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debug Core flagInhomogeneity = true errorDepth = 0 degs = {{-2, -3}, {-2, -4}, {-2, -5}, {0, 1}, {0, 1}, {0, 1}} degmat = transpose matrix degs adjmat = matrix {{-3,1}, {1,0}} a1 = adjmat * degmat adjust = x -> first entries transpose (adjmat * transpose matrix {x}) newdegs = apply ( degs, adjust ) assert ( a1 == transpose matrix newdegs ) repmat = adjmat^-1 repair = x -> first entries transpose (repmat * transpose matrix {x}) assert ( degs == apply( newdegs, repair )) heft0 = {-3, 1} degs1 = {{0, 0}, {0, 0}, {0, 0}, {1, 2}, {1, 3}, {1, 3}, {1, 3}, {1, 3}, {1, 4}, {1, 4}, {1, 4}, {1, 5}, {1, 5}, {1, 5}, {2, 5}, {2, 6}, {2, 6}, {2, 7}, {2, 7}, {2, 7}, {2, 7}, {2, 7}, {2, 7}, {2, 7}, {2, 7}, {2, 7}, {2, 8}, {2, 8}, {2, 8}, {3, 9}, {3, 9}, {3, 9}, {3, 9}, {3, 9}, {3, 9}, {3, 9}}; degs2 = {{0, -2}, {0, -3}, {0, -3}, {0, -4}, {0, -5}, {0, -2}, {0, -3}, {0, -3}, {0, -4}, {0, -5}, {0, -2}, {0, -3}, {0, -3}, {0, -4}, {0, -5}, {1, 0}, {1, -1}, {1, -1}, {1, -2}, {1, -3}, {1, 1}, {1, 0}, {1, 0}, {1, -1}, {1, -2}, {1, 1}, {1, 0}, {1, 0}, {1, -1}, {1, -2}, {1, 1}, {1, 0}, {1, 0}, {1, -1}, {1, -2}, {1, 1}, {1, 0}, {1, 0}, {1, -1}, {1, -2}, {1, 2}, {1, 1}, {1, 1}, {1, 0}, {1, -1}, {1, 2}, {1, 1}, {1, 1}, {1, 0}, {1, -1}, {1, 2}, {1, 1}, {1, 1}, {1, 0}, {1, -1}, {1, 3}, {1, 2}, {1, 2}, {1, 1}, {1, 0}, {1, 3}, {1, 2}, {1, 2}, {1, 1}, {1, 0}, {1, 3}, {1, 2}, {1, 2}, {1, 1}, {1, 0}, {2, 3}, {2, 2}, {2, 2}, {2, 1}, {2, 0}, {2, 4}, {2, 3}, {2, 3}, {2, 2}, {2, 1}, {2, 4}, {2, 3}, {2, 3}, {2, 2}, {2, 1}, {2, 5}, {2, 4}, {2, 4}, {2, 3}, {2, 2}, {2, 5}, {2, 4}, {2, 4}, {2, 3}, {2, 2}, {2, 5}, {2, 4}, {2, 4}, {2, 3}, {2, 2}, {2, 5}, {2, 4}, {2, 4}, {2, 3}, {2, 2}, {2, 5}, {2, 4}, {2, 4}, {2, 3}, {2, 2}, {2, 5}, {2, 4}, {2, 4}, {2, 3}, {2, 2}, {2, 5}, {2, 4}, {2, 4}, {2, 3}, {2, 2}, {2, 5}, {2, 4}, {2, 4}, {2, 3}, {2, 2}, {2, 5}, {2, 4}, {2, 4}, {2, 3}, {2, 2}, {2, 6}, {2, 5}, {2, 5}, {2, 4}, {2, 3}, {2, 6}, {2, 5}, {2, 5}, {2, 4}, {2, 3}, {2, 6}, {2, 5}, {2, 5}, {2, 4}, {2, 3}, {3, 7}, {3, 6}, {3, 6}, {3, 5}, {3, 4}, {3, 7}, {3, 6}, {3, 6}, {3, 5}, {3, 4}, {3, 7}, {3, 6}, {3, 6}, {3, 5}, {3, 4}, {3, 7}, {3, 6}, {3, 6}, {3, 5}, {3, 4}, {3, 7}, {3, 6}, {3, 6}, {3, 5}, {3, 4}, {3, 7}, {3, 6}, {3, 6}, {3, 5}, {3, 4}, {3, 7}, {3, 6}, {3, 6}, {3, 5}, {3, 4}}; degDB = {-1, 