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SimplexInfo

Stanley-Reisner ideal, AlexanderDual complex, ideal of top simplices

Syntax 
SimplexInfo(A: LIST): RECORD

Description
This function compute the Stanley-Reisner ideal, the Alexander Dual complex and ideal of a simplicial complex described by a list of top faces.

Package GeomModelling, by Elisa Palezzato.

Example 
/**/ Use QQ[x[1..5]], DegLex;
/**/ L := [x[1]*x[2]*x[3], x[2]*x[3]*x[4], x[3]*x[4]*x[5]]; -- list top faces
/**/ indent(SimplexInfo(L));
record[
  AlexanderDualCOMPLEX := [x[2]*x[3]*x[5], x[2]*x[3]*x[4], x[1]*x[3]*x[4]],
  AlexanderDualIdeal := ideal(x[4]*x[5], x[1]*x[5], x[1]*x[2]),
  Delta := [x[1]*x[2]*x[3], x[2]*x[3]*x[4], x[3]*x[4]*x[5]],
  StanleyReisnerIdeal := ideal(x[1]*x[4], x[1]*x[5], x[2]*x[5])
]

See Also