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prune.m2
R = ZZ/101[x,y] phi = (minimalPresentation ker matrix{{x^2+1, x, y}}).cache.pruningMap isIsomorphism phi phi^-1 -- fails assert( phi * phi^-1 == 1 ) assert( phi^-1 * phi == 1 ) assert isWellDefined phi^-1 assert isWellDefined phi ----------------------------------------------------------------------------- kk=ZZ/101 R=kk[a,b,c,SkewCommutative=>true] m=map(R^{-1,0},R^{-2,-1},matrix{{a,0},{b*c,a}}) betti m F=res(coker m, LengthLimit=>5) betti F assert( prune coker F.dd_2 == prune image F.dd_1 ) -- and now 'prune' for coherent sheaves S = QQ[x] X = Proj S n = ideal vars S F = OO_X(8) degrees F F' = prune F degrees F' assert( first first degrees F' <= 0 ) -- too much, but that's okay F = OO_X(-8) degrees F F' = prune F degrees F' assert( module F' == S^{0} ) -- on the nose, okay ----------------------------------------------------------------------------- S = QQ[x..z] X = Proj S n = ideal vars S F = S^{8} M = n^3 * F M' = module prune sheaf_X M degrees M' assert ( M' == F ) ----------------------------------------------------------------------------- -- a conceptual problem with the design: R = QQ[x] M = coker matrix {{x,x}} N = prune M assert( target N.cache.pruningMap === M ) P = prune N -- N is already pruned! assert( target P.cache.pruningMap === N ) -- prune PID R=QQ[x] M = module ideal(3*x^4-x^3+x^2-x-2,3*x^4+2*x^3+6*x+4) N = prune M assert(isFreeModule N) assert(rank N == 1) ----------------------------------------------------------------------------- end -- Local Variables: -- compile-command: "make -C $M2BUILDDIR/Macaulay2/packages/Macaulay2Doc/test prune.out" -- End: