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idealsFromGeneratingSets -- creates ideals from sets of monomials

Synopsis

Description

Given a list of sets of monomials, the function converts each set into a monomial ideal.

i1 : n=4; D=2; p=1.0; N=3;
 
i5 : B=randomMonomialSets(n,D,p,N); B/print
                  2                     2               2         2
{x , x , x , x , x , x x , x x , x x , x , x x , x x , x , x x , x }
  1   2   3   4   1   1 2   1 3   1 4   2   2 3   2 4   3   3 4   4
                  2                     2               2         2
{x , x , x , x , x , x x , x x , x x , x , x x , x x , x , x x , x }
  1   2   3   4   1   1 2   1 3   1 4   2   2 3   2 4   3   3 4   4
                  2                     2               2         2
{x , x , x , x , x , x x , x x , x x , x , x x , x x , x , x x , x }
  1   2   3   4   1   1 2   1 3   1 4   2   2 3   2 4   3   3 4   4

o6 = {, , }

o6 : List
 
i7 : idealsFromGeneratingSets(B)

o7 = {monomialIdeal (x , x , x , x ), monomialIdeal (x , x , x , x ),
                      1   2   3   4                   1   2   3   4  
     ------------------------------------------------------------------------
     monomialIdeal (x , x , x , x )}
                     1   2   3   4

o7 : List

In case the option IncludeZeroIdeals is set to false, the function also counts how many sets are converted to the zero ideal.

See also

Ways to use idealsFromGeneratingSets :

For the programmer

The object idealsFromGeneratingSets is a method function with options.