Predicates

The following functions provide decision algorithms for algebraic power series. They may involve recursive resultant computations, hence, have a high complexity and should be used with care.

IsZero(s) : RngPowAlgElt -> BoolElt
Decides if the series is zero.
s eq t : RngPowAlgElt, RngPowAlgElt -> BoolElt
Decides if two series are equal.
IsPolynomial(s) : RngPowAlgElt -> BoolElt, RngMPolElt
Decides whether the series is actually a polynomial (with integral exponents) in the multivariate polynomial domain as returned by Domain(s). In the positive case also returns that polynomial. This function relies on SimplifyRep.

Example RngPowAlg_preds (H52E4)

The previous computations suggest that h2 is 1, in particular it is polynomial (in contrast to h1). In this case h3 would be zero. 
> IsPolynomial(h1);
false
> IsPolynomial(h2);
true 1
> IsEqual(h2, PolyToSeries(One(Qxy)));
true
> IsZero(h3);
true
V2.28, 13 July 2023