1
vote
1answer
43 views

If $A\ne 0$ is a square matrix over a commutative ring with $\det A=0$, then its null space contains an element whose components are minors of $A$

Let $R$ denote a commutative ring and $A\ne 0$ a $n\times n$ matrix over $R$ with $\det A=0$. Then there exists a $x\in\ker A\setminus\left\{0\right\}$ such that all components of $x$ are minors of ...
0
votes
1answer
29 views

software with a routine for the vanishing ideal of a finite set of points

I am looking for an algebraic software package that provides a routine that computes the vanishing ideal of a finite set of points. So far i am working with Macaulay2 but i have not been able to find ...
2
votes
1answer
117 views

Using Janet Basis to solve a nonlinear polynomial system

I am trying to solve a nonlinear polynomial equation system using Janet basis, when they have finite many solutions. For example the solution of the system: $$xy^2-y^3-3x^2=0,x^2+y^2+xy=0.$$ There ...
2
votes
1answer
295 views

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 ...
4
votes
1answer
313 views

Computing with ideals: over $K$ or over $\mathbb{Q}\subseteq K$? does it matter?

I'm beginning to learn to use SINGULAR, the computer algebra system (CAS) for commutative algebra. NOTATION: If $K$ is a field of characteristic $0$, then $\mathbb{Q}\subseteq K$; otherwise ...