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# extend -- rewrites a permutation as a permutation on more symbols

- Usage:
    `extend(w,n)`
- Inputs:
  - w, a permutation,
  - n, an integer,
- Optional inputs:
  - Verify (missing documentation) => ..., default value true,
- Outputs:
  - a permutation,

## Description

A permutation on $n$ symbols is an element of the symmetric group on $n$ symbols, $\mathfrak{S}_n$. However, it can also be regarded as a permutation on $N > n$ symbols as well by fixing the $(n+1)$st through $N$th symbols.

    i1 : p = permutation {3,1,2,5,4}

    o1 = Permutation{3, 1, 2, 5, 4}

    o1 : Permutation

    i2 : extend(p, 7)

    o2 = Permutation{3, 1, 2, 5, 4, 6, 7}

    o2 : Permutation

## See also

- trim -- minimize generators and relations

## Ways to use extend:

- `extend(Permutation,ZZ)`
- `extend(Complex,Complex,Matrix)` -- see extend(Complex,Complex,Matrix,Sequence) -- extend a map of modules to a map of chain complexes
- extend(Complex,Complex,Matrix,Sequence) -- extend a map of modules to a map of chain complexes
- extend(Permutation,Permutation) -- rewrites two permutations to be permutations on the same number of symbols

## For the programmer

The object extend is a method function with options.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Permutations/Documentation/mainDocs.m2:250:0.