This might as well be a mathematics question since I am only looking for a way to solve a basic model of the neutrondistribution in an infinite plane subcritical reactor. So the model for the neutrondistribution looks like this: $\frac{d^{2}\phi}{{dx}^{2}}-\gamma^{2}\phi+\frac{Q}{D}\delta(x)=0$...

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 what is a good reference to learn about?

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 with the commands. Say we have the following equations $$u_{12}+u_{13}+u_{14} = \beta (x_1 x_...

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 specified in Macaulay2 or Singular) and $I$ is an ideal in $R$ given by generators, is there a comm...

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 radical I and hit enter I get error: expect...

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 there a command to compute $I\cap R$? EDIT: The eli...

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 radical ideal for $n=3$ and $i=2$ of the above...

I want to compute Ext with Macaulay2. I see in the website they write how to do it, but I can not do it. Can anyone help me with an example? For example, let $S=k[x,y,z,t]$. How to compute $\mathrm{Ext}^i_S (S/(xy^2,x^2z),S)$ for some $i$? How to interpret it? Thanks.

This question is a technical question about M2. I know that in Macaulay 2 I can use "Grassmannian$(l,k)$" to get ideal of $(l+1)$-plane in $\mathbb{C}^{k+1}$ and the result ideal is in $\mathbb{ZZ}[p_I]$, but how can I work in another field, say, $\mathbb{ZZ}/32003$?

Suppose $$f_1=-4x^4y^2z^2+y^6+3z^5,$$ $$f_2=-4x^2y^2z^2+y^6+3z^5,$$ $$f_3=4x^4y^2z^2+y^6+3z^5,$$ $$f_4=4x^2y^2z^2+y^6+3z^5$$ and $$I=\langle xz-y^2,x^3-z^2\rangle\subset\mathbb C[x,y,z].$$ Is $f_i\in I?$ The answer is Yes in some cases. The question can be checked with Macaulay 2: when...

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 $J_t=\langle tx^2+yz,ty^2 +xz,tz^2+xy\rangle\subset \mathbb{Q}[x,y,z]$ with $t\in\Bbb C$. So...

Here on the page $10$, what does the displayed formula in the $6$th line $$\text {lg}(\eta_\ell)<\omega\Rightarrow \bigcup\{\text{Rang}(\nu_\ell(k):k<\text{lg}(\nu_\ell))\}\cap\bigcup_{k<\omega}M_k\subseteq M_{n(*)}$$ show? I just cannot understand the consequence of the $\subseteq$ relation in ...