0} degs' = apply(degs, adjust) heft' = {1, 0} degs1' = apply(degs1, adjust); degs2' = apply(degs2, adjust); degDB' = adjust degDB comp = (degs,heft0,degs1,degs2,degDB) -> ( R = ZZ/103[X_1..X_3 , x..z, Degrees => degs, Heft => heft0]; F1 = R^degs1; F2 = R^degs2; M = cokernel map( F1, F2, {{x^2+z^2, y^3-2*z^3, x^3, y^4, z^5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, x^2+z^2, y^3-2*z^3, x^3, y^4, z^5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x^2+z^2, y^3-2*z^3, x^3, y^4, z^5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x^2+z^2, y^3-2*z^3, x^3, y^4, z^5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x^2+z^2, y^3-2*z^3, x^3, y^4, z^5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x^2+z^2, y^3-2*z^3, x^3, y^4, z^5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x^2+z^2, y^3-2*z^3, x^3, y^4, z^5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x^2+z^2, y^3-2*z^3, x^3, y^4, z^5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x^2+z^2, y^3-2*z^3, x^3, y^4, z^5, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x^2+z^2, y^3-2*z^3, x^3, y^4, z^5}}); DB = map(M,M, {{0, 0, 0, -42*X_1*y, -X_1, 0, 0, -4*X_1, -X_2, 0, 0, -X_3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, -26*X_1, -X_1, 0, 0, 0, -X_2, 0, 0, -X_3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, -X_1*x, 0, -5*X_1, 0, 0, 0, 0, -X_2, 0, 0, -X_3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {-46*z^2, 6*z^2, -x*y-z^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5*X_2*y-X_1, 14*X_2, 15*X_2, 0, 0, 0, 0, 0, 0, 0, -5*X_3, X_3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 42*y*z^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28*X_3*x*y^2+35*X_3*x*y*z+42*X_3*y^2*z-51*X_3*y*z^2-18*X_3*z^3+45*X_2*y^2-46*X_2*y*z+41*X_2*z^2-42*X_1*x, 47*X_3*x*y-14*X_3*y^2+48*X_3*x*z-33*X_3*y*z-25*X_3*z^2-34*X_2*y-20*X_2*z, -42*X_3*x*y-37*X_3*y^2+36*X_3*x*z+47*X_3*y*z+44*X_3*z^2+2*X_2*x-43*X_2*y-21*X_2*z, 2*X_3*x-2*X_3*y-45*X_3*z-26*X_2, 28*X_3*x-3*X_3*y-40*X_3*z-41*X_2, 49*X_3*x-6*X_3*y-13*X_3*z-46*X_2, -9*X_3*y-40*X_3*z-19*X_2, 4*X_3*x+3*X_3*y+34*X_3*z-31*X_2, 19*X_3*x+16*X_3*y-50*X_3*z-15*X_2, 9*X_3*x-49*X_3*y-21*X_3*z-19*X_2, 42*X_3*y+44*X_3*z, 14*X_3*y+19*X_3*z, 4*X_3, 23*X_3, -38*X_3, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 