Is There a User-Friendly Program for Checking Radical Ideals in Polynomials?

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A user inquired about user-friendly programs for checking if a set of polynomials generates a radical ideal, specifically seeking a Mathematica package. Responses highlighted that Mathematica can handle this through its Groebner bases functionality. Additionally, SageMath, an open-source computer algebra system, was recommended as a viable alternative. It was also noted that many university math departments provide access to Magma, which is excellent for symbolic algebra tasks. These tools can significantly aid in algebraic computations involving radical ideals.
GargleBlast42
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Hello,
I was wondering, if there is some good and easy to use computer programm, that, given a set of polynomials, tells me if they generate a radical ideal. Preferably as a Mathematica package.
 
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Hi GargleBlast42,

I'm not that familiar with these types of problems, but I know that Mathematica implements Groebner bases for sets of polynomials - so it should be able to do this natively. Try this http://reference.wolfram.com/mathematica/tutorial/ComplexPolynomialSystems.html" .

The open source CAS http://www.sagemath.org/" .

Simon
 
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GargleBlast42, I presume that you are associated with a university. Most math departments (that I've seen) have magma available for free.

It's awesome for this, and many other, symbolic algebra problems. If you continue with algebra, it's a really good tool to have at your disposal.
 
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