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a problem in arithmetic dynamics
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Author:  timoe [ Mon Nov 30, 2015 4:38 pm ]
Post subject:  a problem in arithmetic dynamics

Let I be an ideal generated by a finite number of binomials, and let I' be a larger ideal containing all polynomials p such that mp is contained in I for some monomial m. Is there an algorithm for computing I'?

Author:  hannes [ Tue Dec 01, 2015 5:06 pm ]
Post subject:  Re: a problem in arithmetic dynamics

That seems to be the ideal qotient:
I:<x_1,...x_n>:={f, with f*g in I and g in <x_1..x_n>}
or
Code:
quotient(I,maxideal(1))
.
For the algorithm see
http://www.mathematik.uni-kl.de/~zca/Reports_on_ca/02/paper_html/node29.html

Author:  timoe [ Wed Dec 02, 2015 8:24 pm ]
Post subject:  Re: a problem in arithmetic dynamics

Thank you for the answer. However, the given quotient does not in general agree with I'. For example, if I is generated by s2-s and d4e+s, then I' contains the polynomial s-1 which is not in quotient(I,maxideal(1)).

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