Hi, On Tue, 24 Apr 2001, Pearu Peterson wrote:
1) Having relational::get_operator() would be useful (read: necessary) for extensions that can perform symbolic operations like (a < b) && (b > a) -> a < b
There are currently no intentions to target such operations within GiNaC and I don't know anything about the algorithms involved once you get to the nontrivial cases. Be warned: RJF has recently informed somebody on sci.math.symbolic that this is still an ongoing field of research. But for cases of interfacing like yours, yes, we should add something. Patch suggestion? Maybe relational should even be sub-classed???
2) If a,b are compatible pseries then ex(a) * ex(b) would automatically produce ex(a.mul_series(b)) The same for operations +,-,scalar_mul,scalar_div. If a,b are incompatible, then apply current behaviour (that is, do nothing).
I have implemented this behaviour in the GiNaC->Python interface but it does not cover cases where multiplication is carried out inside GiNaC functions. I am thinking of applications where, for example, a matrix consists of compatible pseries and the task is to find its inverse.
To do this in an automated way would probably become quiet involved from the complexity point of view. What is so wrong about reexpanding the pseries? What other cases are there where this happens internally? In the matrix case: can't you just iterate through it and reexpand the elements and assemble a new matrix in case there really _are_ series objects involved?
3) If a,b are compatible matrices (for a given operation) then ex(a) * ex(b) -> ex(a.mul(b)) The same for operations +,-,scalar_mul,scalar_div.
Matrices as derived from basic obey the equivalence relation established by the .compare(). This has some funny consequences. Let A be any n x m matrix. Let B be the same n x m matrix. Compute A-B. You'll get 0, yet not the n x m zero matrix but a plain scalar ex(numeric(0)) by the rules of add::eval(). Incidentally, this happens in Maple too more or less, where for any matrix A you have A - A -> 0. Since multiplication of matrices is O(n^x) where 2<x<3 we had decided a while ago that the rule you are suggesting should not be applied but matrices should be left as unevaluated until somebody triggers full matrix evaluation, maybe by calling a (not yet present) ex::evalm(). This may be somewhat confusing for the novice but should really be considered a feature since it allows us to produce an n x n matrix A, later produce B = pow(A,-1) and then A*B will evaluate to 1 without expensive matrix inversion going on under the hood -- unless of course one says B = pow(A,-1).evalm() and then A*B. Regards -richy. -- Richard Kreckel <Richard.Kreckel@Uni-Mainz.DE> <http://wwwthep.physik.uni-mainz.de/~kreckel/>