then return params[9]; fi; if case = true then params[10] := params[9]; fi; fi; ##Cases 11 & 12: bac=caa=0, cb=baa, cac=kbab (k=1,W) if case = true or case = 11 or case = 12 then Add(params[11],[0,0,0,0,0,0]); Add(params[11],[1,0,0,0,0,0]); if P mod 3 = 1 then Add(params[11],[W,0,0,0,0,0]); Add(params[11],[W^2 mod P,0,0,0,0,0]); fi; Add(params[11],[0,1,0,0,0,0]); Add(params[11],[0,W,0,0,0,0]); if P mod 4 = 1 then Add(params[11],[0,W^2 mod P,0,0,0,0]); Add(params[11],[0,W^3 mod P,0,0,0,0]); fi; if P mod 4 = 1 then xrange:=ShallowCopy(transversal4); Add(xrange,0); for x in xrange do for y in [0..P-1] do Add(params[11],[x,y,0,0,1,0]); Add(params[11],[x,y,0,0,W,0]); od; od; fi; if P mod 4 = 3 then for x in [0..(P-1)/2] do for y in [0..P-1] do Add(params[11],[x,y,0,0,1,0]); od; od; fi; if P mod 3 = 1 then for x in [0..(P-1)/2] do Add(params[11],[x,0,0,0,0,1]); Add(params[11],[x,0,0,0,0,W]); Add(params[11],[x,0,0,0,0,W^2 mod P]); od; for x in transversal3 do Add(params[11],[0,x,0,0,0,1]); Add(params[11],[0,x,0,0,0,W]); Add(params[11],[0,x,0,0,0,W^2 mod P]); od; fi; if P mod 3 = 2 then for x in [0..(P-1)/2] do Add(params[11],[x,0,0,0,0,1]); od; for x in [1..P-1] do Add(params[11],[0,x,0,0,0,1]); od; fi; for y in [0..P-1] do for z in [0..(P-1)/2] do for t in [0..(P-1)/2] do Add(params[11],[0,y,1,0,z,t]); Add(params[11],[0,y,W,0,z,t]); od; od; od; for y in [0..P-1] do for x in [1..(P-1)/2] do for z in [0..(P-1)/2] do Add(params[11],[x,y,1,0,z,0]); Add(params[11],[x,y,W,0,z,0]); od; od; od; for y in [0..P-1] do for x in [1..(P-1)/2] do for t in [1..(P-1)/2] do for z in [0..P-1] do Add(params[11],[x,y,1,0,z,t]); Add(params[11],[x,y,W,0,z,t]); od; od; od; od; if P mod 3 = 1 then for x in [0..P-1] do Add(params[11],[x,0,0,1,0,0]); Add(params[11],[x,0,0,W,0,0]); Add(params[11],[x,0,0,W^2 mod P,0,0]); od; for y in transversal3 do Add(params[11],[1,y,0,1,0,0]); Add(params[11],[W,y,0,W,0,0]); Add(params[11],[W^2 mod P,y,0,W^2 mod P,0,0]); od; for x in transversal6 do for y in [0..P-1] do for z in [0..P-1] do Add(params[11],[y,z,0,1,x,0]); Add(params[11],[y,z,0,W,x,0]); Add(params[11],[y,z,0,W^2 mod P,x,0]); od; od; od; for x in [0..P-1] do for z in [1..(P-1)/2] do Add(params[11],[x,0,0,1,0,z]); Add(params[11],[x,0,0,W,0,z]); Add(params[11],[x,0,0,W^2 mod P,0,z]); od; od; for y in transversal3 do for z in [1..(P-1)/2] do Add(params[11],[1,y,0,1,0,z]); Add(params[11],[W,y,0,W,0,z]); Add(params[11],[W^2 mod P,y,0,W^2 mod P,0,z]); od; od; fi; if P mod 3 = 2 then for x in [0..P-1] do Add(params[11],[x,0,0,1,0,0]); od; for y in [1..P-1] do Add(params[11],[1,y,0,1,0,0]); od; for x in [1..(P-1)/2] do for y in [0..P-1] do for z in [0..P-1] do Add(params[11],[y,z,0,1,x,0]); od; od; od; for x in [0..P-1] do for z in [1..(P-1)/2] do Add(params[11],[x,0,0,1,0,z]); od; od; for y in [1..P-1] do for z in [1..(P-1)/2] do Add(params[11],[1,y,0,1,0,z]); od; od; fi; if Length(params[11]) <> (P^4+P^3+4*P^2+P-1+(P^2+2*P+3)*Gcd(P-1,3)+(P+2)*Gcd(P-1,4))/2 then Error("params[11] wrong"); fi; if case = 11 then return params[11]; fi; if case = 12 then return params[11]; fi; if case = true then params[12] := params[11]; fi; fi; ##Case 13, cb=bac=0, caa=baa, cac=-bab if case = true or case = 13 then ##pb=pc=0 Add(params[13],[0,0,0,0,0,0]); Add(params[13],[1,0,0,0,0,0]); Add(params[13],[0,1,0,0,0,0]); ##pb=0, pc=baa or wbaa Add(params[13],[0,0,0,0,1,0]); Add(params[13],[0,0,0,0,W,0]); Add(params[13],[0,1,0,0,1,0]); Add(params[13],[0,1,0,0,W,0]); Add(params[13],[0,W,0,0,1,0]); Add(params[13],[0,W,0,0,W,0]); for y in [0..P-1] do Add(params[13],[1,y,0,0,1,0]); Add(params[13],[1,y,0,0,W,0]); od; ##pb=0, pc=bab for x in [0..P-1] do Add(params[13],[x,0,0,0,0,1]); od; Add(params[13],[-1,1,0,0,0,1] mod P); Add(params[13],[-1,W,0,0,0,1] mod P); ##pb=pc=bab Add(params[13],[0,0,0,1,0,1]); Add(params[13],[1,0,0,1,0,1]); Add(params[13],[0,1,0,1,0,1]); ##pb=bab, pc=-bab for x in [0..P-1] do