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HyperplaneArrangements :: graphic

graphic -- Make a graphic arrangement

Synopsis

Description

A graph G has vertices 1, 2, ..., n, and its edges are a list of lists of length 2. The graphic arrangement A(G) of G is, by definition, the subarrangement of the type A_(n-1) arrangement with hyperplanes x_i-x_j for each edge {i,j} of G
i1 : G = {{1,2},{2,3},{3,4},{4,1}}; -- a four-cycle
i2 : AG = graphic G

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

o2 : Hyperplane Arrangement 
i3 : describe AG

o3 = {- x  + x , - x  + x , - x  + x , x  - x }
         1    2     2    3     3    4   1    4
i4 : rank AG -- the number of vertices minus number of components

o4 = 3
i5 : ring AG

o5 = QQ[x ..x ]
         1   4

o5 : PolynomialRing
i6 : ring graphic(G,ZZ[x,y,z,w])

o6 = ZZ[x..z, w]

o6 : PolynomialRing

See also

Ways to use graphic :

For the programmer

The object graphic is a method function.