getMons -- calculates the monomials of a ring

Usage:

getMons(R, I)

getMons I

getMons S

getMons R
Inputs:
- R, a polynomial ring,
- I, an ideal, a homogeneous ideal of a polynomial ring
- S, a quotient ring, a quotient of a polynomial ring R and a homogeneous ideal I of R
Optional inputs:
- MaxDegree => a number, default value 10, the maximum degree of a monomial to calculate
Outputs:
- a list,

Description

Given a polynomial ring R and a homogeneous ideal of R (an ideal generated by homogeneous elements of R) called I, the function getMons gets the monomials of the quotient ring R/I.

i1 : R = QQ[x,y]

o1 = R

o1 : PolynomialRing

i2 : I = ideal(x^3, y^3)

             3   3
o2 = ideal (x , y )

o2 : Ideal of R

i3 : getMons(R, I)

             2   2    2 2          2      2
o3 = {1, x, x , x y, x y , x*y, x*y , y, y }

o3 : List

i4 : J = ideal(x*y - y^2, x^4, x^3 * y, x^2 * y^2)

                   2   4   3    2 2
o4 = ideal (x*y - y , x , x y, x y )

o4 : Ideal of R

i5 : getMons(R / J)

             2   3      2   3
o5 = {1, x, x , x , y, y , y }

o5 : List

For quotient rings with infinitely many monomials, the optional argument MaxDegree can be used to calculate monomials up to a certain degree. If this is left blank, the default value used will be 10.

i6 : I = ideal(x^2 - y^2)

            2    2
o6 = ideal(x  - y )

o6 : Ideal of R

i7 : getMons(R/I, MaxDegree=>10)
Ideal is not finite over the base (quotient ring has infinitely many monomials)
Monomials up to degree 10 given

                2          2   3   4     3     4   5   6     5     6   7   8 
o7 = {1, x, y, y , x*y, x*y , y , y , x*y , x*y , y , y , x*y , x*y , y , y ,
     ------------------------------------------------------------------------
        7     8   9   10     9
     x*y , x*y , y , y  , x*y }

o7 : List

Caveat

The optional argument MaxDegree is only meant to be used for quotient rings where there are infinitely many monomials. For quotient rings with finitely many monomials, MaxDegree will be ignored regardless of it's value.

Ways to use getMons:

getMons(Ideal)
getMons(PolynomialRing)
getMons(PolynomialRing,Ideal)
getMons(QuotientRing)

For the programmer

The object getMons is a method function with options.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/MacaulayPosets.m2:1624:0.

getMons -- calculates the monomials of a ring

Description

Caveat

See also

Ways to use getMons:

For the programmer