Add(params[13],[x,0,0,1,0,-1] mod P); od; Add(params[13],[2,1,0,1,0,-1] mod P); ##pb=bab, pc=baa or wbaa for x in [0..P-1] do for y in [0..P-1] do Add(params[13],[x,y,0,1,1,0]); Add(params[13],[x,y,0,1,W,0]); od; od; ##pb=pc=baa Add(params[13],[0,0,1,0,1,0]); Add(params[13],[1,0,1,0,1,0]); Add(params[13],[0,1,1,0,1,0]); Add(params[13],[1,1,1,0,1,0]); ##pb=baa, pc=baa+bab for x in [0..P-2] do ##Note that -1 is excluded Add(params[13],[x,0,1,0,1,1]); y:=((x+1)/2)*One(F); y:=IntFFE(y); Add(params[13],[x,y,1,0,1,1]); od; Add(params[13],[-1,0,1,0,1,1] mod P); Add(params[13],[-1,1,1,0,1,1] mod P); ##pb=baa, pc=-baa Add(params[13],[0,0,1,0,-1,0] mod P); Add(params[13],[0,1,1,0,-1,0] mod P); Add(params[13],[0,W,1,0,-1,0] mod P); for y in [0..P-1] do Add(params[13],[1,y,1,0,-1,0] mod P); od; ##pb=baa, pc=-baa+bab half:=(P+1)/2; Add(params[13],[1,-half,1,0,-1,1] mod P); Add(params[13],[1,half,1,0,-1,1] mod P); Add(params[13],[1,W-half,1,0,-1,1] mod P); if P mod 4 = 1 then Add(params[13],[1,W^2-half,1,0,-1,1] mod P); Add(params[13],[1,W^3-half,1,0,-1,1] mod P); fi; for y in [0..P-1] do Add(params[13],[0,y,1,0,-1,1] mod P); Add(params[13],[1-W,y,1,0,-1,1] mod P); od; ##pb=pc=wbaaa Add(params[13],[0,0,W,0,W,0]); Add(params[13],[1,0,W,0,W,0]); Add(params[13],[0,1,W,0,W,0]); Add(params[13],[1,1,W,0,W,0]); ##pb=wbaa, pc=wbaa+bab for x in [0..P-2] do ##Note that -1 is excluded Add(params[13],[x,0,W,0,W,1]); y:=One(F)*((x+1)/(2*W)); y:=IntFFE(y); Add(params[13],[x,y,W,0,W,1]); od; Add(params[13],[-1,0,W,0,W,1] mod P); Add(params[13],[-1,1,W,0,W,1] mod P); if Length(params[13]) <> 2*P^2+11*P+27+Gcd(P-1,4) then Error("params[13] wrong"); fi; if case = 13 then return params[13]; fi; fi; ##Case 14, bac=0, cb=caa=baa, cac=-bab if case = true or case = 14 then ##1. v <> +/- y for y in [1,W] do for u in [0..P-1] do for x in [0..(P-1)/2] do zrange:=[0..P-1]; if x = 0 then zrange:=[0..(P-1)/2]; fi; for z in zrange do Add(params[14],[0,u,0,x,y,z]); od; od; od; od; for u in [1,W] do for x in [0..(P-1)/2] do zrange:=[0..P-1]; if x = 0 then zrange:=[0..(P-1)/2]; fi; for z in zrange do Add(params[14],[0,u,1,x,-1,z] mod P); od; od; od; for x in [0..P-1] do for z in [0..P-1] do new:=true; for a in [1..P-1] do x1:=One(F)*((x+z+x*a^2-z*a^2)/(2*a^3)); x1:=IntFFE(x1); z1:=One(F)*((x+z-x*a^2+z*a^2)/(2*a^3)); z1:=IntFFE(z1); if [x1,z1] < [x,z] then new:=false; break; fi; od; if new then Add(params[14],[0,0,1,x,-1,z] mod P); fi; od; od; for v in [1,W] do for x in [0..P-1] do for z in [0..P-1] do if x = (z+1) mod P then continue; fi; x1:=(-x) mod P; z1:=(-z) mod P; if [z1,x1] < [x,z] then continue; fi; Add(params[14],[1,0,v,x,v,z]); od; od; od; for x in [0..P-1] do for z in [0..P-1] do if x = (z+1) mod P then continue; fi; new:=true; for a in [1..P-1] do x1:=One(F)*((x+z+x*a^3-z*a^3)/(2*a^3)); x1:=IntFFE(x1); z1:=One(F)*((x+z-x*a^3+z*a^3)/(2*a^3)); z1:=IntFFE(z1); if [x1,z1] < [x,z] then new:=false; break; fi; od; if new then Add(params[14],[1,0,0,x,0,z]); fi; od; od; for v in [1,W] do for u in [0..(P-1)/2] do Add(params[14],[1,u,v,0,v,-1] mod P); od; od; for z in [0..P-1] do Add(params[14],[1,1,0,z+1,0,z] mod P); od; for z in [0..P-1] do new:=true; for a in [1..P-1] do z1:=One(F)*((-a^3+2*z+1)/(2*a^3)); z1:=IntFFE(z1); if z1 < z then new:=false; break; fi; od; if new then Add(params[14],[1,0,0,z+1,0,z] mod P); fi; od; for v in [1,W] do for z in [1..