Re: [sage-devel] Re: integration algorithms

2017-03-21 Thread rjf
On Monday, March 20, 2017 at 11:50:00 PM UTC-7, parisse wrote: > > I think that people who never wrote symbolic integration algorithms > underestimate the work required (this is also true in other areas, for > example simplification, UI, etc.). I believe that the current symbolic > integration

Re: [sage-devel] Re: integration algorithms

2017-03-20 Thread parisse
I think that people who never wrote symbolic integration algorithms underestimate the work required (this is also true in other areas, for example simplification, UI, etc.). I believe that the current symbolic integration implementations are good enough whatever you choose in Maxima, Axiom flav

Re: [sage-devel] Re: integration algorithms

2017-03-20 Thread William Stein
On Mon, Mar 20, 2017 at 10:01 PM, rjf wrote: > People have been working on computer programs for integration since about > 1961. There are > at least 8 PhD theses on the topic. > > If you think there is "low hanging fruit" like writing a better > simplification program, or > using binary search

Re: [sage-devel] Re: integration algorithms

2017-03-01 Thread rjf
Maxima's version of Risch is about 13 pages of code, not counting some material that may reside in other files having to do with finding appropriate algebraic or transcendental extensions. I suspect no one has looked at it seriously in 40 years. On Wednesday, March 1, 2017 at 1:26:04 PM UTC-8

Re: [sage-devel] Re: integration algorithms

2017-03-01 Thread hebisch
W dniu wtorek, 28 lutego 2017 09:03:52 UTC użytkownik Dima Pasechnik napisał: > > The problem with Risch "algorithm" is that's not very implementable. > No system ever had a complete implementation; it's true that results and > implementations by Manuel Bronstein >

Re: [sage-devel] Re: integration algorithms

2017-02-28 Thread Dima Pasechnik
Fricas does some integrals very well (also, gives more compact form, as it does not introduce as many field extensions as other packages), and some pretty badly. IMHO one first has to classify the integrals and only then choose a good backend. On Tuesday, February 28, 2017 at 9:21:35 AM UTC, Ra

Re: [sage-devel] Re: integration algorithms

2017-02-28 Thread Ralf Stephan
Assuming the Fricas implementation is as good as Axiom's, would this alone not be enough reason to make Fricas a standard package (and call it first when integrating)? On Tue, Feb 28, 2017 at 10:03 AM Dima Pasechnik wrote: > The problem with Risch "algorithm" is that's not very implementable. >

Re: [sage-devel] Re: integration algorithms

2017-02-28 Thread Dima Pasechnik
The problem with Risch "algorithm" is that's not very implementable. No system ever had a complete implementation; it's true that results and implementations by Manuel Bronstein (this is a memorial page, for he died 12 years ago)

Re: [sage-devel] Re: integration algorithms

2017-02-28 Thread Ralf Stephan
Fricas was forked from Axiom, according to https://en.wikipedia.org/wiki/Axiom_(computer_algebra_system)#History and Axiom had the complete Risch algorithm implemented. On Tue, Feb 28, 2017 at 9:01 AM Thierry Dumont wrote: > Following https://en.wikipedia.org/wiki/Risch_algorithm ,the Risch > al

Re: [sage-devel] Re: integration algorithms

2017-02-28 Thread Thierry Dumont
Following https://en.wikipedia.org/wiki/Risch_algorithm ,the Risch algorithm is able to find an antiderivative of: x |-> x/sqrt(x^4+10*x^2-96*x-71) but not of: x |-> x/sqrt(x^4+10*x^2-96*x-72) . What can do Sage? # fok(x)=x/sqrt(x^4+10*x^

Re: [sage-devel] Re: integration algorithms

2017-02-27 Thread Ralf Stephan
Rubi should rather be seen as a useful collection of knowledge that can be implemented in different ways. I encourage the Maxima authors to e.g. have a look at Rubi's chapter 1.2.1. They seem to have completely missed that the integral of (a+bx+cx^2)^p, p rational, has a general solution in terms o