Macaulay2 » Documentation
Packages » NumericalSemigroups :: fractionalIdeal
next | previous | forward | backward | up | index | toc

fractionalIdeal -- turn a fractional ideal into a proper ideal

Synopsis

Description

sgrp is a list of ZZ_{>0}, interpreted as generators of a semigroup; mons is a list of ZZ interpreted as generating a module in the quotient field of sgrp with the option "Ideal" => false we get a list of integers belonging to the semigroup, otherwise a proper ideal of the semigroup ring. of the ring semigroupRing sgrp. In both cases, the program chooses the generators of least possible degree.

This is perhaps most useful when regarding a blowup or iterated blowup as a module over the original ring. For example, the sequence of blowups of the semigroupRing {5,9} is given by semigroupRing{4,5}, semigroupRing{1}:

i1 : sgrp = {5,9}

o1 = {5, 9}

o1 : List
 
i2 : sgrp1 = {4,5}

o2 = {4, 5}

o2 : List
 
i3 : sgrp2 = {1}

o3 = {1}

o3 : List
 
i4 : fractionalIdeal(sgrp, sgrp1, "Ideal"=>false)

o4 = {9, 10, 14, 15, 18, 19}

o4 : List
 
i5 : fractionalIdeal(sgrp, sgrp2)

o5 = ideal 1

               ZZ
              ---[x , x ]
              101  0   4
o5 : Ideal of -----------
                 9    5
                x  - x
                 0    4

See also

Ways to use fractionalIdeal:

For the programmer

The object fractionalIdeal is a method function with options.