(P-1)/2] do Add(params[14],[0,0,v,0,v,z]); od; od; Add(params[14],[0,0,0,0,0,1]); if P mod 3 = 1 then Add(params[14],[0,0,0,0,0,W]); Add(params[14],[0,0,0,0,0,W^2 mod P]); fi; Add(params[14],[0,0,0,1,0,-1] mod P); Add(params[14],[0,0,W,1,W,-1] mod P); Add(params[14],[0,0,W^2,1,W^2,-1] mod P); for v in [1,W] do for u in [0,1] do Add(params[14],[0,u,v,0,v,0]); od; od; xrange:=[0,1]; if P mod 3 = 1 then xrange:=[0,1,W,W^2 mod P]; fi; for u in [0,1] do for x in xrange do Add(params[14],[0,u,0,x,0,x]); od; od; if Length(params[14]) <> P^3+2*P^2+6*P+10+(P+4)*Gcd(P-1,3) then Error("params[14] wrong"); fi; if case = 14 then return params[14]; fi; fi; ##Case 15, cb=baa=bac=caa=0 if case = true or case = 15 then Add(params[15],[0,0,0,0,0,0]); Add(params[15],[0,0,0,0,1,0]); Add(params[15],[0,0,0,1,1,0]); if P mod 3 = 1 then Add(params[15],[0,0,0,1,W,0]); fi; Add(params[15],[0,1,0,0,0,0]); Add(params[15],[0,W,0,0,0,0]); Add(params[15],[0,1,0,0,1,0]); Add(params[15],[0,W,0,0,1,0]); Add(params[15],[0,1,0,1,0,0]); Add(params[15],[0,W,0,1,0,0]); Add(params[15],[0,1,0,1,1,0]); Add(params[15],[0,W,0,1,1,0]); if P mod 3 = 1 then Add(params[15],[0,1,0,1,W,0]); Add(params[15],[0,W,0,1,W,0]); Add(params[15],[0,1,0,1,W^2 mod P,0]); Add(params[15],[0,W,0,1,W^2 mod P,0]); fi; Add(params[15],[1,1,0,0,0,0]); Add(params[15],[W,W,0,0,0,0]); Add(params[15],[1,1,0,0,1,0]); Add(params[15],[W,W,0,0,1,0]); for u in [1..(P-1)/2] do u1:=One(F)*u^-1; u1:=IntFFE(u1); if u1 < u or (P-u1) < u then continue; fi; Add(params[15],[1,1,0,1,u,0]); Add(params[15],[W,W,0,1,u,0]); od; Add(params[15],[1,W,0,0,0,0]); Add(params[15],[1,W,0,0,1,0]); Add(params[15],[1,W,0,1,0,0]); for u in [1..(P-1)/2] do Add(params[15],[1,W,0,1,u,0]); od; Add(params[15],[0,0,0,0,0,1]); Add(params[15],[0,0,0,0,1,1]); Add(params[15],[0,0,0,0,W,1]); Add(params[15],[0,1,0,0,0,1]); Add(params[15],[0,1,0,0,1,1]); Add(params[15],[0,1,0,0,W,1]); Add(params[15],[0,W,0,0,0,1]); Add(params[15],[0,W,0,0,1,1]); Add(params[15],[0,W,0,0,W,1]); Add(params[15],[1,0,0,0,0,1]); Add(params[15],[1,0,0,0,1,1]); Add(params[15],[1,0,0,0,W,1]); Add(params[15],[W,0,0,0,0,1]); Add(params[15],[W,0,0,0,1,1]); Add(params[15],[W,0,0,0,W,1]); for x in [1,W] do for y in [1,W] do for u in [0..P-1] do Add(params[15],[x,y,0,0,u,1]); od; od; od; for x in [1,W] do for y in [0..P-1] do for u in [0..P-1] do Add(params[15],[x,y,0,1,u,1]); od; od; od; for y in [0,1,W] do for u in [0..P-1] do Add(params[15],[0,y,0,1,u,1]); od; od; for t in [0..P-2] do for u in [t+1..P-1] do Add(params[15],[0,0,1,t,u,1]); Add(params[15],[0,1,1,t,u,1]); Add(params[15],[0,W,1,t,u,1]); for y in [0..P-1] do Add(params[15],[1,y,1,t,u,1]); Add(params[15],[W,y,1,t,u,1]); od; od; od; range:=[]; for k in [1..(P-1)/2] do k2:=k^2 mod P; km2:=One(F)*(k2^-1); km2:=IntFFE(km2); if k2 <= km2 then AddSet(range,k2); fi; od; for t in [0..P-1] do Add(params[15],[0,0,1,t,t,1]); Add(params[15],[0,1,1,t,t,1]); Add(params[15],[0,W,1,t,t,1]); for k2 in range do Add(params[15],[1,k2,1,t,t,1]); Add(params[15],[W,W*k2,1,t,t,1] mod P); od; for k in [1..(P-1)/2] do Add(params[15],[1,W*k^2,1,t,t,1] mod P); od; od; if Length(params[15]) <> P^3+(7*P^2+17*P+59+5*Gcd(P-1,3)+(P+1)*Gcd(P-1,4))/2 then Error("params[15] wrong"); fi; if case = 15 then return params[15]; fi; fi; ##Case 16, cb=bac=caa=0, baa=cac if case = true or case = 16 then for y in [0,1,W] do Add(params[16],[0,y,0,0,0,0]); Add(params[16],[0,y,0,1,0,0]); Add(params[16],[0,y,0,W,0,0]); for t in [0..P-1] do Add(params[16],[1,y,0,t,0,0]); Add(params[16],[W,y,0,t,0,0]); od; od; Add(params[16],[0,0,1,0,0,0]); Add(params[16],[0,0,W,0,0,0]); Add(params[16],[0,1,1,0,0,0]); Add(params[16],[0,1,W,0,0,0]); Add(params[16],[0,W,1,0,0,0]); Add(params[16],[0,W,W,0,0,0]); if P mod 4 = 1 then Add(params[16],[0,W^2 mod P,1,0,0,0]); Add(params[16],[0,W^2 mod P,W,0,0,0]); Add(params[16],[0,W^3 mod P,1,0,0,0]); Add(params[16],[0,W^3 mod P,W,0,0,0]); fi; for y in [0..P-1] do Add(params[16],[0,y,1,1,0,0]); Add(params[16],[0,y,W,1,0,0]); Add(params[16],[0,y,1,W,0,0]); Add(params[16],[0,y,W,W,0,0]); od; for y in [0..P-1] do for t in [0..P-1] do Add(params[16],[1,y,1,t,0,0]); Add(params[16],[1,y,W,t,0,0]); Add(params[16],[W,y,1,t,0,0]); Add(params[16],[W,y,W,t,0,0]); od; od; Add(params[16],[0,0,0,0,0,1]); Add(params[16],[0,0,1,0,0,1]); Add(params[16],[0,0,W,0,0,1]); if P mod 3 = 1 then Add(params[16],[0,0,W^2 mod P,0,0,1]); Add(params[16],[0,0,W^3 mod P,0,0,1]); Add(params[16],[0,0,W^4 mod P,0,0,1]); Add(params[16],[0,0,W^5 mod P,0,0,1]); fi; for z in [0..P-1] do Add(params[16],[0,0,z,1,0,1]); Add(params[16],[0,0,z,W,0,1]); od; for z in [0..P-1] do for t in [0..P-1] do Add(params[16],[0,1,z,t,0,1]); Add(params[16],[0,W,z,t,0,1]); od; od; for y in [0..P-1] do for z in [0..P-1] do for t in [0..P-1] do Add(params[16],[1,y,z,t,0,1]); Add(params[16],[W,y,z,t,0,1]); od; od; od; Add(params[16],[0,0,0,0,1,0]); Add(params[16],[0,1,0,0,1,0]); Add(params[16],[0,W,0,0,1,0]); if P mod 3 = 1 then Add(params[16],[0,W^2 mod P,0,0,1,0]); Add(params[16],[0,W^3 mod P,0,0,1,0]); Add(params[16],[0,W^4 mod P,0,0,1,0]); Add(params[16],[0,W^5 mod P,0,0,1,0]); fi; if P mod 4 = 1 then for v in [1,W,W^2 mod P,W^3 mod P] do for y in [0..(P-1)/2] do Add(params[16],[0,y,0,0,1,v]); od; od; fi; if P mod 4 = 3 then for v in [1,W] do for y in [0..P-1] do Add(params[16],[0,y,0,0,1,v]); od; od; fi; for v in [0..P-1] do for y in [0..P-1] do Add(params[16],[0,y,0,1,1,v]); Add(params[16],[0,y,0,W,1,v]); od; od; for t in [0..P-1] do for v in [0..P-1] do for y in [0..P-1] do Add(params[16],[0,y,1,t,1,v]); Add(params[16],[0,y,W,t,1,v]); od; od; od; for z in [0..P-1] do for t in [0..P-1] do for v in [0..P-1] do for y in [0..P-1] do Add(params[16],[1,y,z,t,1,v]); Add(params[16],[W,y,z,t,1,v]); od; od; od; od; if Length(params[16]) <> 2*P^4+4*P^3+8*P^2+14*P+11+4*Gcd(P-1,3)+3*Gcd(P-1,4) then Error("params[16] wrong"); fi; if case = 16 then return params[16]; fi; fi; ##Case 17, cb=bac=0, cac=baa, caa=bab if case = true or case = 17 then mats:=[]; for y5 in [0,1,lns] do for y6 in [0..P-1] do for y3 in [0..P-1] do for y4 in [0..P-1] do A:=One(F)*MyCutVector([y3,y4,y5,y6], 2); if A = 0*A then Add(mats,A); continue; fi; new:=1; index:=P^3*y5+P^2*y6+P*y3+y4; for a in [1..P-1] do for x in CU do c:=a*x; B:=One(F)*MyCutVector([a^-1*c^2,0,0,c], 2); C:=One(F)*MyCutVector([a*c^2,0,0,a^2*c], 2); D:=B*A*C^-1; z3:=IntFFE(D[1][1]); z4:=IntFFE(D[1][2]); z5:=IntFFE(D[2][1]); z6:=IntFFE(D[2][2]); ind1:=P^3*z5+P^2*z6+P*z3+z4; if ind1 < index then new:=0; fi; B:=One(F)*MyCutVector([0,a^-1*c^2,c,0], 2); C:=One(F)*MyCutVector([0,a*c^2,a^2*c,0], 2); D:=B*A*C^-1; z3:=IntFFE(D[1][1]); z4:=IntFFE(D[1][2]); z5:=IntFFE(D[2][1]); z6:=IntFFE(D[2][2]); ind1:=P^3*z5+P^2*z6+P*z3+z4; if ind1 < index then new:=0; fi; if new = 0 then break; fi; od; if new = 0 then break; fi; od; if new = 1 then Add(mats,A); fi; od; od; od; od; for AS in mats do stab1:=[]; stab2:=[]; for a in [1..P-1] do for x in CU do c:=a*x; B:=One(F)*MyCutVector([a^-1*c^2,0,0,c], 2); C:=One(F)*MyCutVector([a*c^2,0,0,a^2*c], 2); D:=B*AS*C^-1; if D = AS then Add(stab1,One(F)*MyCutVector([a,0,0,0,a^-1*c^2,0,0,0,c], 3)); Add(stab2,C); fi; B:=One(F)*MyCutVector([0,a^-1*c^2,c,0], 2); C:=One(F)*MyCutVector([0,a*c^2,a^2*c,0], 2); D:=B*AS*C^-1; if D = AS then Add(stab1,One(F)*MyCutVector([a,0,0,0,0,a^-1*c^2,0,c,0], 3)); Add(stab2,C); fi; od; od; y3:=IntFFE(AS[1][1]); y4:=IntFFE(AS[1][2]); y5:=IntFFE(AS[2][1]); y6:=IntFFE(AS[2][2]); for y1 in [0..P-1] do for y2 in [0..P-1] do A:=One(F)*MyCutVector([y1,y2,y3,y4,y5,y6], 3); if A = 0*A then Add(params[17],[0,0,0,0,0,0]); continue; fi; new:=1; index:=P*y1+y2; for ii in [1..Length(stab1)] do B:=stab1[ii]; C:=stab2[ii]; D:=B*A*C^-1; z1:=IntFFE(D[1][1]); z2:=IntFFE(D[1][2]); ind1:=P*z1+z2; if ind1 < index then new:=0; fi; if new = 0 then break; fi; od; if new = 1 then Add(params[17],[y1,y2,y3,y4,y5,y6]); fi; od; od; od; if Length(params[17]) <> (P^4+2*P^3+3*P^2+4*P+2)*(P-1)/Gcd(P-1,3)+3*P+4+(P^2+P+1)*Gcd(P-1,4)/2 then Error("params[17] wrong"); fi; if case = 17 then return params[17]; fi; fi; ##Case 18, cb=bac=0, cac=baa, caa=wbab (p=1mod3 only) if case = true or case = 18 then if P mod 3 = 1 then mats:=[]; for y5 in [0,1,lns] do for y6 in [0..P-1] do for y3 in [0..P-1] do for y4 in [0..P-1] do A:=One(F)*MyCutVector([y3,y4,y5,y6], 2); if A = 0*A then Add(mats,A); continue; fi; new:=1; index:=P^3*y5+P^2*y6+P*y3+y4; for a in [1..P-1] do