41*y*z^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14*X_3*x*y^2-34*X_3*x*y*z+7*X_3*y^2*z+49*X_3*y*z^2-17*X_3*z^3-21*X_2*y^2+47*X_2*y*z-20*X_2*z^2-41*X_1*x, -28*X_3*x*y-15*X_3*y^2+24*X_3*x*z-X_3*y*z+27*X_3*z^2+20*X_2*y+32*X_2*z, 19*X_3*x*y-47*X_3*y^2+2*X_3*x*z+17*X_3*y*z-27*X_3*z^2-6*X_2*x-8*X_2*y-8*X_2*z, -42*X_3*x+42*X_3*y+13*X_3*z-45*X_2, 14*X_3*x-24*X_3*y-X_3*z+20*X_2, -27*X_3*x-46*X_3*y+50*X_3*z-38*X_2, -4*X_3*y-38*X_3*z-21*X_2, -23*X_3*x+40*X_3*y-38*X_3*z-18*X_2, 8*X_3*x-27*X_3*y-46*X_3*z-22*X_2, 4*X_3*x-X_3*y-42*X_3*z-21*X_2, X_3*x+44*X_3*y-38*X_3*z, -4*X_3*y+16*X_3*z, -43*X_3, 46*X_3, -26*X_3, 0, 0, 0, 0, 0, 0, 0}, {39*y*z^2+50*z^3, 17*x*y^2-40*y*z^2+13*z^3, -25*x*y^2-34*z^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 38*X_3*x*y^2+4*X_3*x*y*z+36*X_3*y^2*z+30*X_3*y*z^2+20*X_3*z^3-40*X_2*y^2+50*X_2*y*z-40*X_2*z^2+35*X_1*y, -27*X_3*x*y-50*X_3*y^2-21*X_3*x*z+22*X_3*y*z-19*X_3*z^2+23*X_2*y-5*X_2*z+35*X_1, -10*X_3*x*y+15*X_3*y^2-51*X_3*x*z-37*X_3*y*z-4*X_3*z^2-12*X_2*x+38*X_2*y-27*X_2*z-19*X_1, -37*X_3*x+37*X_3*y-20*X_3*z-40*X_2, -38*X_3*x+47*X_3*y-11*X_3*z+40*X_2, -15*X_3*x+6*X_3*y-41*X_3*z-33*X_2, -17*X_3*y-14*X_3*z, 45*X_3*x-4*X_3*y+20*X_3*z+23*X_2, -35*X_3*x+13*X_3*y+48*X_3*z-43*X_2, 17*X_3*x+31*X_3*y+25*X_3*z-19*X_2, 41*X_3*y-33*X_3*z, -50*X_3*y-50*X_3*z, -7*X_3, 26*X_3, -18*X_3, 0, 0, 0, 0, 0, 0, 0}, {-32*y*z^2, 40*y*z^2, -41*x*y^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -38*X_3*x*y^2-4*X_3*x*y*z+27*X_3*y^2*z-42*X_3*y*z^2-29*X_3*z^3-45*X_2*y^2-21*X_2*y*z-45*X_2*z^2-41*X_1*x-41*X_1*y, 27*X_3*x*y+8*X_3*y^2+21*X_3*x*z-41*X_3*y*z+36*X_3*z^2+13*X_2*y+33*X_2*z, 14*X_3*x*y-23*X_3*y^2+44*X_3*x*z-9*X_3*y*z+43*X_3*z^2+38*X_2*x+17*X_2*y+34*X_2*z, 43*X_3*x-43*X_3*y+15*X_3*z-45*X_2, 38*X_3*x+36*X_3*y-43*X_3*z+45*X_2, 15*X_3*x-12*X_3*y-29*X_3*z-50*X_2, 33*X_3*y-34*X_3*z, -4*X_3*x+13*X_3*y+46*X_3*z+13*X_2, -51*X_3*x+35*X_3*y+49*X_3*z+46*X_2, -33*X_3*x+28*X_3*y+7*X_3*z-21*X_2, 19*X_3*y-10*X_3*z, 7*X_3*y+25*X_3*z, 12*X_3, -42*X_3, 7*X_3, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36*X_3*x*y^2*z+51*X_3*y^2*z^2+36*X_1*y^2+27*X_1*y*z+36*X_1*z^2, 32*X_3*x*y^2-37*X_3*x*y*z+31*X_3*y^2*z+36*X_3*y*z^2-X_3*z^3+12*X_1*y-9*X_1*z, 39*X_3*x*y^2+46*X_3*x*y*z-15*X_3*y^2*z+35*X_3*y*z^2+3*X_3*z^3-51*X_1*x-37*X_1*y-12*X_1*z, -18*X_3*x*y+37*X_3*y^2+25*X_3*x*z-45*X_3*y*z+47*X_3*z^2, -25*X_3*x*y-19*X_3*y^2+22*X_3*x*z-26*X_3*y*z+49*X_3*z^2-36*X_1, -43*X_3*x*y+19*X_3*y^2+33*X_3*x*z+22*X_3*y*z-23*X_3*z^2+40*X_1, 