On Monday, March 2, 2015 at 12:33:51 AM UTC+5:30, Aaron Meurer wrote: > > On Sat, Feb 28, 2015 at 10:53 PM, AMiT Kumar <dtu....@gmail.com > <javascript:>> wrote: > > One correction: > > * System of Multivariate Equations: > > We CAN implement this for comparatively lower order polynomial in new > > solveset. > > > > The only thing We can't implement is Multivariate inequalities, as we > will > > need CAD for that. > > It's still a good idea to think about them when designing the APIs, as > we will hopefully eventually get a CAD implementation. >
Indeed. I agree on that. > Aaron Meurer > > > > > > > On Friday, February 27, 2015 at 6:58:51 PM UTC+5:30, AMiT Kumar wrote: > >> > >> 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 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 > >> (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+un...@googlegroups.com <javascript:>. > > To post to this group, send email to sy...@googlegroups.com > <javascript:>. > > Visit this group at http://groups.google.com/group/sympy. > > To view this discussion on the web visit > > > https://groups.google.com/d/msgid/sympy/de89e1e3-d053-439d-bb9a-32777f3a6b80%40googlegroups.com. > > > > > > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sympy" group. 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