Re: [fricas-devel] traps in working with powerseries
> > 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. > 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. OK. -- Waldek Hebisch -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
Re: [fricas-devel] traps in working with powerseries
On 11/29/18 3:48 AM, Andrey G. Grozin wrote: > On Wed, 28 Nov 2018, Ralf Hemmecke wrote: >> 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 >> > I suppose the same is true for sinx^2+cosx^2, where sinx and cosx are > the series for sin(x) and cos(x), right? >From the type of series that you get, certainly. But the problem ist not the series itself, it comes from what "terms" has to return. In other words, if for c=p*p' or c=sinx^2+cosx^2, then one can compute coefficient(c, n) for any natural number n without any problem. The internal representation of the series makes this possible even in the case of SparseUnivariateTaylorSeries, which is supposed to store only non-zero terms. The trick is that internally, it stores additionally a value that corresponds to the biggest power it is ever asked for. Since that entry is ignored by the returned stream of "terms", the above problem arises. It's, of course, bad for naive programming, but unavoidable. So instead of "series terms c", one would have to do something like "series coefficients c". Bad luck, if the (other) series you work with are very very sparse. My original problem, for example, was to create from f(n) a subseries f(m*n) for some natural number m. > > Andrey > -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
Re: [fricas-devel] traps in working with powerseries
On Wed, 28 Nov 2018, Ralf Hemmecke wrote: 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 I suppose the same is true for sinx^2+cosx^2, where sinx and cosx are the series for sin(x) and cos(x), right? Andrey -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