51*X_3*x*y+18*X_3*y^2+3*X_3*x*z+23*X_3*y*z-42*X_3*z^2+19*X_1, X_3*x*y-4*X_3*y^2+49*X_3*x*z-30*X_3*y*z-11*X_3*z^2-21*X_1, -16*X_3*x*y+13*X_3*y^2-51*X_3*x*z+47*X_3*y*z-43*X_3*z^2+37*X_1, -16*X_3*x*y+31*X_3*y^2-15*X_3*x*z-21*X_3*y*z+16*X_3*z^2, -47*X_3*x*y-25*X_3*y^2-3*X_3*x*z-18*X_3*y*z+34*X_3*z^2, 10*X_3*x*y+11*X_3*y^2+50*X_3*x*z+51*X_3*y*z-45*X_3*z^2, -29*X_3*x+39*X_3*y+21*X_3*z, 36*X_3*x+42*X_3*y+11*X_3*z, 12*X_3*x-18*X_3*y+24*X_3*z, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -22*X_3*x*y^2*z+33*X_3*y^2*z^2-16*X_1*y^2+16*X_1*y*z-16*X_1*z^2, -35*X_3*x*y^2+10*X_3*x*y*z+27*X_3*y^2*z+31*X_3*y*z^2-15*X_3*z^3+40*X_1*y-27*X_1*z, -44*X_3*x*y^2+40*X_3*x*y*z+15*X_3*y^2*z+4*X_3*y*z^2+36*X_3*z^3-46*X_1*x-7*X_1*y+39*X_1*z, -36*X_3*x*y-45*X_3*y^2+34*X_3*x*z-33*X_3*y*z+31*X_3*z^2, -48*X_3*x*y+37*X_3*y^2-21*X_3*y*z+44*X_3*z^2+16*X_1, -19*X_3*x*y-10*X_3*y^2+6*X_3*x*z-4*X_3*y*z-39*X_3*z^2-2*X_1, X_3*x*y+21*X_3*y^2-34*X_3*x*z+49*X_3*y*z+48*X_3*z^2, -10*X_3*x*y+16*X_3*y^2+27*X_3*x*z-15*X_3*y*z+32*X_3*z^2, 51*X_3*x*y+51*X_3*y^2+21*X_3*x*z+X_3*y*z-20*X_3*z^2, 3*X_3*x*y-21*X_3*y^2-29*X_3*x*z-36*X_3*y*z-36*X_3*z^2, -34*X_3*x*y+13*X_3*y^2-47*X_3*x*z-2*X_3*y*z+49*X_3*z^2, -19*X_3*x*y-35*X_3*y^2+13*X_3*x*z-3*X_3*y*z+26*X_3*z^2, -27*X_3*x-41*X_3*y-32*X_3*z, 9*X_3*x+36*X_3*y-13*X_3*z, 42*X_3*x-31*X_3*y-27*X_3*z, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29*X_3*x*y^2*z+17*X_3*y^2*z^2+5*X_1*x*y+2*X_1*y^2-29*X_1*y*z-3*X_1*z^2, 12*X_3*x*y^2+11*X_3*x*y*z-25*X_3*y^2*z+17*X_3*y*z^2-39*X_3*z^3-14*X_1*x+3*X_1*y+46*X_1*z, 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24*X_3*z^3+6*X_2*x*y-8*X_2*x*z+29*X_2*y*z+40*X_2*z^2, -27*X_3*z^3-14*X_2*x*y-15*X_2*x*z-22*X_2*y*z-2*X_2*z^2}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 49*z^2, z^2, -x*y-z^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23*X_3*z^3+14*X_2*x*y+X_2*y^2-43*X_2*x*z-22*X_2*y*z+X_2*z^2+16*X_1*x, 9*X_3*z^3+34*X_2*x*y-29*X_2*y^2+10*X_2*x*z+47*X_2*y*z-5*X_2*z^2-43*X_1*x, 20*X_3*z^3+13*X_2*x*y+47*X_2*y^2-14*X_2*x*z-51*X_2*y*z+24*X_2*z^2-4*X_1*x, 31*X_3*z^3-28*X_2*x*y+38*X_2*y^2-47*X_2*x*z-42*X_2*y*z-19*X_2*z^2+35*X_1*x, -45*X_3*z^3+36*X_2*x*y+30*X_2*x*z+5*X_2*y*z+41*X_2*z^2+9*X_1*x, 17*X_3*z^3-43*X_2*x*y-9*X_2*x*z+22*X_2*y*z-X_2*z^2-24*X_1*x, -32*X_3*z^3+2*X_2*x*y+12*X_2*x*z+27*X_2*y*z-X_2*z^2+27*X_1*x}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4*x*y*z-33*y^2*z+46*y*z^2-38*z^3, -x*y*z-46*y^2*z+5*y*z^2+29*z^3, 27*x*y*z-27*y^2*z-22*y*z^2+30*z^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20*X_3*y^2*z^2-18*X_2*x*y*z+42*X_2*y^2*z-14*X_2*y*z^2+11*X_2*z^3+29*X_1*y^2-30*X_1*x*z-45*X_1*y*z+27*X_1*z^2, 5*X_3*y^2*z^2+9*X_2*x*y*z-14*X_2*y^2*z-4*X_2*y*z^2+47*X_2*z^3-12*X_1*x*y+33*X_1*y^2-43*X_1*x*z-39*X_1*y*z, 6*X_3*y^2*z^2-10*X_2*x*y*z-3*X_2*y^2*z-50*X_2*y*z^2+50*X_2*z^3+23*X_1*x*y+2*X_1*y^2-41*X_1*x*z-38*X_1*y*z-13*X_1*z^2, -20*X_3*y^2*z^2+14*X_2*x*y*z+3*X_2*y^2*z-21*X_2*y*z^2-35*X_2*z^3-25*X_1*x*y+28*X_1*y^2+35*X_1*x*z-7*X_1*y*z+5*X_1*z^2, 9*X_3*y^2*z^2-36*X_2*x*y*z+51*X_2*y^2*z-10*X_2*y*z^2+25*X_2*z^3-33*X_1*x*y+51*X_1*y^2+6*X_1*x*z+44*X_1*y*z-51*X_1*z^2, 37*X_3*y^2*z^2+12*X_2*x*y*z+14*X_2*y^2*z+41*X_2*y*z^2+49*X_2*z^3-2*X_1*x*y+42*X_1*y^2+38*X_1*x*z-15*X_1*y*z-5*X_1*z^2, -33*X_3*y^2*z^2+42*X_2*x*y*z+36*X_2*y^2*z-13*X_2*y*z^2-49*X_2*z^3-28*X_1*x*y+10*X_1*y^2+37*X_1*x*z-21*X_1*y*z-51*X_1*z^2}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24*x*y*z-51*y*z^2+13*z^3, 19*x*y*z-47*y^2*z+8*y*z^2+25*z^3, -10*x*y*z-23*y*z^2-20*z^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12*X_3*y^2*z^2+42*X_2*x*y*z-31*X_2*y^2*z-29*X_2*y*z^2+33*X_2*z^3+36*X_1*y^2-42*X_1*x*z+44*X_1*y*z-22*X_1*z^2, -37*X_3*y^2*z^2+23*X_2*x*y*z-49*X_2*y^2*z+23*X_2*y*z^2-31*X_2*z^3-9*X_1*x*y+9*X_1*y^2+11*X_1*x*z-18*X_1*y*z-19*X_1*z^2, 31*X_3*y^2*z^2-48*X_2*x*y*z-50*X_2*y^2*z+45*X_2*y*z^2+43*X_2*z^3+19*X_1*x*y+38*X_1*y^2+2*X_1*x*z-38*X_1*y*z-49*X_1*z^2, -8*X_3*y^2*z^2+34*X_2*x*y*z-39*X_2*y^2*z+10*X_2*y*z^2-49*X_1*x*y+17*X_1*y^2-20*X_1*x*z+46*X_1*y*z-31*X_1*z^2, 28*X_3*y^2*z^2-18*X_2*x*y*z+21*X_2*y^2*z+3*X_2*y*z^2-31*X_2*z^3-9*X_1*x*y+42*X_1*y^2-10*X_1*x*z-40*X_1*y*z-40*X_1*z^2, 8*X_3*y^2*z^2-39*X_2*x*y*z-13*X_2*y^2*z+47*X_2*y*z^2-9*X_2*z^3-38*X_1*x*y-26*X_1*y^2+16*X_1*x*z-15*X_1*y*z+43*X_1*z^2, X_3*y^2*z^2-44*X_2*x*y*z-17*X_2*y^2*z+14*X_2*y*z^2+37*X_2*z^3-17*X_1*x*y-16*X_1*y^2-43*X_1*x*z+25*X_1*y*z-10*X_1*z^2}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 36*y^2*z^2, 0, 4*x*y*z+6*y^2*z-3*y*z^2+43*z^3, -2*x*y*z-37*y^2*z+10*y*z^2-34*z^3, 47*x*y*z+33*y^2*z-18*y*z^2-16*z^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -41*X_3*y^2*z^2-5*X_2*x*y*z+25*X_2*y^2*z-37*X_2*y*z^2+43*X_2*z^3+X_1*x*y+16*X_1*y^2-5*X_1*x*z+12*X_1*y*z-3*X_1*z^2, -17*X_3*y^2*z^2+11*X_2*x*y*z+20*X_2*y^2*z+4*X_2*y*z^2-4*X_2*z^3-21*X_1*x*y-43*X_1*y^2+25*X_1*x*z+9*X_1*y*z+34*X_1*z^2, -13*X_3*y^2*z^2+30*X_2*x*y*z+26*X_2*y^2*z+33*X_2*y*z^2-16*X_2*z^3-37*X_1*x*y-4*X_1*y^2+21*X_1*x*z-19*X_1*y*z+23*X_1*z^2, 