subArrangement -- Subarrangement containing a fixed flat

Synopsis

• Usage:

  subArrangement(A,F) or subArrangement(F)

• Inputs:
  • A, a hyperplane arrangement
  • F, an intersection of hyperplane(s)
• Outputs:
  • a hyperplane arrangement, the subarrangement of A contained in F

Description

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 : flats(2,A)

o2 = {{0, 1, 3}, {0, 2, 4}, {0, 5}, {1, 4}, {1, 2, 5}, {2, 3}, {3, 4, 5}}

o2 : List

i3 : B := subArrangement first oo

o3 = {x  - x , x  - x , x  - x }
       1    2   1    3   2    3

o3 : Hyperplane Arrangement 

i4 : ring B

o4 = QQ[x ..x ]
         1   4

o4 : PolynomialRing

See also

• Arrangement _ Flat -- Subarrangement containing a fixed flat