for x in CU do c:=a*x; B:=One(F)*MyCutVector([a^-1*c^2,0,0,c], 2); C:=One(F)*MyCutVector([a*c^2,0,0,a^2*c], 2); D:=B*A*C^-1; z3:=IntFFE(D[1][1]); z4:=IntFFE(D[1][2]); z5:=IntFFE(D[2][1]); z6:=IntFFE(D[2][2]); ind1:=P^3*z5+P^2*z6+P*z3+z4; if ind1 < index then new:=0; fi; if new = 0 then break; fi; od; if new = 0 then break; fi; od; if new = 1 then Add(mats,A); fi; od; od; od; od; for AS in mats do stab1:=[]; stab2:=[]; for a in [1..P-1] do for x in CU do c:=a*x; B:=One(F)*MyCutVector([a^-1*c^2,0,0,c], 2); C:=One(F)*MyCutVector([a*c^2,0,0,a^2*c], 2); D:=B*AS*C^-1; if D = AS then Add(stab1,One(F)*MyCutVector([a,0,0,0,a^-1*c^2,0,0,0,c], 3)); Add(stab2,C); fi; od; od; y3:=IntFFE(AS[1][1]); y4:=IntFFE(AS[1][2]); y5:=IntFFE(AS[2][1]); y6:=IntFFE(AS[2][2]); for y1 in [0..P-1] do for y2 in [0..P-1] do A:=One(F)*MyCutVector([y1,y2,y3,y4,y5,y6], 3); if A = 0*A then Add(params[18],[0,0,0,0,0,0]); continue; fi; new:=1; index:=P*y1+y2; for ii in [1..Length(stab1)] do B:=stab1[ii]; C:=stab2[ii]; D:=B*A*C^-1; z1:=IntFFE(D[1][1]); z2:=IntFFE(D[1][2]); ind1:=P*z1+z2; if ind1 < index then new:=0; fi; if new = 0 then break; fi; od; if new = 1 then Add(params[18],[y1,y2,y3,y4,y5,y6]); fi; od; od; od; if Length(params[18]) <> (2*P^5+2*P^4+2*P^3+2*P^2+14*P+17)/3 then Error("params[18] wrong"); fi; fi; if case = 18 then return params[18]; fi; fi; ##Case 19, cb=baa=caa=cac=0 if case = true or case = 19 then Add(params[19],[0,0,0,0,0,0]); Add(params[19],[1,0,0,0,0,0]); Add(params[19],[W,0,0,0,0,0]); Add(params[19],[0,1,0,0,0,0]); for x in [0,1,W] do for y in [0,1] do Add(params[19],[x,y,1,0,0,0]); od; od; Add(params[19],[0,0,0,1,0,0]); Add(params[19],[1,0,0,1,0,0]); Add(params[19],[W,0,0,1,0,0]); Add(params[19],[0,1,0,1,0,0]); for t in [0..P-1] do Add(params[19],[0,0,1,t,1,0]); Add(params[19],[0,1,1,t,1,0]); Add(params[19],[0,W,1,t,1,0]); for y in [0..P-1] do Add(params[19],[1,y,1,t,1,0]); Add(params[19],[W,y,1,t,1,0]); od; od; for x in [0,1,W] do for t in [0,1,W] do Add(params[19],[x,0,0,t,1,0]); od; od; for x in [1,W] do for t in [0..P-1] do Add(params[19],[x,1,0,t,1,0]); od; od; Add(params[19],[0,1,0,0,1,0]); Add(params[19],[0,1,0,1,1,0]); Add(params[19],[0,1,0,W,1,0]); if P mod 4 = 1 then Add(params[19],[0,1,0,W^2 mod P,1,0]); Add(params[19],[0,1,0,W^3 mod P,1,0]); fi; half:=(P+1)/2; for x in [0..P-1] do if x = half then continue; fi; for z in [0,1,W] do for t in [0,1] do Add(params[19],[z,t,x,0,0,1]); od; od; od; Add(params[19],[1,0,half,0,0,1]); Add(params[19],[W,0,half,0,0,1]); Add(params[19],[1,0,half,1,0,1]); Add(params[19],[W,0,half,1,0,1]); Add(params[19],[0,0,half,0,0,1]); Add(params[19],[0,0,half,1,0,1]); Add(params[19],[0,1,half,0,0,1]); Add(params[19],[0,1,half,1,0,1]); Add(params[19],[0,W,half,1,0,1]); if Length(params[19]) <> 2*P^2+11*P+27+Gcd(P-1,4) then Error("params[19] wrong"); fi; if case = 19 then return params[19]; fi; fi; ##Case 20, cb=baa=cac, caa=bab if case = true or case = 20 then for u in [0,1,W] do Add(params[20],[0,0,0,0,u,0]); Add(params[20],[0,0,0,1,u,0]); Add(params[20],[0,0,0,W,u,0]); for t in [0..P-1] do Add(params[20],[1,0,0,t,u,0]); Add(params[20],[W,0,0,t,u,0]); od; od; Add(params[20],[0,1,0,0,0,0]); Add(params[20],[0,1,0,0,1,0]); Add(params[20],[0,1,0,0,W,0]); if P mod 3 = 1 then Add(params[20],[0,1,0,0,W^2 mod P,0]); Add(params[20],[0,1,0,0,W^3 mod P,0]); Add(params[20],[0,1,0,0,W^4 mod P,0]); Add(params[20],[0,1,0,0,W^5 mod P,0]); fi; for u in [0..P-1] do Add(params[20],[0,1,0,1,u,0]); Add(params[20],[0,1,0,W,u,0]); od; for t in [0..P-1] do for u in [0..P-1] do Add(params[20],[1,1,0,t,u,0]); Add(params[20],[W,1,0,t,u,0]); od; od; Add(params[20],[0,0,0,0,0,1]); Add(params[20],[0,1,0,0,0,1]); Add(params[20],[0,W,0,0,0,1]); if P mod 4 = 1 then Add(params[20],[0,W^2 mod P,0,0,0,1]); Add(params[20],[0,W^3 mod P,0,0,0,1]); fi; for y in [0..P-1] do Add(params[20],[0,y,0,0,1,1]); Add(params[20],[0,y,0,0,W,1]); od; for y in [0..P-1] do