46*X_3*y^2*z^2-3*X_2*x*y*z-35*X_2*y^2*z-20*X_2*y*z^2-3*X_2*z^3-15*X_1*x*y+35*X_1*y^2-28*X_1*x*z+27*X_1*y*z+42*X_1*z^2, -45*X_3*y^2*z^2-18*X_2*x*y*z+10*X_2*y^2*z+34*X_2*y*z^2+43*X_1*x*y+9*X_1*y^2-39*X_1*x*z+24*X_1*y*z+49*X_1*z^2, 7*X_3*y^2*z^2-46*X_2*x*y*z-39*X_2*y^2*z-37*X_2*y*z^2+35*X_2*z^3+4*X_1*x*y-24*X_1*y^2-48*X_1*x*z-10*X_1*y*z-3*X_1*z^2, -15*X_3*y^2*z^2+26*X_2*x*y*z-11*X_2*y^2*z-16*X_2*y*z^2+50*X_2*z^3-35*X_1*x*y+27*X_1*y^2-18*X_1*x*z+2*X_1*y*z-44*X_1*z^2}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -25*x*y^2*z+48*y^2*z^2, 31*x*y^2+29*x*y*z+35*y*z^2, -33*x*y^2-33*x*y*z-3*y*z^2-18*z^3, -44*x*y-44*z^2, 31*x*y-48*z^2, -28*x*y+20*z^2, -48*x*y-12*z^2, 3*x*y+12*z^2, 38*x*y-22*z^2, -48*x*y-48*z^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8*x*y^2*z+12*y^2*z^2, -19*x*y^2-33*x*y*z-19*y^2*z+49*y*z^2-26*z^3, 6*x*y^2+15*x*y*z+16*y^2*z-14*y*z^2+8*z^3, -36*x*y+20*x*z-11*y*z+43*z^2, 28*x*y-42*y^2+50*x*z+10*y*z-49*z^2, 25*x*y+31*y^2-25*x*z+40*y*z-z^2, 29*x*y-50*x*z+3*y*z+47*z^2, 29*x*y-31*x*z-35*y*z+14*z^2, -5*x*y-38*x*z-15*y*z+29*z^2, 45*x*y-40*x*z-12*y*z-44*z^2, 18*x*y-48*y^2+31*x*z-51*y*z+8*z^2, -22*y^2-9*x*z-22*y*z-6*z^2, x+41*z, -14*z, -3*z, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32*x*y^2*z+10*y^2*z^2, 6*x*y^2+20*x*y*z-2*y^2*z-4*y*z^2-45*z^3, -21*x*y^2-12*x*y*z-20*y^2*z+45*y*z^2-32*z^3, 27*x*y+33*x*z+41*z^2, 37*x*y+5*y^2+9*x*z-24*y*z+38*z^2, -46*x*y+38*y^2-51*x*z-10*y*z-34*z^2, 50*x*y-7*x*z-20*y*z-10*z^2, -32*x*y-17*x*z+26*z^2, 34*x*y-12*x*z-4*z^2, -8*x*y-47*x*z-19*z^2, 35*x*y-25*y^2-25*x*z-38*y*z-8*z^2, 8*x*y+16*y^2+14*x*z+11*y*z+8*z^2, 32*z, x-11*z, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7*x*y^2*z-48*y^2*z^2, 14*x*y^2-42*x*y*z-14*y^2*z+31*y*z^2-48*z^3, 41*x*y^2+32*x*y*z-37*y^2*z-22*z^3, -20*x*y-10*x*z-11*y*z-13*z^2, 38*x*y-3*y^2-6*x*z+27*y*z-41*z^2, 13*x*y+39*y^2+17*x*z-12*y*z+2*z^2, -38*x*y+33*x*z-21*y*z-43*z^2, -2*x*y+42*x*z-35*y*z-7*z^2, -42*x*y+20*x*z-15*y*z-39*z^2, 25*x*y-30*x*z-12*y*z-21*z^2, 33*x*y-3*y^2-18*x*z+31*y*z-42*z^2, -27*x*y+42*y^2+51*x*z-31*y*z-17*z^2, -3*z, 43*z, x-3*z, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48*x*y^2*z-37*y^2*z^2, 