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semigroupIdeal -- The ideal defining the semigroup ring

Synopsis

Description

The semingroup ideal of the semigroup generated by L is the kernel of the map kk[x_0..x_(#L)] -> kk[t] sending x_i to t^(L_i), where kk is the specified BaseField, defaulting to ZZ/101 and x is the specified VariableName. If the option "MinimalGenerators" is set to true, the default, then the program first computes a minimal set of generators from L; if it is set to false, the program uses L itself.

i1 : semigroupIdeal {5,7}

            7    5
o1 = ideal(x  - x )
            0    2

               ZZ
o1 : Ideal of ----[x , x ]
              1009  0   2
 
i2 : semigroupIdeal({5,7,10}, "MinimalGenerators" => false)

             2            5        3
o2 = ideal (x    - x   , x  - x   x   )
             0,0    1,0   2    0,0 1,0

               ZZ
o2 : Ideal of ----[x   , x , x   ]
              1009  0,0   2   1,0

See also

Ways to use semigroupIdeal:

For the programmer

The object semigroupIdeal is a method function with options.