for u in [0..P-1] do Add(params[20],[0,y,0,1,u,1]); Add(params[20],[0,y,0,W,u,1]); od; od; for y in [0..P-1] do for t in [0..P-1] do for u in [0..P-1] do Add(params[20],[1,y,0,t,u,1]); Add(params[20],[W,y,0,t,u,1]); od; od; od; for v in [0..P-1] do Add(params[20],[0,0,1,0,0,v]); Add(params[20],[0,1,1,0,0,v]); Add(params[20],[0,W,1,0,0,v]); if P mod 4 = 1 then Add(params[20],[0,W^2 mod P,1,0,0,v]); Add(params[20],[0,W^3 mod P,1,0,0,v]); fi; for y in [0..P-1] do Add(params[20],[0,y,1,0,1,v]); Add(params[20],[0,y,1,0,W,v]); od; for y in [0..P-1] do for u in [0..P-1] do Add(params[20],[0,y,1,1,u,v]); Add(params[20],[0,y,1,W,u,v]); od; od; for y in [0..P-1] do for t in [0..P-1] do for u in [0..P-1] do Add(params[20],[1,y,1,t,u,v]); Add(params[20],[W,y,1,t,u,v]); od; od; od; od; if Length(params[20]) <> 2*P^4+4*P^3+6*P^2+11*P+11+2*Gcd(P-1,3)+(P+1)*Gcd(P-1,4) then Error("params[20] wrong"); fi; if case = 20 then return params[20]; fi; fi; ##Case 21, cb=caa=cac=0, bab=baa if case = true or case = 21 then Add(params[21],[0,0,0,0,0,0]); Add(params[21],[1,0,0,0,0,0]); Add(params[21],[W,0,0,0,0,0]); Add(params[21],[0,1,0,0,0,0]); for x in [0..P-1] do Add(params[21],[x,0,1,0,0,0]); Add(params[21],[x,0,W,0,0,0]); Add(params[21],[x,1,1,0,0,0]); Add(params[21],[x,1,W,0,0,0]); od; Add(params[21],[1,0,0,1,0,0]); Add(params[21],[W,0,0,1,0,0]); for x in [0..P-1] do Add(params[21],[0,x,0,1,0,0]); od; for y in [0..P-1] do for z in [0..P-1] do for t in [0..P-1] do Add(params[21],[1,y,z,t,1,0]); Add(params[21],[W,y,z,t,1,0]); od; od; od; for y in [0..P-1] do for t in [0..P-1] do Add(params[21],[0,y,1,t,1,0]); Add(params[21],[0,y,W,t,1,0]); od; od; for t in [0..P-1] do Add(params[21],[0,1,0,t,1,0]); Add(params[21],[0,W,0,t,1,0]); if P mod 4 = 1 then Add(params[21],[0,W^2 mod P,0,t,1,0]); Add(params[21],[0,W^3 mod P,0,t,1,0]); fi; od; Add(params[21],[0,0,0,0,1,0]); Add(params[21],[0,0,0,1,1,0]); Add(params[21],[0,0,0,W,1,0]); if P mod 4 = 1 then Add(params[21],[0,0,0,W^2 mod P,1,0]); Add(params[21],[0,0,0,W^3 mod P,1,0]); fi; for x in [0..P-1] do if x = 1 then continue; fi; for z in [0..P-1] do for t in [0,1] do Add(params[21],[x,0,z,t,0,1]); od; od; od; for x in [0..P-1] do if x = W then continue; fi; for z in [0..P-1] do for t in [0,1] do Add(params[21],[x,0,z,t,0,W]); od; od; od; half:=(P+1)/2; wover2:=One(F)*(W/2); wover2:=IntFFE(wover2); for z in [0..P-1] do if z = half then continue; fi; Add(params[21],[1,0,z,0,0,1]); Add(params[21],[1,1,z,0,0,1]); od; for z in [0..P-1] do if z = wover2 then continue; fi; Add(params[21],[W,0,z,0,0,W]); Add(params[21],[W,1,z,0,0,W]); od; Add(params[21],[1,0,half,0,0,1]); Add(params[21],[W,0,wover2,0,0,W]); Add(params[21],[1,0,half,1,0,1]); Add(params[21],[W,0,wover2,1,0,W]); for t in [0..P-1] do Add(params[21],[1,1,half,t,0,1]); Add(params[21],[W,1,wover2,t,0,W]); od; if Length(params[21]) <> 2*P^3+6*P^2+7*P+7+(P+1)*Gcd(P-1,4) then Error("params[21] wrong"); fi; if case = 21 then return params[21]; fi; fi; ##Case 22, cb=baa=caa=0, cac=wbab if case = true or case = 22 then mats:=[]; bcrange:=[[0,1]]; for i in [0..P-1] do Add(bcrange,[1,i]); od; for y3 in [0,1] do for y4 in [0..P-1] do for y5 in [0..P-1] do for y6 in [0..P-1] do A:=One(F)*MyCutVector([y3,y4,y5,y6], 2); if A = 0*A then Add(mats,A); continue; fi; new:=1; index:=P^3*y3+P^2*y4+P*y5+y6; for bc in bcrange do b:=bc[1]; c:=bc[2]; for m in [-1,1] do B:=One(F)*MyCutVector([W*b,m*c,W*c,W*m*b], 2); C:=One(F)*MyCutVector([W*(W*b^2+c^2),m*2*W*b*c,2*W^2*b*c,m*W*(W*b^2+c^2)], 2); D:=B*A*C^-1; if D[1][1] <> Zero(F) then D:=D[1][1]^-1*D; fi; if D[1][1] = Zero(F) and D[1][2] <> Zero(F) then D:=D[1][2]^-1*D; fi; if D[1][1] = Zero(F) and D[1][2] = Zero(F) and D[2][1] <> Zero(F) then D:=D[2][1]^-1*D; fi; if D[1][1]=Zero(F) and D[1][2]=Zero(F) and D[2][1]=Zero(F) and D[2][2]<>Zero(F) then D:=D[2][2]^-1*D; fi; z3:=IntFFE(D[1][1]); z4:=IntFFE(D[1][2]); z5:=IntFFE(D[2][1]); z6:=IntFFE(D[2][2]); ind1:=P^3*z3+P^2*z4+P*z5+z6; if