Let $T = (t_1,t_2,\cdots,t_k)$ be a triangular set (i.e., their main variables are distinct). This method verifies if the following properties hold:
(i) the main degree of $t_i$ is one for $i=1,\dots,k-1$,
(ii) $t_k$ is an irreducible polynomial.
If these properties hold then the saturated ideal of $T$ is a prime ideal.
i1 : R = QQ[x,y,z,MonomialOrder=>Lex]; |
i2 : F = {x*y^2 - y*z, y^3 + z^2}; |
i3 : T = triaSystem(R,F,{y}); |
i4 : isPrimeSimple(T) o4 = true |
i5 : I = saturate T 2 2 o5 = ideal (x*z + y , x*y - z, x + y) o5 : Ideal of R |
i6 : isPrime I o6 = true |
The object isPrimeSimple is a method function.