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# mingens -- minimal generator matrix

## Description

Every ideal and module in Macaulay2 comes equipped with a generating set, which is sometimes a larger generating set than is required. This routine returns a matrix whose columns generate the given ideal or module.

## See also

- trim -- minimize generators and relations
- prune -- prune, e.g., compute a minimal presentation
- minimalPresentation -- compute a minimal presentation

### Menu

- `mingens(...,Strategy=>...)` -- see Complement -- a Strategy option value

## Ways to use mingens:

- mingens(GroebnerBasis) -- (partially constructed) minimal generator matrix
- `mingens(Ideal)` -- see mingens(Module) -- minimal generator matrix
- mingens(Module) -- minimal generator matrix
- `mingens(MonomialIdeal)` -- see mingens(Module) -- minimal generator matrix

## For the programmer

The object mingens is a method function with options.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Macaulay2Doc/functions/mingens-doc.m2:58:0.