> # This program computes cohomological dimensions
> # of Z_p [T, T^{-1}] / (h(T)) where deg(h(T))=2,
> # with the coefficients A=Z_q, q=2,3,5,7,11.
> 
> restart:
> with(linalg):
Warning, new definition for norm
Warning, new definition for trace
> # The initial data are specified here (p and h(T)).
>  
>  assign(p=2): #mod p LX
>  Rel0:=T^2+T+1: #order ideal
>  Rel1:=T^2=-T-1: # ideal solved for T^2
>  Rel2:=T^(-1)=-T-1: #inverse rel from Rel1
>  
>  # Quandle operation:
>  g:=proc(a,b)
>  algsubs(Rel1, expand(T*a+(1-T)*b))mod p: end:
>  
> # The following converts integers to quandle elements:
> f:=array[0..p^2-1]:
>    for jj from 0 to p^2-1 do
>    jj1:=iquo(jj,p):
>    jj2:=irem(jj,p):
>    f[jj]:=jj2+jj1*T:
>    od:
> 
>  # List of prime numbers for q:
>  PRIME:=[2,3,5,7,11]:
>  for qq from 1 to 5 do
>  q:=op(qq,PRIME):
>  
>  # Making a matrix of 3-cocycle condition:
>  A:=array(sparse,1..(p^8+2*p^4),1..p^6):
>  
>  ind:=0:
>  
>  for x from 0 to p^2-1 do
>  for y from 0 to p^2-1 do
>  for z from 0 to p^2-1 do
>  for s from 0 to p^2-1 do
>  
>  xstry:=coeff(g(f[x],f[y]),T,0)+coeff(g(f[x],f[y]),T,1)*p:
>  xstrz:=coeff(g(f[x],f[z]),T,0)+coeff(g(f[x],f[z]),T,1)*p:
>  xstrs:=coeff(g(f[x],f[s]),T,0)+coeff(g(f[x],f[s]),T,1)*p:
>  ystrz:=coeff(g(f[y],f[z]),T,0)+coeff(g(f[y],f[z]),T,1)*p:
>  ystrs:=coeff(g(f[y],f[s]),T,0)+coeff(g(f[y],f[s]),T,1)*p:
>  zstrs:=coeff(g(f[z],f[s]),T,0)+coeff(g(f[z],f[s]),T,1)*p:
>  
>  #print(xstry,xstrz,xstrs,ystrz,ystrs,zstrs);
>  
>  ind:=ind+1:
>  if abs(x-y)>0 then
>  if abs(y-z)>0 then
>   A[ind,x*p^4 + y*p^2 + z +1]:= 
>   (1+A[ind,x*p^4 +  y*p^2 + z +1]) mod q:
>  fi:
>  fi:
>  
>  if abs(x-z) > 0 then
>  if abs(z-s) > 0 then
>   A[ind,x*p^4 + z*p^2 +s+1] := 
> (1 + A[ind,x*p^4 + z*p^2 +s+1]) mod q:
>  fi: 
>  fi:
>  
>  if abs(xstrz-ystrz) >0 then
>  if abs(ystrz-s) >0 then
>   A[ind,xstrz*p^4 + ystrz*p^2 +s+1]:= 
> (1+ A[ind,xstrz*p^4 + ystrz*p^2+s+1]) mod q:
>  fi:
>  fi:
>  
>  if abs(xstry-z) >0 then
>  if abs(z-s) >0 then
>    A[ind,xstry*p^4 + z* p^2 + s+1]:=
>  (-1+A[ind,xstry*p^4 + z* p^2 + s+1]) mod q:
>  fi:
>  fi:
>  
>  if abs(x-y) >0 then
>  if abs(y-s) >0 then
>   A[ind,x*p^4+y*p^2+s+1]:=
>   (-1+A[ind,x*p^4+y*p^2+s+1]) mod q:
>  fi:
>  fi:
>  
>  if abs(xstrs-ystrs) > 0 then
>  if abs(ystrs-zstrs) > 0 then
> 
> A[ind,xstrs*p^4+ystrs*p^2+zstrs+1]:=
> (-1+A[ind,xstrs*p^4+ystrs*p^2+zstrs+1]) mod q:
>  fi:
>  fi:
>  od: od: od: od:
>  
>  for w1 from 0 to p^2-1 do
>  for w2 from 0 to p^2-1 do
>  A[p^6 + w1*p^2 +w2 +1, w1*p^4 + w1*p^2 +w2 +1]:=1:
>  A[p^6 + p^4+w1*p^2+w2+1,w1*p^4+w2*p^2+w2+1]:=1:
>  od:
>  od:
>  
>  #print(A);
> 
>  # End of definition os a matrix of 3-cocycle condition.
>  # Now we solve the equation of 3-cocycle conditions:
> 
>  Sol:=Linsolve(A,vector(p^8+2*p^4,0),'rank',c) mod q;
>  
>  # Next we define a matrix of coboundary conditions.
>  AA:=array(sparse,1..p^4,1..p^6):
>  
>  for xx from 0 to p^2-1 do
>  for yy from 0 to p^2-1 do
>  for zz from 0 to p^2-1 do
>  
>  
>  xxstryy:=coeff(g(f[xx],f[yy]),T,0)
> +coeff(g(f[xx],f[yy]),T,1)*p:
>  xxstrzz:=coeff(g(f[xx],f[zz]),T,0)
> +coeff(g(f[xx],f[zz]),T,1)*p:
>  yystrzz:=coeff(g(f[yy],f[zz]),T,0)
> +coeff(g(f[yy],f[zz]),T,1)*p:
>  
>  if abs(xx-yy) > 0 then
>  if abs(yy-zz) > 0 then
>  if xx <> zz then
>  AA[xx*p^2+zz+1, xx*p^4 +yy*p^2 +zz +1]:=(AA[xx*p^2+zz+1, xx*p^4
> +yy*p^2
> +zz +1]+ 1) mod q:
>  fi:
>  if xx <> yy then
>  AA[xx*p^2+yy+1, xx*p^4 +yy*p^2 +zz +1]:=
>  (AA[xx*p^2+yy+1, xx*p^4 +yy*p^2+zz +1]-1) mod q:
>  fi:
>  if xxstrzz <> yystrzz then
>  AA[xxstrzz*p^2+yystrzz+1, xx*p^4 +yy*p^2 +zz +1]:=
> (AA[xxstrzz*p^2+yystrzz+1, xx*p^4 +yy*p^2 +zz +1]+1) mod q:
>  fi:
>  if xxstryy <> zz then
>  AA[xxstryy*p^2+zz+1, xx*p^4 +yy*p^2 +zz +1]:= (AA[xxstryy*p^2+zz+1,
> xx*p^4 +yy*p^2 +zz +1]-1) mod q:
>  fi:
>  fi:fi:
>  
>  od: od: od:
>  
>  
>  #print(wer,AA);
> 
>  # end of coboundary matrix, now solve it:
>  cobsol:=Linsolve(AA,vector(p^4,0),'rrank',cob) mod q;
>  
>  # Computing the cohomological dimensions: 
>  CHdim:=(p^6 - rank) - rrank:
>  print(q, CHdim, p^6-rank, rrank);
>  
>  od:
>  
> 

                             2, 3, 11, 8


                              3, 0, 9, 9


                              5, 0, 9, 9


                              7, 0, 9, 9


                             11, 0, 9, 9


                             13, 0, 9, 9


                             17, 0, 9, 9


                             19, 0, 9, 9