Macaulay2 is a software system devoted to supporting research in algebraic geometry and commutative algebra.
Questions tagged [macaulay2]
72 questions
6
votes
2 answers
Computing contractions of ideals in Macaulay2
Does Macaulay2 compute contractions of ideals under ring homomorphisms. Specifically, if $R\subseteq S$ is a ring extension (say polynomial rings over $\mathbb{Q}$ which can be specified in M2) and $I$ is an ideal in $S$ given by generators, is…
Amd
- 61
6
votes
1 answer
How can I get Macaulay2 to tell me if this ideal is prime?
I am trying to get Macaulay2 to confirm if $(y+zi,x^2 - z^2 - 1)$ is a prime ideal in $\Bbb{C}[x,y,z]$. Now as a small test, I tried to compute its radical by doing R = CC[x,y,z] and then setting I = ideal (y+z*ii,x^2 - z^2 - 1). However when I put…
user38268
6
votes
1 answer
Can Macaulay2 do computations with symbolic parameters?
I'm trying to figure out how to use Macaulay2 to do some ideal membership computations, and I'm running into a problem with symbolic parameters. Here is a practical example.
Consider the family of ideals $J_t=\langle tx^2+yz,ty^2…
Semiclassical
- 18,592
6
votes
0 answers
How to find all integral elements over a subring using Macaulay2?
I have the following question about Macaulay2. How to find all integral elements over a subring?
What I mean is the following. Suppose $A$ is a subring of $B$. How can I find the following set?
$$L=\{x\in B : x \text{ is integral over }A\}$$
Here…
Ben
- 3,758
5
votes
1 answer
Solving a polynomial system using Groebner basis computations.
I have discovered that Groebner basis computations may help in a problem I am working on. However, I am having some very specific problems. First, the literature I have discovered on Groebner basis calculations are either extremely advanced or…
user6213
4
votes
2 answers
Macaulay2: How to compute the remainder when dividing a polynomial by a set of polynomials (in some order)?
I'm writing Buchberger's Criterion in a program in Macaulay2 to check whether or not the set of polynomials I have form a Grobner basis for the ideal it generates. However, I have not been able to find a method that gives me the remainder when a…
user528318
4
votes
0 answers
Primary decomposition of large ideals
Short version:
I'd like to do a primary decomposition of an ideal with 38 generators in a polynomial ring with 44 generators. However, the ideal seems far too large to naively decompose in, say, Macaulay2 (suffice to say I let my computer work all…
Fredrik Meyer
- 20,690
3
votes
0 answers
Using Macaulay 2 to find free divisors.
Given a hypersurface $D = h^{-1}(0)$ for some polynomial $h \in \mathbb{C} [x,y,z]$ I want to be able to use Macaulay 2 to tell if it's a free divisor or not.
What I've got so far;
Let $h_{p}$ be the reduced equation for $h$. For $D$ to be a free…
3
votes
1 answer
Plücker relations in Sagemath from Macaulay2
I am trying to implement the Plücker relations in Sagemath. Sage has an interface for Macaulay2, and this latter has a command Grassmannian(k-1, n-1) for computing the Plücker relations of the Grassmannian $\text{Gr}(k,n)$.
My problem is: when I do…
Dario Antolini
- 154
3
votes
1 answer
How to define this set using Macaulay2
Context
Consider a polynomial in $d$ variables of degree $N>1$. When $d=1$, it is a well-established fact that such a polynomial can be expressed as a product of polynomials, each of degree 1. However, for $d>1$, this is no longer the case. A…
Baloo
- 208
3
votes
1 answer
How to say a variable is invertible in Macaulay2?
I'm a very beginner in Macaulay2, so I apologize if this question is too trivial...
I'm using Macaulay2 for a computation involving over $30$ variables. Roughly speaking I have a $4\times 4$ matrix where entries are polynomials while coefficients…
3
votes
2 answers
Radical ideal computation (Macaulay2)
Is there a way to find the radical ideal of $I_i=(a^n-u^{n-i+1}v^{n-i},
b^n-u^{i-1}v^i, uv-ab)$ for $1\leq i \leq n$ in $\mathbb{C}[u,v,a,b]?$
This is the generalization of my question here where I wanted to use Macaulay2 software to compute the…
Ehsan M. Kermani
- 9,566
3
votes
1 answer
Radical of an ideal using Macaulay2 software.
What is the radical ideal of $(u^2v-a^3,uv^2-b^3,uv-ab)$ in $\mathbb{C}[u,v,a,b]?$
Above all, to learn how to fish, what would be code that I can use to get the radical? I have not worked with Macaulay2 (computational algebra software) before, so…
Ehsan M. Kermani
- 9,566
3
votes
1 answer
Calculating syzygies with Macaulay2
I'm trying to calculate the syzygies of a set of elements on the polinomial ring of 6 variables. But I'm trying to specify the number of generator in each degree the syzygies have. I know that Macaulay2 can give me the syzygies of the sistem very…
User43029
- 1,376
3
votes
1 answer
Computing Betti numbers using Macaulay2
Let $k$ be a field and $R=k[x,y,z]$, let $M=R/\langle x^2,xy,yz^2,y^4\rangle$ be $R$-module, how can we compute the left free resolution of $M$, and also the Betti numbers of this resolution?
user27759