IgnorePrimes -- Ignores certain primes when computing top minimal primes.

Description

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

Caveat

This may not be faster than simply using minimalPrimes and counting generators.

Functions with optional argument named IgnorePrimes :

topMinimalPrimesIP(...,IgnorePrimes=>...)

For the programmer

The object IgnorePrimes is a symbol.