The option IgnorePrimes should be a list of prime ideals. If a IgnorePrimes is provided, topMinimalPrimesIP will not include any primes containing those ideals in the computation and will find the minimal primes with maximal dimension other than the ignored ones.
i1 : R = QQ[x,y,z,w,v]; |
i2 : I = monomialIdeal(y^12, x*y^3, z*w^3, z*v*y^10, z*x^10, v*z^10, w*v^10, y*v*x*z*w); o2 : MonomialIdeal of R |
i3 : ScipPrintLevel = 0; |
i4 : L1 = topMinimalPrimesIP I
o4 = {monomialIdeal (y, z, v), monomialIdeal (y, z, w)}
o4 : List
|
i5 : L2 = topMinimalPrimesIP(I, IgnorePrimes=>L1)
o5 = {monomialIdeal (x, y, w, v)}
o5 : List
|
i6 : minimalPrimes I
o6 = {monomialIdeal (y, z, w), monomialIdeal (y, z, v), monomialIdeal (x, y,
------------------------------------------------------------------------
w, v)}
o6 : List
|
This may not be faster than simply using minimalPrimes and counting generators.
The object IgnorePrimes is a symbol.