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: preds (ex-e6b227)

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

Run in calculatorCopy input