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galois.m2
-- warm up first: k=ZZ/5 R1=k[s,t] R2=k[x,y,z,w] f = map(R1,R2,{s^4,s^3*t-t^2*s^2,s*t^3,t^4}) ker f isHomogeneous f isHomogeneous ker f assert(f (ker f) == 0) P0 = projectiveHilbertPolynomial 0 P1 = projectiveHilbertPolynomial 1 assert ( hilbertPolynomial coker gens ker f == 4 * P1 - 3 * P0 ) -- now over a Galois field k=GF(5,2,Variable=>a) R1=k[s,t] R2 = k[x,y,z,w] assert( substitute(a*x-1,{x=>a}) == a^2 - 1 ) f = map(R1,R2,{s^4,s^3*t-a*t^2*s^2,s*t^3,t^4},DegreeMap => v -> 4*v) ker f assert(f (ker f) == 0) P0 = hilbertPolynomial (R2/(x,y,z)) P1 = hilbertPolynomial (R2/(x,y)) assert ( hilbertPolynomial coker gens ker f == 4 * P1 - 3 * P0 ) -- some other stuff k = GF(2,3,Variable=>x) k = GF(2,3,Variable=>x) k = GF(2,3,Variable=>x) x+x^2 k = GF(2,3,Variable=>a) assert( length degree id_(k^1) == 0 ) end -- Local Variables: -- compile-command: "make -C $M2BUILDDIR/Macaulay2/packages/Macaulay2Doc/test galois.out" -- End: