# reesIdeal(...,MinimalGenerators=>...) -- Whether the saturation step returns minimal generators

## Synopsis

• Usage:
reesIdeal(...,MinimalGenerators => X)

## Description

Here X is of type boolean. Each of these functions involves the computation of a Rees algebra, which may involve a saturation step. This optional argument determines whether or not the output of the saturation step will be forced to have a minmimal generating set. This is described in the documentation node for saturate.

## Further information

• Default value: true
• Function: reesIdeal -- Compute the defining ideal of the Rees Algebra
• Option key: MinimalGenerators -- whether to compute minimal generators and return a trimmed set of generators

## Functions with optional argument named MinimalGenerators :

• "associatedPrimes(...,MinimalGenerators=>...)" -- see associatedPrimes -- find associated primes
• "intersect(Ideal,Ideal,MinimalGenerators=>...)" -- see intersect(Ideal,Ideal) -- compute an intersection of a sequence of ideals or modules
• "intersect(Module,Module,MinimalGenerators=>...)" -- see intersect(Ideal,Ideal) -- compute an intersection of a sequence of ideals or modules
• "intersectInP(...,MinimalGenerators=>...)" -- see intersectInP(...,BasisElementLimit=>...) -- Option for intersectInP
• "decompose(Ideal,MinimalGenerators=>...)" -- see minimalPrimes -- minimal primes of an ideal
• "minimalPrimes(...,MinimalGenerators=>...)" -- see minimalPrimes -- minimal primes of an ideal
• "primaryDecomposition(...,MinimalGenerators=>...)" -- see primaryDecomposition -- irredundant primary decomposition of an ideal
• "quotient(...,MinimalGenerators=>...)" -- see quotient(Module,Module) -- ideal or submodule quotient