next | previous | forward | backward | up | index | toc

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

## Synopsis

• Function: prune
• Usage:
prune A
• Inputs:
• Optional inputs:
• Exclude => ..., default value {}, this optional input is ignored by this function
• Outputs:
• , 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