That's exactly what SymPy is doing. You can look at the design document, if you are interested:
http://code.google.com/p/sympy/wiki/HowItWorks You can also look at ginac, they are basically doing the same as SymPy (only a little more complicated). But the basic things like x+y+x = 2*x+y is SAGE doing as well, at least if I understand it correctly, the relevant code is in: devel/sage/sage/structure/element.pyx see the method: RingElement.__mul__() and RingElement.__add__() and the documentation at the top of the module. Ondrej On 4/30/07, Joshua Kantor <[EMAIL PROTECTED]> wrote: > > I am actually interested in the internal representations and > manipulation required to do this sort of thing. I.e. how would one > duplicate the internal workings of maxima in python. > > > Josh > > On Apr 29, 10:21 pm, Michel <[EMAIL PROTECTED]> wrote: > > The way maxima works that from the view point > > of the user there are very few automatic simplifications. > > There are however a lot of "expression manipulation commands" like > > "expand", > > "ratsimp", "factor", "trigexpand" etc... > > > > Some automatic simplifications are 12+14=26, x+x=2*x. > > > > Internally of course such manipulations are done a lot. Maxima > > uses a trick that if a subexpression has been simplified then > > a flag is added to that expression so that it is not resimplified > > again. > > > > Also noteworthy is that maxima makes a distinction between > > evaluation and simplification. Evaluation replaces > > variables by their values. Simplification replaces > > an expression by an equivalent one, independently of > > variable bindings. > > > > Somewhat strangely evaluation is not recursive which > > sometimes leads to counterintuitive behaviour. > > > > Michel > > > > On Apr 30, 6:22 am, Joshua Kantor <[EMAIL PROTECTED]> wrote: > > > > > Disclaimer: I think this may have more or less been covered in the > > > earlier mega-discussion on symbolic computation. Also the whole reason > > > we use maxima is to avoid dealing with the problems I'm describing but > > > I still > > > would like to think about it a bit and am curious if anyone has any > > > insight. > > > > > I have been thinking a lot about symbolic algebra. I was thinking > > > about what would be required to do symbolic manipulations without > > > using maxima. If we represent symbolic expressions as trees of > > > operations and operands > > > then it seems what is needed is some sort of ability to define rules > > > to transform trees. > > > > > I will represent trees as lists in lisp notation so [+ a b] is the > > > tree > > > > > a > > > / > > > / > > > + > > > \ > > > \ > > > b > > > > > Consider a + b +a, this will be stored as [+ a [+ b a]] (or maybe [+ > > > [+a b] a] ) > > > > > Obviously this should become 2*a + b > > > > > If we could define rules that > > > > > [+ a b] = [+ b a] > > > [+ [+ a b] c] = [+ a [+ b c]] > > > [* 1 a] = a > > > [+ a [* c a ]] = [* (c+1) c] > > > > > then we could make this simplification, however even in this simple > > > case, I don't really know how one would automatically do this > > > simplification. > > > > > Perhaps one could make a rule that multiplication is simpler than > > > addition, squaring is simpler than multiplication, etc and rank the > > > expressions by their complexity under this ranking and search for > > > simpler expressions, > > > i.e. since we would find a way to replace an addition by a > > > multiplication, 2*a+b is a simpler expression. > > > > > We would also need pattern matching capabilities to deal with sub- > > > expressions. > > > > > i.e. we should be able to infer that > > > > > [+ a [+ b c] ] = [+ [+ b c] a] > > > > > and matching [+ a [+ b c] ] to an abstract expresion of the form of > > > the first rule above. > > > > > Does anybody know how this works in general. > > > > > Josh > > > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
