Hi,
working with powerseries has quite some traps.
Suppose, p is an infinite powerseries and p' is it's inverse. Then
c=p*p' is a series that only has zero coefficients after the constant term.
Then creating the stream of (coefficient, exponent)-pairs, i.e. calling
terms(c) leads to a stream that cannot compute its second entry.
http://fricas.github.io/api/UnivariatePowerSeriesCategory.html#l-univariate-power-series-category-terms
Z ==> Integer
Q ==> Fraction Z
L ==> UnivariateLaurentSeries(Q, 't, 0)
t := monomial(1$Q,1)$L
p := 1/(1-t)
pp := 1/p
c := p*pp
s := terms c;
s.1
s.2
Yes, it's clear that it cannot return anything, because it is just
looking for the next non-zero coefficient (which doesn't exist).
Nevertheless, wouldn't it be advantageous to add a remark to the
specification of the terms function that one should be careful with
series that are not (constructively) known to be finite.
For example
series terms c
does not give a laurent series that one can ask for the second coefficient.
Proposed patch is attached.
Opinions?
Ralf
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From fb5bd8b27e4067c9adaa692d853298f4e5e84688 Mon Sep 17 00:00:00 2001
From: Ralf Hemmecke <r...@hemmecke.org>
Date: Wed, 28 Nov 2018 19:07:04 +0100
Subject: add warning to "terms" function documentation
---
src/algebra/pscat.spad | 3 +++
1 file changed, 3 insertions(+)
diff --git a/src/algebra/pscat.spad b/src/algebra/pscat.spad
index 7cdd62e6..6a7dfbe4 100644
--- a/src/algebra/pscat.spad
+++ b/src/algebra/pscat.spad
@@ -85,6 +85,9 @@ UnivariatePowerSeriesCategory(Coef, Expon) : Category == Definition where
++ \spad{terms(f(x))} returns a stream of non-zero terms, where a
++ a term is an exponent-coefficient pair. The terms in the stream
++ are ordered by increasing order of exponents.
+ ++ Warning: If the series f has only finitely many non-zero terms,
+ ++ then accessing the resulting stream might lead to an infinite
+ ++ search for the next non-zero coefficient.
--series: Stream Term -> %
--++ \spad{series(st)} creates a series from a stream of non-zero terms,
--++ where a term is an exponent-coefficient pair. The terms in the
--
2.17.1
