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# prune(Arrangement) -- makes a new hyperplane arrangement in a polynomial ring

- Function: prune
- Usage:
    `prune A`
- Inputs:
  - A, a hyperplane arrangement,
- Optional inputs:
  - Exclude => ..., default value {}, this optional input is ignored by this function
- Outputs:
  - a hyperplane arrangement, an isomorphic to the input but defined over a polynomial ring

## Description

A hyperplane arrangement may sensibly be defined over a quotient of a polynomial ring by a linear ideal. However, sometimes this is inconvenient. This method creates an isomorphic hyperplane arrangement in a polynomial ring.

    i1 : A = typeA 3

    o1 = {x  - x , x  - x , x  - x , x  - x , x  - x , x  - x }
           1    2   1    3   1    4   2    3   2    4   3    4

    o1 : Hyperplane Arrangement

    i2 : A'' = restriction(A,0) -- restrict A to its first hyperplane

    o2 = {x  - x , x  - x , x  - x , x  - x , x  - x }
           2    3   2    4   2    3   2    4   3    4

    o2 : Hyperplane Arrangement

    i3 : ring A''

          QQ[x ..x ]
              1   4
    o3 = ------------
         (x  - x , 0)
           1    2

    o3 : QuotientRing

    i4 : B = prune A''

    o4 = {x  - x , x  - x , x  - x , x  - x , x  - x }
           2    3   2    4   2    3   2    4   3    4

    o4 : Hyperplane Arrangement

    i5 : ring B

    o5 = QQ[x ..x ]
             2   4

    o5 : PolynomialRing

## See also

- trim(Arrangement) -- make a simple hyperplane arrangement
- compress(Arrangement) -- extract nonzero equations
- restriction(Arrangement,ZZ) -- construct the restriction a hyperplane arrangement to a subspace

## Ways to use this method:

- prune(Arrangement) -- makes a new hyperplane arrangement in a polynomial ring

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/HyperplaneArrangements.m2:2872:0.