tailMonomials -- find tail monomials

Synopsis

Usage:

L = tailMonomials M

L = tailMonomials(M, m)
Inputs:
- M, an ideal, $M$ should be a monomial ideal (an ideal generated by monomials)
- m, a ring element, optional, only return a single list of the tail monomials for this monomial
Optional inputs:
- AllStandard => a Boolean value, default value false, which monomials should be considered tail monomials of a monomial $m$: either all standard monomials of a given degree, or all monomials smaller than $m$ in the given term order (but still of the same degree)
Outputs:
- L, a list, a list of lists: for each generator $m$ of $M$, the list of all tail monomials If instead $m$ is given, the list of the tail monomials of $m$ is returned

Description

Inputting an ideal $M$ generated by monomials returns a list of lists of tail monomials for each generator of $M$ (in the same order).

i1 : R = ZZ/32003[a..d];

i2 : M = ideal (a^2, b^2, a*b*c);

o2 : Ideal of R

i3 : tailMonomials M

                       2                  2               2                
o3 = {{a*b, a*c, b*c, c , a*d, b*d, c*d, d }, {a*c, b*c, c , a*d, b*d, c*d,
     ------------------------------------------------------------------------
      2       2     2   3                        2      2     2     2   3
     d }, {a*c , b*c , c , a*b*d, a*c*d, b*c*d, c d, a*d , b*d , c*d , d }}

o3 : List

i4 : tailMonomials(M, AllStandard => true)

                       2                  2                    2           
o4 = {{a*b, a*c, b*c, c , a*d, b*d, c*d, d }, {a*b, a*c, b*c, c , a*d, b*d,
     ------------------------------------------------------------------------
           2       2     2   3                        2      2     2     2 
     c*d, d }, {a*c , b*c , c , a*b*d, a*c*d, b*c*d, c d, a*d , b*d , c*d ,
     ------------------------------------------------------------------------
      3
     d }}

o4 : List

i5 : tailMonomials(M, b^2)

                 2                  2
o5 = {a*c, b*c, c , a*d, b*d, c*d, d }

o5 : List

i6 : tailMonomials(M, b^2, AllStandard=>true)

                      2                  2
o6 = {a*b, a*c, b*c, c , a*d, b*d, c*d, d }

o6 : List

Ways to use tailMonomials :

tailMonomials(Ideal)
tailMonomials(Ideal,RingElement)

For the programmer

The object tailMonomials is a method function with options.

tailMonomials -- find tail monomials

Synopsis

Description

See also

Ways to use tailMonomials :

For the programmer