Data Types, Functions, and Programming

Abstract

In this chapter we present an introduction to the structure of Macaulay 2 commands and the writing of functions in the Macaulay 2 language. For further details see the Macaulay 2 manual distributed with the program [1].

The scattering variety

“…In this section, we concentrate our study on the cases of 3-dimensional varieties, that is V ϕ for n = 2 and V * ϕ for n = 3. Our findings for χ using [17,18] are presented in table 7.…”

“…and tabulate the results. We can extract these geometrical quantities using standard computational geometric packages, such as [17,18] as well as software interfacing with Mathematica [19]. The tensor coefficients from (2.8) are kept as generic non-vanishing parameters λ S = 0 satisfying the highest weight condition (2.8).…”

“…Using this notation, it is expedient to tabulate our findings of the various Hilbert series obtained through explicit computation [17,18]. First, before imposing the Möbius transformation, we obtain the results for V ϕ presented in table 2.…”

“…Again, Hilbert series can be obtained through explicit computation [17,18] and the resulting Hilbert series are summarized in table 3.…”

On the Algebraic Geometry of Polynomial Dynamical Systems

“…Conversely, every such minimal diagram provides generators for a minimal prime of the ideal M . This algorithm has been implemented in Macaulay2 [8]. The algorithm comes with a collection of probability distributions on the set of minimal primes that can be used for model selection.…”