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HyperplaneArrangements :: typeA

typeA -- Type A reflection arrangement

Synopsis

Description

The hyperplane arrangement with hyperplanes x_i-x_j. 
i1 : A3 = 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 : describe A3

o2 = {x  - x , x  - x , x  - x , x  - x , x  - x , x  - x }
       1    2   1    3   1    4   2    3   2    4   3    4
 
i3 : ring A3

o3 = QQ[x ..x ]
         1   4

o3 : PolynomialRing
Alternatively, one may specify a coordinate ring, 
i4 : S = ZZ[w,x,y,z];
 
i5 : A3' = typeA(3,S)

o5 = {w - x, w - y, w - z, x - y, x - z, y - z}

o5 : Hyperplane Arrangement 
i6 : describe A3'

o6 = {w - x, w - y, w - z, x - y, x - z, y - z}
or a coefficient ring: 
i7 : A4 = typeA(4,ZZ/3)

o7 = {x  - x , x  - x , x  - x , x  - x , x  - x , x  - x , x  - x , x  - x , x  - x , x  - x }
       1    2   1    3   1    4   1    5   2    3   2    4   2    5   3    4   3    5   4    5

o7 : Hyperplane Arrangement 
i8 : ring A4

     ZZ
o8 = --[x ..x ]
      3  1   5

o8 : PolynomialRing

See also

Ways to use typeA :

For the programmer

The object typeA is a method function.