Questions tagged [macaulay2]
Macaulay2 is a software system devoted to supporting research in algebraic geometry and commutative algebra.
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Radical computations in Macaulay2
I'm trying to learn how to compute the radical of polynomial ideals in multiple variables over the real numbers in Macaulay2. From what I've gathered in some stack exchange posts([1], [2]), I just ...
- 990
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Solving Diophantine Equation in Macaulay2
I have to write a function which solves the diophantine equation $p(s)x^2 = q(s)$ (in $x$) where $p,q$ are integers polynomials in $s.$ This is doable since $p(s) \mid q(s)$ has only finite solutions (...
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Toric edge ring in Macaulay2
Consider the following bipartite graph $G$, given by $V(G)= \{ s_1,s_2,s_3 \} \cup \{t_1,t_2\}$ and $E(G)=\{ \{ s_1,t_1\},\{s_1,t_2\},\{s_2,t_1\},\{s_2,t_2\},\{s_3,t_2\} \}.$
I want to define the ...
- 185
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Can Macaulay2 detect if an element has the strong/weak Lefschetz property?
Let $A$ be a graded Artinian ring. An element $r$ of degree $i$ has the strong Lefschetz property if multiplication by $r$ on each graded component, $A_d \xrightarrow{r} A_{d+i}$ is of full rank ...
- 184
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Degree of a monomial in Macaulay2?
Instead of defining a monomial ordering in Macaulay2, I would like to get the vector of degrees of a monomial. For example, if I define
R=QQ[x,y]
p=x^2*y^5
I would ...
- 141
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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 ...
- 154
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Different results on Hilbert series in sage and Macaulay2
I am recently trying to compute some complicated Hilbert series. I tried sage and Macaulay2.
More precisely, I tried the following command in M2:
SS = QQ[ x1, x2, x3, x7, x8, x9, x13, x14, x17, x4, ...
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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. ...
- 218
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Induced matrix on degrees Macaulay2
I would like to compute the matrix associated with a map between graded modules with help of Macaulay2. For instance, if I have $R = \mathbb{Q}[x,y]$, and a map $\times (x+y): R \to R$, I would like ...
- 1,264
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Monomial order in Macaulay2
When I define the ring to work on in Macaulay2, I would like to change the order of the variables for building the Grobner basis of ideals with respect to this new order. For instance, if set
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- 185
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How to define ideals of quotient rings in Macaulay2?
I am trying to see that the localization of ring $A={\mathbb{C}[x,y,z]\over \left<xy, xz, yz \right>}$ on the ideal $\overline{\mathfrak{p}}=\left<\overline{x},\overline{y},\overline{z}\right&...
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relation between Krull dimension of ideal and dimension of solutions to polynomial equations
I would like to solve a system of polynomial equations
to do this in Macaulay2, I wrote it as an ideal, and compute its dimension which is given as $5$.
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- 1,052
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Macaulay2 error: expected a $0$-dimensional system [closed]
What does the error stdio:28:6:(3): error: expected a 0-dimensional system mean and how to avoid it?
Thanks in advance for any help!
Below is the code:
...
- 1,052
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How to understand this Macaulay2 code?
I am trying to understand the m2 code (source) shown in the following:
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- 1,052
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Using Macaulay2 to Write the Canonical Module as a Quotient of a Free Module
Let $S$ be a polynomial ring over a field. Let $I$ be a homogeneous parameter ideal of $S.$ Observe that $S/I$ is an Artinian local ring, so it is Cohen-Macaulay, and it is finitely generated as an $S$...
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