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HyperplaneArrangements :: typeD

typeD -- Type D reflection arrangement

Synopsis

Usage:

typeD(n) or typeD(n,R) or typeD(n,k)
Inputs:
- n, an integer, the rank
- R, a polynomial ring, a polynomial (coordinate) ring in n variables
- k, a ring, a coefficient ring; by default, QQ
Outputs:
- a hyperplane arrangement, the D_n reflection arrangement

Description

The hyperplane arrangement with hyperplanes defined by the type D_n root system: for example,

i1 : D4 = typeD(4)

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

o1 : Hyperplane Arrangement

i2 : describe D4

o2 = {x  - x , x  + x , x  - x , x  + x , x  - x , x  + x , x  - x , x  + x ,
       1    2   1    2   1    3   1    3   1    4   1    4   2    3   2    3 
     ------------------------------------------------------------------------
     x  - x , x  + x , x  - x , x  + x }
      2    4   2    4   3    4   3    4

i3 : ring D4

o3 = QQ[x ..x ]
         1   4

o3 : PolynomialRing

See also

typeA -- Type A reflection arrangement
typeB -- Type B reflection arrangement

Ways to use `typeD` :

"typeD(ZZ)"
"typeD(ZZ,PolynomialRing)"
"typeD(ZZ,Ring)"

For the programmer

The object typeD is a method function.