# Questions tagged [macaulay2]

Macaulay2 is a software system devoted to supporting research in algebraic geometry and commutative algebra.

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### How can I get maximal ideal containing an ideal using Macaulay2?

In Macaulay2, I have written the following codes to find the maximal ideal in the ring $Q[x,y,z]$ containing the ideal generated by $x^2y+z$ and $xz-y$. R=QQ[x,y,z] I=ideal(x^2y+z,xz-y) M=getMaxIdeal ...
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### Macaulay2 Monomial Order

In Macaulay2, one can define a polynomial ring with a certain monomial order as follows: R=QQ[x,y,z,MonomialOrder=>{Lex=>2,Position=>Up}] This means $R$ is ...
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### 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 ...
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### Localization of a Weyl-Algebra module

My aim is to understand how to describe the localization of modules over the Weyl algebra. I want to be able to do simple examples by hand. I wrote the following code in Macaulay2. ...
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### Twisted cubic curve; finding a representation as an ideal of minors of a 2 by 3 matrix of linear forms

Looking at a particular twisted cubic curve I was playing with getting the representation as the 2 by 2 minors of a 2 by 3 matrix of linear forms. See e.g. G. Ellingsrud, R. Piene and S.A. Strømme On ...
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### Finding the length of the kernel of a map in Macaulay2

Given an equigenerated monomial ideal $I$ over a polynomial ring, I am trying to check if a sequence $L={l_1,\ldots,l_t}$ is almost $I$-regular, i.e. for each $i$, the kernel of the multiplication map ...
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### Bhargava Higher Composition Laws I Computations

as a project for a class I'm currently taking, I've decided to undertake the execution of the proofs in Manjul Bhargava's expositional article, "Higher composition laws I: A new view on Gauss ...
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### Create list with a for loop on Macaulay2

I'm trying to write a function on Macaulay2 such that, given a square polynomial matrix in input, put out a list $\{(1,p_1(x)), \ldots , (r,p_r(x))\}$ where $r$is the rank of the matrix and $p_i(x)$ ...
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### Macaulay Matrix Reduction in Macaulay2

I am trying to get the Groebner bases of an ideal in Macaulay 2 through the triangularization of the Macaulay matrix. Indeed, I would like to know how far I should go -how big the matrix should be- ...
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### which mehod can easily design index of Grassmannian and its k and n or any function for this in Macaulay2 and how to convert poset to this index?

how to know k and n and its index of Grassmannian? which mehod can easily design index of Grassmannian and its k and n or any library or function for this in Macaulay2? is there any library or ...
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### 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 ...
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### Finding complementary of a collection in Macaulay2

Having a collection A of sets of the same cardinality t, I am trying to find all elements in 2^[n]\A of cardinality t. Is it possible to do so in Macaulay2? If so, which packages are required? How ...
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### Ring of formal power series in Macaulay2

How does one define the ring $\mathbb{C}[[x,y]]$ of formal power series in two variables over $\mathbb{C}$ in Macaulay2? Or Singular? I have seen some papers that claim to perform calculations in ...
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### 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 ...
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### Decomposing an ideal using Macaulay2

I give Macaulay2 the ideal $I=(y^2, x) \in Q[x , y]$ and then I put decompose I. The result is $(x , y)$ but I do not understand why. Does it mean that $I = (x , y)$...
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### Open cones in Macaulay2

I need to create some polyhedral cones and form their intersections. Macaulay2 looks like a great tool for this, and so I set up M2 on a Linux box. I've been able to make the cones and form ...
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### What does Hilbert series of monomial ideals describe?

I am trying to understand the point of Hilbert series of monomial ideals. I am confused because Macaulay has commands for hilbertSeries, hilbertPolynomial and hilbertFunction. What does Hilbert ...
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### 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 ...
164 views

### Computing extensions of an ideal in Singular or Macaulay2

Does Macaulay2 or Singular compute extensions of ideals under ring homomorphisms? Specifically, if $\phi : R \to S$ is a ring homomorphism (say polynomial rings over $\mathbb{Q}$ which can be ...
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### Finding the number of solutions of a system of equations in Macaulay 2

I just started working with Macaulay 2 and need some help. I need to find the number of solutions of a system of equations. I am having difficulty imputing this into the software so please be specific ...
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### 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 ...
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### 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 ...
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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 ...
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### 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 ...
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### How to make such a matrix multiplication as fast as possible in Macaulay2?

Given two matrices, $A$ ($m$ rows and $n$ columns) and $B$ ($n$ rows and $k$ columns), we want to compute matrix $A$ acting on each row of matrix $B$, and expect $mk$-dimensional matrix $C$, namely ...
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### 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, ...
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?
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 $I$...