I have two questions regarding the program Macaulay2. I'm new to it, and I'm wondering how to access elements of modules of the form R^n where R is a ring.(adsbygoogle = window.adsbygoogle || []).push({});

To take an example: say I define the ring R = QQ[x,y], i.e. the ring of polynomials in x and y over Q. Then I define the R-module M = R^2, which is just the cartesian product. How am I to access the elements of M? On what form are they?

My other goal is, illustrated by this example, is to get a basis for the subset of M consisting of elements (a,b) where a is of some degree, and b is of another.

For example, if the degree of a is 1, and the degree of b is 2, the basis I want is the matrix

[tex]\begin{pmatrix} x & y & 0 & 0 & 0 \\ 0 & 0 & x^2 & xy & y^2 \end{pmatrix}[/tex]

R^2 <--- R^5

I know how to get a basis where a and b are of the same degree, (in which case I can write basis(n,M)), but not when they are different.

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# Modules in Macaulay2

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