Dear Marik, > Burcin wrote: > I really dislike the idea of adding a new function for each > functionality of this kind. This makes it very hard for users to > figure out the function name they need for a specific task. > > We should be able to provide an interface to all these "rewriting" > tasks through a few conceptually defined methods like rewrite(), expand > () and combine()( or contract()?). > > Francois Maltey had a proposal for a possible interface to all this. > Maybe he can comment here, or we can discuss his proposal on sage- > devel. > ------------------------------ > > > It would be great to find some simple and clean solution which gives > access to many posibilities included in Maxima or/and other CAS. I > think that if we take into account the many possibilities how to > simplify expressions, it will be difficult to do this job. > I dislike simplify word.
Look at theses 2 examples : what is the simplified formula . 2*cos(x)^2-1 : you wait the combined formula cos(2*x) cos(2*x)+1 : you wait the expanded formula 2*cos(x)^2 a simplify function must have a purpose. This purpose is only in the user mind, not in any computer algebra algorithms. But expand has a clean description : An expand formula has more transcendent function calls with smaller arguments. sin (x+y) == sin(x)*cos(y)+cos(x)*sin(y) The opposite way may be a combine or a contract function : less transcendent call but larger arguments : combine(exp(a)^3/exp(b))=exp(3*a-b). > I do not like the approach in Maple and Mathematica, where > user has one big command for many simplifications and it is not easy > to find out, what to do, if we do not want to use some of > simplifications and rewriting rules included in this big command. > Please, let me have the opposite taste. I can only record a very small number of functions in my mind. I also can explain a little number of theory to my students. So I prefer choose a complete theory or a large transform and then refine it by options or examples. In your case, it may be possible to add optional parameters to expand functions. By example you may choose a target : only logarithms or trigonometric functions. Burcin proposed a target parameter. So imagine a Sage 4.xyz with y = log(2)+log(3)+exp(2)*exp(3) contract (y) # log(6)+exp(5) contract(y, target=log) # log(6)+exp(2)*exp(3) contract(y, target=exp) # log(2)+log(3)+exp(5) An other option may be a predicate select in order to restrain the tested subexpression. contract (exp(x+1)*exp(x-1)*exp(y), target=exp, select=lambda subexpr : has(subexpr, x)) # the answer will be exp(2*x)*exp(y) And the last option may add a mainBranchCut option. In a normal (complex) calculus it's impossible to simplify log(x)+log(y) to log(x*y). Try with x=y=-1. But a mainBranchCut option overwrite the general rule and suppose the right hypothesis to get log(x*y), and 1/2*log(x) give log(sqrt(x)). > I think that it is better to have small functions which do their small > job - they do what the user wants. I think that this is Maxima > approach. > It's very difficult to have an complete view of maxima rules. There are too many functions. With only one function, the help docstring can explains all the refinement options. And options in a main functions can make the (only one) little transforms you want to apply. You don't like maple way because I don't think that maple has this ability to restrain the convert transform. > If such a complete solution for rewriting tasks appears, it would be > great to give to the users enough power for fine tunning, like current > expand_trig(). > An other question : How theses rewriting rules may be coded : 1/ With maxima kernel call ? 2/ In Ginac library ? 3/ By a sage interpreter call ? My vote goes to the number-3/. I don't like maxima method with its numerous flags. Look at the previous mail in sage-support about integrate (sqrt(sin(x)^2+cos(x)^2), x, 0, 2*pi) = only pi because there was a little change to an inner flag of maxima. The 2/ way is the longer method. If I want to code it I must learn sage and also the ginac code. This method looks like to the axiom(s) language. A function can be right for the interpreter language, but it takes hours and hours to code it in the axiom kernel with other compiled rules.(1) The 3/ is the easiest way to read and to understand the code. When you read sage files then you understand its functions. It's almost the maple way with "the verbose option and print the function" and it was the mupad way. Bug are easiest to find. Interpreted code isn't so slow, you may wait 1 second more, and there is less wasted time than in (1). --~--~---------~--~----~------------~-------~--~----~ To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
