Items tagged with polynomialideals

Hi, I have a big system with 27 polynomial equations in 16 unknowns: f_1=...=f_27=0.  I can store these equations but I cannot calculate a Grobner basis of the ideal  J generated by my polynomials (allocation problem) - I use the library "with(FGb)"-  What interests me is whether my system is minimal in the following sense.

If, for example,  I remove f_1, is the ideal generated by (f_2,...f_27)  J again ? That is to say, is f_1 in the ideal generated by f_2,...,f_27 ? I would like to get an answer "yes" or "no" for each removed  f_i.

My question: can we solve the problem above  without calculating a Grobner basis of J?

Thanks in advance.






After using the Groebner and PolynomialIdeals packages, Maple goes into a long calculation when I make an entry of the form

name:=polynomial expression. This can take 10's of minutes for an expression of two lines. The only solution I have found is to save the sheet and restart it and enter the line name:= etc. before loading Groebner and PolynomialIdeals. This is most inconvenient. Is there a better workaround?

How to create polynomial ideals over algebraic extensions of the field of  rationals Q with Maple?
The Maple help to PolynomialIdeals
"All package commands support computations over the rational numbers, algebraic number fields, rational function fields, and algebraic function fields, as well as finite fields. Coefficients from algebraic extension fields can be specified using radicals or RootOfs"
is too poor. I also don't find any example on this topic in examples,PolynomialIdeals.

I think that I found a bug in Maple! Please run the following command:

I need the Generators of above Ideal. What is your idea?!

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