# saturate(...,Strategy=>...)

## Description

There are four strategy values:

## Iterate

saturate(I,J,Strategy => Iterate) -- indicates that successive ideal or module quotients should be used.

This value is the default.

## Linear

saturate(I,J,Strategy => Linear)Strategy => Linear -- indicates that the reverse lex order should be used to compute the saturation.

This presumes that J is a single, linear polynomial, and that I is homogeneous.

## Bayer

saturate(I,f,Strategy => Bayer) -- indicates that the method of Bayer's thesis should be used.

The method is to compute (I:f) for I and f homogeneous, add a new variable z, compute a Gröbner basis of (I,f-z) in reverse lex order, divide by z, and finally replace z by f.

## Eliminate

saturate(I,f,Strategy => Eliminate) -- indicates that the saturation (I:f) should be computed by eliminating fz from (I,f*z-1), where z is a new variable.

## Further information

• Default value: null
• Function: saturate -- saturation of ideal or submodule
• Option key: Strategy -- an optional argument