Hi, I was trying to explore solvers for multivariate functions in other CAS like Maple and Mathematica and Maxima, Here is the documentation I found about solvers in Maxima: https://github.com/andrejv/maxima/blob/master/share/algebra/solver/solver1-en.html
I think we need to be very specific about the problem set we are going to tackle for 'Multivariate Functions' in the solveset. Here are the cases where we encounter Multivariate Functions: * System of Multivariate Equations: This is a lot of work <https://github.com/sympy/sympy/wiki/GSoC-2015-Ideas#multivariate-polynomials-and-factorization>in the Polynomials module, which needs to be done, before addressing it in solvers. * Multivariate Inequalities: This can also not be addressed in solvers until we have CAD <https://github.com/sympy/sympy/wiki/GSoC-2015-Ideas#cylindrical-algebraic-decomposition> (Cylindrical Algebraic Decomposition), which is itself a GSoC Project. The couple of cases which are in the scope of current discussion are: * Multivariate Single Equation with Point solution. We can only solve equations which are of the form (x - a)*(y - b)*(z - c)*... or convertible to this form. Though other popular CAS are also not good for solving equations other than this form. If we don't know the solution we can just return it in terms of other variables as in next case. * Multivariate Single Equation with non-point solution. In this case, we can output results in the form of the other variables: For Example: In []: solve(x**2 + y**3 == 1, (x, y)) Out[]: {x, sqrt(1 - y**3)} # x: arbitrary Similiar to Wolframalpha: http://www.wolframalpha.com/input/?i=solve%28x**2+%2B+y**2+%3D%3D+1%29 Or else in this case we could have some functionality for curve detection (maybe using geometry module), to return information about curves in cases like: In []: solve(x**2 + y**2 == 4) Out[]: {Circle, (0, 0), 2} (as Here we know that the output: x = +/-sqrt(y**2 - 1) is not of much significance.) We need not worry much about multivariate, the focus should be more on: 1) Solving Transcendental equations, such as 'Equation solvable by LambertW. 2) Linear Systems (system of linear equations) 3) Modularising the current code. 4) What else set infrastructure we need. I would also like to discuss more about the sub-modules in which the current solve needs to broken, such as: linear systems, transcendental Equations, etc. AMiT Kumar 3rd Year Undergrad Delhi Technological University www.iamit.in On Friday, February 6, 2015 at 12:08:45 AM UTC+5:30, AMiT Kumar wrote: > > Hi, > I am AMiT Kumar, I would be GSoC Applicant to SymPy this year. I have been > following the SymPy Community for quite sometime now and have also got > around 11-12 patches Merged in the Code base. So, now, I have got a decent > idea of `How things works`. > > I would like to work on Solvers as Mentioned on the Ideas Page. Last year > Harsh Gupta did a very good job by Rewriting the Univariate solvers > (solveset.py), I have gone through his work. After having conversation with > him and digging into solveset, I got to know there is still a lot of work > which needs to be done. > > I could see a couple of entry points on the Ideas page: > https://github.com/sympy/sympy/issues/8725 (I have Merged a PR for this) > https://github.com/sympy/sympy/issues/8711 (Replace all internal solve() > calls with solveset() ): TODO > > Things, I would like to implement in solveset includes: > > Multivariate Equation solving: > > I think for solving multivariate equations, the order of variables should > be given as input, so that we don't need to have a dict as output and we > can return Set, as if we automatically detect variables, we need to output > the dict of results. > > - Multivariate functions with non point solution: (solvemv) > - > > In [0] solveset((x - 1)*(y - 2), (x, y)) > Out[1] {{1, arbitrary}, {arbitrary, 2}} > > > or we may return: > > Out[1] {{1, (-oo, oo)}, {(-oo, oo), 2}} > > > > - Multivariate functions with point solutions: (solvemv) > > > > - > > In [0] solveset(x**2 + y**2, (x, y)) > Out[1] {0, 0} > > > Solve System of Equation: (solvesys) > (For system of Equation, we can have this): > > > - > > In [0] solveset([x + y == 1, x - y == 0], (x,y)) > Out[1] {{1/2, 1/2}} > > - For inequality solver (or for solvers in general) we also need to > extend singularities module (though useful in general), so as to prevent > getting wrong results, caused due to incorrect simplification of > expression, as we saw in this issue: > https://github.com/sympy/sympy/issues/8715 , Example: x + 1/x > -2 + > 1/x this inequality is written as expr = expr. lhs - expr.rhs , which > cancels 1/x and gives wrong result, by including singular point in the > solution. > - inequality solver in solveset currently uses inequalities.py > (dependent on solve) (some discussion here: > https://groups.google.com/forum/#!topic/sympy/Yp5NqrXmp2U). It is > related to the next point below. > - All internal solve() calls needs to be replaced with solveset() , this > is very important for bringing out the solveset from sandbox to > eventually replace solve(). (we need to consider the output API > (return type) also while replacing). > - We also need to extend the set - boolean (relational) conversion > methods to handle multivariate variables. > - Complex set Infrastructure is also not there (though I see a WIP PR > for that), and yes we also need to see what other set capabilities we need > to implement to support various other kinds of solutions. > > And also other solvers as mentioned on ideas page like 'Equations > solvable by LambertW function' also needs to work. > > I would love to get feedback from the community before presenting my > proposal. > > Cheers! > AMiT Kumar > 3rd Year Undergrad > Delhi Technological University > www.iamit.in > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To post to this group, send email to sympy@googlegroups.com. 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