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schenck-book-1.m2
R=QQ[s,t] S=QQ[x,y,z,w] assert( (f = map(R,S,{s^4,s^3*t,s*t^3,t^4})) === map(R,S,{s^4, s^3*t, s*t^3, t^4}) ) assert( (I = kernel f) === ideal(y*z-x*w,z^3-y*w^2,x*z^2-y^2*w,y^3-x^2*z) ) assert( (E3 = prune Ext^3(coker gens I, S)) === cokernel map(S^{{5}},S^{{4},{4},{4},{4}},{{w, z, y, x}}) ) assert( (hilbertFunction(-5,E3)) === 1 ) end print generateAssertions /// R=QQ[s,t] S=QQ[x,y,z,w] f = map(R,S,{s^4,s^3*t,s*t^3,t^4}) I = kernel f E3 = Ext^3(coker gens I, S) hilbertFunction(-5,E3) ///
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