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# biBasis -- constructs a reduced Boolean Gröbner basis for the given Ideal, if the second argument is true (default), and reduced Boolean Pommaret basis otherwise.

- Usage:
    `biBasis(I, toGroebner => true)`
- Inputs:
  - I, an ideal
- Optional inputs:
  - toGroebner => ..., default value true
- Outputs:
  - P, an ideal

## Description

    i1 : R = ZZ/2[x, y, MonomialOrder => GRevLex]

    o1 = R

    o1 : PolynomialRing

    i2 : I = ideal(x*y + x + 1)

    o2 = ideal(x*y + x + 1)

    o2 : Ideal of R

    i3 : P = biBasis(I, toGroebner => true)

    o3 = ideal (x + 1, y)

    o3 : Ideal of R

## Caveat

- biBasis assumes coefficient Ring of the given Ideal is ZZ/2
- biBasis always treats the given Ideal as a Boolean one
- biBasis assumes the following monomials orders: Lex, GLex, GRevLex

## See also

- gb -- compute a Gröbner basis
- gbBoolean (missing documentation)

## Ways to use biBasis:

- `biBasis(Ideal)`

## For the programmer

The object biBasis is a method function with options.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/BIBasis.m2:83:0.