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# ExtendField -- an option used to specify if extending the finite field is permissible here

- Usage:
    `ExtendField => b`
- Inputs:
  - b, a Boolean value, whether the base field is allowed to be extended

## Description

Various functions which produce points, or call functions which produce points, may naturally find scheme theoretic points that are not rational over the base field (for example, by intersecting with a random linear space). Setting ExtendField => true will tell the function that such points are valid. Setting ExtendField => false will tell the function ignore such points. This sometimes can slow computation, and other times can speed it up. In some cases, points over extended fields may also have better randomness properties for applications.

## See also

- randomPoints -- a function to find random points in a variety.
- findANonZeroMinor -- finds a non-vanishing minor at some randomly chosen point
- extendIdealByNonZeroMinor -- extends the ideal to aid finding singular locus

## Functions with optional argument named ExtendField:

- `extendIdealByNonZeroMinor(...,ExtendField=>...)`
- `findANonZeroMinor(...,ExtendField=>...)`
- `randomPoints(...,ExtendField=>...)`

## For the programmer

The object ExtendField is a symbol.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/RandomPoints.m2:1607:0.