[GAP Forum] manipulating polynomials

[kroeker]

Dear Forum and dear Alexander,


recently Marc Bogaerds asked how to get the constant term of a polynomial.
Instead of using ExtRepPolynomialRatFun directly it is thinkable  to 
provide additional functions like 'ConstantTerm' or 
'CoefficientOfPolynomial'

Now you may ask why this is useful?
The core GAP polynomial manipulation function set is sufficient but very 
basic. Extensive polynomial manipulation using ExtRepPolynomialRatFun 
would be very tedious and computationally expensive
( e.g. coefficient access compexity) and I experienced this in a recent 
join project to compute Hurwitz map approximations.

An example and working definition for 'ConstantTerm' and 
'CoefficientOfPolynomial' is attached. In fact, I defined even more 
useful functions as attached
(e.g. evaluating/differentiating a polynomial tensor,
coercing polynomials to different rings,
counting variables appeared in a polynomial,
a more handy format for factors of a polynomial in comparison to 
'Factors', etc.)

Please let me know, if you would like to see some this functions in a 
special package or in the GAP core
or whatever.



Best,


Jakob






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