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Packages » HyperplaneArrangements :: toList(Flat)

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toList(Flat) -- the indices of a flat

Synopsis

Function: toList
Usage:

toList F
Inputs:
- F, a flat in an hyperplane arrangement,
Outputs:
- a list, the indices of the hyperplanes of a $F$

Description

As stated in Flat, flats are treated in this package as lists of indices of hyperplanes in the arrangement. This method returns that list.

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 : F = flat(A3, {3,4,5})

o2 = {3, 4, 5}

o2 : Flat of {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 : assert(toList F === {3,4,5})

Often one wants the corresponding linear forms. This can be accomplished using subscripts:

i4 : (hyperplanes A3)_(toList F)

o4 = {x  - x , x  - x , x  - x }
       2    3   2    4   3    4

o4 : List

See also

toList(Arrangement) -- the defining linear forms of an arrangement

Ways to use this method:

toList(Flat) -- the indices of a flat