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codim.m2
R = ZZ[x,y] assert ( 0 == codim ( R^2, Generic => true) ) assert ( 0 == codim (ideal 0_R, Generic => true)) assert ( 0 == codim ( cokernel map(R^3, R^0, 0) , Generic => true) ) assert ( 1 == codim (ideal ( 2*x ), Generic => true ) ) assert ( 2 == codim (ideal ( 2*x , 3*y ), Generic => true ) ) assert ( infinity == codim (R^0, Generic => true ) ) assert ( infinity == codim (ideal 1_R, Generic => true)) f = (M,N) -> assert( codim (M++N, Generic => true) == min(codim(M, Generic => true), codim(N, Generic => true)) ) f(quotient module ideal x, quotient module ideal(x,y)) f(quotient module ideal x, quotient module ideal 0_R) f(quotient module ideal 1_R, quotient module ideal(x,y)) R = QQ[x,y] assert ( 0 == codim ( R^2 ) ) assert ( 0 == codim (ideal 0_R )) assert ( 0 == codim ( cokernel map(R^3, R^0, 0) ) ) assert ( 1 == codim (ideal ( 2*x ) ) ) assert ( 2 == codim (ideal ( 2*x , 3*y ) ) ) assert ( infinity == codim (R^0 ) ) assert ( infinity == codim (ideal 1_R )) f(quotient module ideal x, quotient module ideal(x,y)) f(quotient module ideal x, quotient module ideal 0_R) f(quotient module ideal 1_R, quotient module ideal(x,y)) R2=(R/ideal(x,y))[t]; assert ( 1 == codim ideal t)
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