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galois1.m2
-- test galois substitution A = ZZ/5[c]/(c^2+c+1) assert( baseName c === symbol c ) k = GF(A,PrimitiveElement => - c - 2) assert( class c === k ) assert( baseName c === symbol c ) e = 16 assert( k.PrimitiveElement^e == c ) -- three cases: -- 1. both rings are k-algebras, and we don't specify where c goes p = map(k,k) assert(p c == c) R = k[x..z] p = map(R,R) assert( p (c*x-3) == (c*x-3) ) p = map(R,R,{z,y,x}) assert( p (c*x-3) == (c*z-3) ) -- 2. both rings are k-algebras, but we specify where c goes p = map(k,k,{c}) assert(p c == c) p = map(R,R,{x,y,z,c}) assert( p (c*x-3) == (c*x-3) ) p = map(R,R,{z,y,x,c}) assert( p (c*x-3) == (c*z-3) ) -- 3. target is not c k-algebra, but it has a generator of the same name S = ZZ[c] p = map(S,k) -- 4. target is not a k-algebra, and it has no generator of the same name S = ZZ[a] p = map(S,k) use k p c --assert(p c == (-2_S)^e ) -- this behavior has changed (15 June 2014): assert(p c == 0) -- 5. target is not a k-algebra, but we specify where c goes S = ZZ[t] p = map(S,k,{t}) --assert( p c == (-t-2)^e ) -- this behavior has changed (15 June 2014): assert(p c == t) S = ZZ[t,q,r] p = map(S,R,{q*r,q^2,r^2,t}) --assert( p (c*x) == (-t-2)^e * q*r ) -- this behavior has changed (15 June 2014): assert( p (c*x) == t*q*r) -- # Local Variables: -- # compile-command: "make -k -C $M2BUILDDIR/Macaulay2/packages/Macaulay2Doc/test galois1.out " -- # End: