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typeB -- Type B reflection arrangement

Synopsis

Usage:
typeB(n) or typeB(n,R) or typeB(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 B_n reflection arrangement

Description

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

i1 : B3 = typeB(3)

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

o1 : Hyperplane Arrangement

i2 : describe B3

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

i3 : ring B3

o3 = QQ[x , x , x ]
         1   2   3

o3 : PolynomialRing

See also

typeA -- Type A reflection arrangement
typeD -- Type D reflection arrangement

Ways to use `typeB` :

typeB(ZZ)
typeB(ZZ,PolynomialRing)
typeB(ZZ,Ring)