ind1 < index then new:=0; fi; if new = 0 then break; fi; od; if new = 0 then break; fi; od; if new = 1 then Add(mats,A); fi; od; od; od; od; for AS in mats do stab1:=[]; stab2:=[]; for b in [0..P-1] do for c in [0..P-1] do for m in [-1,1] do if b+c = 0 then continue; fi; B:=One(F)*MyCutVector([W*b,m*c,W*c,W*m*b], 2); C:=One(F)*MyCutVector([W*(W*b^2+c^2),m*2*W*b*c,2*W^2*b*c,m*W*(W*b^2+c^2)], 2); D:=B*AS*C^-1; if D[1][1] <> Zero(F) then D:=D[1][1]^-1*D; fi; if D[1][1] = Zero(F) and D[1][2] <> Zero(F) then D:=D[1][2]^-1*D; fi; if D[1][1] = Zero(F) and D[1][2] = Zero(F) and D[2][1] <> Zero(F) then D:=D[2][1]^-1*D; fi; if D[1][1]=Zero(F) and D[1][2]=Zero(F) and D[2][1]=Zero(F) and D[2][2]<>Zero(F) then D:=D[2][2]^-1*D; fi; if D = AS then Add(stab1,One(F)*MyCutVector([1,0,0,0,W*b,m*c,0,W*c,W*m*b], 3)); Add(stab2,C); fi; od; od; od; y3:=IntFFE(AS[1][1]); y4:=IntFFE(AS[1][2]); y5:=IntFFE(AS[2][1]); y6:=IntFFE(AS[2][2]); for y1 in [0..P-1] do for y2 in [0..P-1] do A:=One(F)*MyCutVector([y1,y2,y3,y4,y5,y6], 3); if A = 0*A then Add(params[22],[0,0,0,0,0,0]); continue; fi; new:=1; index:=P*y1+y2; for ii in [1..Length(stab1)] do B:=stab1[ii]; C:=stab2[ii]; D:=B*A*C^-1; z1:=IntFFE(D[1][1]); z2:=IntFFE(D[1][2]); ind1:=P*z1+z2; if ind1 < index then new:=0; fi; if new = 0 then break; fi; od; if new = 1 then Add(params[22],[y1,y2,y3,y4,y5,y6]); fi; od; od; od; if Length(params[22]) <> (2*P^3+3*P^2+3*P+13-Gcd(P-1,3)+(P+1)*Gcd(P-1,4))/2 then Error("params[22] wrong"); fi; if case = 22 then return params[22]; fi; fi; ## Case 23, cb=baa=0, caa=bac, cac=wbab if case = true or case = 23 then sol:=0; if P mod 3 = 2 then for x in [1..P-1] do if One(F)*(12*W*x^2+1) = Zero(F) then sol:=x; break; fi; od; fi; mats:=[]; for y5 in [0,1,lns] do for y6 in [0..P-1] do for y3 in [0..P-1] do for y4 in [0..P-1] do A:=One(F)*MyCutVector([y3,y4,y5,y6], 2); if A = 0*A then Add(mats,A); continue; fi; new:=1; index:=P^3*y5+P^2*y6+P*y3+y4; for a in [1..P-1] do for m in [-1,1] do B:=One(F)*MyCutVector([a,0,0,m*a], 2); C:=One(F)*MyCutVector([a^3,0,0,m*a^3], 2); D:=B*A*C^-1; z3:=IntFFE(D[1][1]); z4:=IntFFE(D[1][2]); z5:=IntFFE(D[2][1]); z6:=IntFFE(D[2][2]); ind1:=P^3*z5+P^2*z6+P*z3+z4; if ind1 < index then new:=0; fi; if P mod 3 = 2 and new = 1 then for b in [sol,-sol] do B:=One(F)*MyCutVector([-2*W*a*b,a,m*W*a,-2*m*W*a*b], 2); C:=One(F)*MyCutVector([8/3*W^2*a^3*b,4/3*W*a^3,4/3*m*W^2*a^3,8/3*m*W^2*a^3*b], 2) D:=B*A*C^-1; z3:=IntFFE(D[1][1]); z4:=IntFFE(D[1][2]); z5:=IntFFE(D[2][1]); z6:=IntFFE(D[2][2]); ind1:=P^3*z5+P^2*z6+P*z3+z4; if ind1 < index then new:=0; fi; if new = 0 then break; fi; od; fi; if new = 0 then break; fi; od; if new = 0 then break; fi; od; if new = 1 then Add(mats,A); fi; od; od; od; od; for AS in mats do stab1:=[]; stab2:=[]; for a in [1..P-1] do for m in [-1,1] do B:=One(F)*MyCutVector([a,0,0,m*a], 2); C:=One(F)*MyCutVector([a^3,0,0,m*a^3], 2); D:=B*AS*C^-1; if D = AS then Add(stab1,One(F)*MyCutVector([a,0,0,0,a,0,0,0,m*a], 3)); Add(stab2,C); fi; if P mod 3 = 2 then for b in [sol,-sol] do B:=One(F)*MyCutVector([-2*W*a*b,a,m*W*a,-2*m*W*a*b], 2); C:=One(F)*MyCutVector([8/3*W^2*a^3*b,4/3*W*a^3,4/3*m*W^2*a^3,8/3*m*W^2*a^3*b], 2) D:=B*AS*C^-1; if D = AS then Add(stab1, One(F)*MyCutVector([4*W*a*b,-3*W*a*b,a/2,0,-2*W*a*b,a,0,m*W*a,-2*m*W*a*b], 3)); Add(stab2,C); fi; od; fi; od; od; y3:=IntFFE(AS[1][1]); y4:=IntFFE(AS[1][2]); y5:=IntFFE(AS[2][1]); y6:=IntFFE(AS[2][2]); for y1 in [0..P-1] do for y2 in [0..P-1] do A:=One(F) * MyCutVector([y1,y2,y3,y4,y5,y6], 3); if A = 0*A then Add(params[23],[0,0,0,0,0,0]); continue; fi; new:=1; index:=P*y1+y2; for ii in [1..Length(stab1)] do B:=stab1[ii]; C:=stab2[ii]; D:=B*A*C^-1; z1:=IntFFE(D[1][1]); z2:=IntFFE(D[1][2]); ind1:=P*z1+z2; if ind1 < index then new:=0; fi; if new = 0 then break; fi; od; if new = 1 then Add(params[23],[y1,y2,y3,y4,y5,y6]); fi; od; od; od; if P mod 3 = 1 then