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minprimes-test.m2
R = QQ[x,y,z]/ideal(x^6-z^6-y^2*z^4) time S = integralClosure R assert isHomogeneous S ideal S -- i8 : ideal S -- -- 2 2 2 2 2 -- o8 = ideal (x - w z, w x - w z, w - w x, w - y - z ) -- 6 6 7 6 7 7 T = ring ideal S use T assert( ideal S == ideal(x^2-T_1*z,T_1*x-T_0*z,T_1^2-T_0*x,T_0^2-y^2-z^2) ) -- this may change and still be correct trim ideal S assert( 4 == numgens trim ideal S ) -- the ideal has swelled since 1.1 R = QQ[w_1, w_2, x, y, z, Degrees => {3,3,1,1,1}, MonomialOrder => GRevLex => 5] I = ideal (x,y^2*z+z^3,w_2*z,w_1*z,w_2^2,w_1*w_2,w_1^2) assert isHomogeneous I m = minimalPrimes I assert all(m, isHomogeneous) assert( intersect m == radical I )