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TriangularSets :: isPrimeSimple

isPrimeSimple -- simple primality test of triangular systems

Synopsis

Description

Let T = (t1,t2,…,tk) be a triangular set (i.e., their main variables are distinct). This method verifies if the following properties hold:

(i) the main degree of ti is one for i=1,…,k-1,

(ii) tk 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

      

See also

Ways to use isPrimeSimple :