expect:=P^5+P^4+P^3+P^2+P+2+(P^2+P+1)*Gcd(P-1,4)/2; else expect:=P^5/3+P^4/3+P^3/3+P^2/3+P+2+(P^2+P+1)*Gcd(P-1,4)/2; fi; if Length(params[23]) <> expect then Error("params[23] wrong"); fi; if case = 23 then return params[23]; fi; fi; ## Case 24, cb=baa=0, caa=xbab+bac, cac=wbab ## where x is not a value of y(y^2+3w)/(3y^2+w) if case = true or case = 24 then if P mod 3 = 2 then val:=[]; for x in [0..P-1] do if One(F)*(3*x^2+W) <> Zero(F) then a:=One(F)*(x*(x^2+3*W))*(One(F)*(3*x^2+W))^-1; AddSet(val,IntFFE(a)); fi; od; for a in [1..P-1] do if not a in val then s:=a; break; fi; od; for y in [1..P-1] do if One(F)*(W*y^2+3) = Zero(F) then b:=y; break; fi; od; B1:=One(F)*MyCutVector([2,2*b,2*W*b,2], 2); C1:=One(F)*MyCutVector([32,-32*b,-32*W*b,32], 2); B2:=One(F)*MyCutVector([2,-2*b,-2*W*b,2], 2); C2:=One(F)*MyCutVector([32,32*b,32*W*b,32], 2); BB1:=One(F)*MyCutVector([-4,s*b+3,3*s*W^-1+b,0,2,2*b,0,2*W*b,2], 3); BB2:=One(F)*MyCutVector([-4,-s*b+3,3*s*W^-1-b,0,2,-2*b,0,-2*W*b,2], 3); mats:=[]; for y5 in [0,1,lns] do for y6 in [0..P-1] do for y3 in [0..P-1] do for y4 in [0..P-1] do A:=One(F)*MyCutVector([y3,y4,y5,y6], 2); if A = 0*A then Add(mats,A); continue; fi; new:=true; index:=P^3*y5+P^2*y6+P*y3+y4; A1:=B1*A*C1^-1; A2:=B2*A*C2^-1; for a in [1..(P-1)/2] do D:=(One(F)*a)^-2*A; z3:=IntFFE(D[1][1]); z4:=IntFFE(D[1][2]); z5:=IntFFE(D[2][1]); z6:=IntFFE(D[2][2]); ind1:=P^3*z5+P^2*z6+P*z3+z4; if ind1 < index then new:=false; break; fi; D:=(One(F)*a)^-2*A1; z3:=IntFFE(D[1][1]); z4:=IntFFE(D[1][2]); z5:=IntFFE(D[2][1]); z6:=IntFFE(D[2][2]); ind1:=P^3*z5+P^2*z6+P*z3+z4; if ind1 < index then new:=false; break; fi; D:=(One(F)*a)^-2*A2; z3:=IntFFE(D[1][1]); z4:=IntFFE(D[1][2]); z5:=IntFFE(D[2][1]); z6:=IntFFE(D[2][2]); ind1:=P^3*z5+P^2*z6+P*z3+z4; if ind1 < index then new:=false; break; fi; od; if new then Add(mats,A); fi; od; od; od; od; for AS in mats do stab1:=[]; stab2:=[]; AS1:=B1*AS*C1^-1; AS2:=B2*AS*C2^-1; for a in [1..(P-1)/2] do D:=(One(F)*a)^-2*AS; if D = AS then Add(stab1,One(F)*MyCutVector([1,0,0,0,1,0,0,0,1], 3)); Add(stab2,One(F)*MyCutVector([a^2,0,0,a^2], 2)); fi; D:=(One(F)*a)^-2*AS1; if D = AS then Add(stab1,BB1); Add(stab2,a^2*C1); fi; D:=(One(F)*a)^-2*AS2; if D = AS then Add(stab1,BB2); Add(stab2,a^2*C2); fi; od; y3:=IntFFE(AS[1][1]); y4:=IntFFE(AS[1][2]); y5:=IntFFE(AS[2][1]); y6:=IntFFE(AS[2][2]); for y1 in [0..P-1] do for y2 in [0..P-1] do A:=One(F)*MyCutVector([y1,y2,y3,y4,y5,y6], 3); if A = 0*A then Add(params[24],[0,0,0,0,0,0,s]); continue; fi; new:=1; index:=P*y1+y2; for ii in [1..Length(stab1)] do B:=stab1[ii]; C:=stab2[ii]; D:=B*A*C^-1; z1:=IntFFE(D[1][1]); z2:=IntFFE(D[1][2]); ind1:=P*z1+z2; if ind1 < index then new:=0; fi; if new = 0 then break; fi; od; if new = 1 then Add(params[24],[y1,y2,y3,y4,y5,y6,s]); fi; od; od; od; if Length(params[24]) <> 2*(P^5+P^4+P^3+P^2)/3+2*P+3 then Error("params[24] wrong"); fi; fi; if case = 24 then return params[24]; fi; fi; if Sum(List(params, Length))<> 2*P^5+7*P^4+19*P^3+49*P^2+128*P+256 +(P^2+7*P+29)*Gcd(P-1,3)+ (P^2+7*P+24)*Gcd(P-1,4)+(P+3)*Gcd(P-1,5) then Error("sum is wrong"); fi; for i in [1..Length(params)] do if not Length(params[i]) = Length(Set(params[i])) then Error("params ",i," has duplicates"); fi; if not IsSubset( [0..P-1], Set(Flat(params[i]))) then Error("params ",i," is out of range"); fi; od; return params; end ); BindGlobal( "ValsFunction28", function(P, case) local vals, i; vals := ValsPreFunction28(P, case); if IsInt(case) and case < 24 then return List(vals, x -> [x[4], x[5], x[6], x[1], x[2], x[3]]); elif IsInt(case) and case = 24 then return List(vals, x -> [x[4], x[5], x[6], x[1], x[7], x[2], x[3]]); else for i in [1..23] do vals[i] := List(vals[i], x->[x[4],x[5],x[6],x[1],x[2],x[3]]); od; vals[24] := List(vals[24], x->[x[4],x[5],x[6],x[1],x[7],x[2],x[3]]); return vals; fi; end ); [ Verzeichnis aufwärts0.72unsichere Verbindung Übersetzung europäischer Sprachen durch Browser ] |
2026-04-02