4*x*y^2+14*x*y*z-21*y^2*z+6*z^3, -45*x*y^2-11*x*y*z+34*y^2*z-45*y*z^2+18*z^3, 34*x*y+48*x*z-33*y*z-35*z^2, 43*x*y+15*y^2+34*x*z+y*z-14*z^2, 20*x*y-4*y^2+16*x*z+4*y*z+41*z^2, 30*x*y+38*y^2+38*x*z-43*y*z+36*z^2, 34*x*y-21*x*z+49*y*z-26*z^2, -23*x*y-10*y*z+14*z^2, -29*x*y-35*x*z-36*y*z+39*z^2, 36*x*y-33*y^2-47*x*z+18*y*z-26*z^2, -4*x*y+33*y^2-8*x*z+y*z+10*z^2, y+27*z, -38*z, -20*z, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28*x*y^2*z-18*y^2*z^2, 23*x*y^2-42*y^2*z-36*y*z^2+34*z^3, -38*x*y^2-32*x*y*z-8*y^2*z-27*y*z^2+48*z^3, 50*x*y+8*x*z+20*y*z-45*z^2, 40*x*y-18*y^2-x*z+46*y*z+17*z^2, -29*x*y+23*y^2+46*x*z-35*y*z+26*z^2, -21*x*y-3*x*z+14*z^2, 22*x*y-15*x*z-47*y*z+4*z^2, -8*x*y+16*x*z-42*y*z-22*z^2, -11*x*y-35*x*z-25*y*z-31*z^2, -43*x*y-41*y^2+38*x*z-23*y*z+28*z^2, 48*x*y+5*y^2-47*x*z+4*y*z-10*z^2, -20*z, y-33*z, 7*z, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -27*x*y^2*z-20*y^2*z^2, 40*x*y^2+32*x*y*z+49*y^2*z+47*y*z^2-17*z^3, -27*x*y^2-19*x*y*z+26*y^2*z-9*y*z^2+13*z^3, -18*x*y+38*y^2-6*x*z+46*y*z-18*z^2, 23*x*y+28*y^2-23*x*z+41*y*z+41*z^2, -16*x*y+50*y^2+18*x*z+17*y*z+39*z^2, 21*x*y-31*y^2-23*x*z-3*y*z-35*z^2, 19*x*y+46*y^2+37*x*z-50*y*z+22*z^2, 46*x*y+5*y^2+19*x*z-49*y*z+41*z^2, 6*x*y+4*y^2+34*x*z-6*y*z+17*z^2, 51*x*y-45*y^2-36*x*z-32*y*z+50*z^2, 9*x*y-9*y^2-48*x*z+49*y*z-10*z^2, 9*z, 41*z, y+12*z, 0, 0, 0, 0, 0, 0, 0}}, Degree => degDB); assert isHomogeneous DB; assert(DB * DB == 0); << "computing E = minimalPresentation homology(DB,DB)" << endl; time E = minimalPresentation homology(DB,DB); << "computing hilbertSeries E" << endl; time hE = hilbertSeries E; << "size numerator hilbertSeries E is : " << size numerator hE << endl; print hE; << "computing res E" << endl; time BE = betti res E; print BE; ) u = new Tally from {{-3, -7} => 7, {-3, -6} => 7, {0, 1} => 3, {0, 2} => 4, {-4, -9} => 4, {-4, -8} => 1, {-4, -7} => 1, {-1, -2} => 4, {-2, -5} => 3, {-2, -4} => 8} << "first we do the computation with adjusted degrees" << endl comp (degs',heft',degs1',degs2',degDB') t' = tally apply( degrees target presentation E, repair ) assert ( t' === u ) << "then we do the computation with unadjusted degrees" << endl comp (degs,heft0,degs1,degs2,degDB) t = tally degrees target presentation E assert ( t === u ) -- Local Variables: -- compile-command: "make -C $M2BUILDDIR/Macaulay2/packages/Macaulay2Doc/test ext-total.out" -- End: