trim(Arrangement) -- make a simple hyperplane arrangement

Function: trim
Usage:

trim A
Inputs:
- A, a hyperplane arrangement,
Optional inputs:
- Strategy => ..., default value null,
Outputs:
- a hyperplane arrangement, a simple arrangement

Description

A hyperplane arrangement is simple if none of its linear forms is identically $0$ and no hyperplane is cut out out by more than one form. This method returns a simple arrangement by reducing the multiplicities of the hyperplanes and eliminating the zero equation (if necessary).

i1 : R = QQ[x, y];

i2 : A = arrangement{x,x,0_R,y,y,y,x+y,x+y,x+y,x+y,x+y}

o2 = {x, x, 0, y, y, y, x + y, x + y, x + y, x + y, x + y}

o2 : Hyperplane Arrangement

i3 : A' = trim A

o3 = {x + y, y, x}

o3 : Hyperplane Arrangement

i4 : assert(ring A' === R)

i5 : assert(trim A' == A')

i6 : assert(trim A' == A')

Some natural operations produce non-simple hyperplane arrangements.

i7 : A'' = restriction(A, y)

o7 = {x, x, x, x, x, x, x}

o7 : Hyperplane Arrangement

i8 : trim A''

o8 = {x}

o8 : Hyperplane Arrangement

i9 : A''' = dual arrangement{x, y, x-y}

o9 = {-x , x , x }
        1   1   1

o9 : Hyperplane Arrangement

i10 : trim A'''

o10 = {x }
        1

o10 : Hyperplane Arrangement

Ways to use this method:

trim(Arrangement) -- make a simple hyperplane arrangement

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/HyperplaneArrangements.m2:1699:0.

trim(Arrangement) -- make a simple hyperplane arrangement

Description

See also

Ways to use this method: