> - Your example > > In[]: soln = solve(sin(x)*sin(y), (x, y), input_set = Interval(0, > 4)*Interval(0, 4)) > > is a bit confusing to me. The input_set argument gives a 2-dimensional > set, but how are you to know which axis is x and which is y?
The axis is determined by the order of variables in which they appear in the argument of solve. Defining the input set in this way will give us special advantage of being able to take values from the sets which are traditionally hard to define. For example if we want the variable to come from a circle we can do it like. In[]: solve(f(x, y), (x, y), input_set = imageset((x, y), x**2 + y**2 < 1, S.Reals*S.Reals)) For a L shape domain we can do In[]: solve(f(x, y), (x, y), input_set = Intersection(Interval(0, 2)*Interval(0, 3), Interval(1, 2)*Interval(1, 3)) I cannot be sure that sets will be able to seamlessly handle such sets, but I really think this API will scale. > What about the input API? > > solve(f, *symbols, dict=False, set=False, exclude=(), check=True, > numerical=True, minimal=False, warning=False, simplify=True, > force=False, rational=True, manual=False, implicit=False, > minimal=False, quick=False) I think most of the flags are not needed. The flags like `dict` and `set`, won't be need as we are unifying the output to set. Do we have any estimate of how many of these flags are actually used by users? > - You talk a lot about using sets, which I think is a good idea. But > you should think about how you can also use the assumptions. Maybe > there is a clean way that we can go back and forth between assumptions > and sets that requires minimal code duplication, and also allows each > to take advantage of the algorithms implemented in the other (by the > way, when I say assumptions, you should probably only worry about the > new assumptions, i.e., the stuff in the Q object). As mentioned in the comment by Matthew https://github.com/sympy/sympy/pull/2948#issuecomment-36592347 Assumptions can answer questions like if k is in N, is k*(k+1)/2 in N? This will clearly help in resolving some of the set operations. btw I think assumptions is wrong in this result. In [20]: with assuming(Q.integer(k/2)): ...: print(k in S.Integers) ...: False > - How will we handle that situation (finding all solutions)? What if > we can't say anything? Can we still represent objects in such a way > that it is not wrong (basically by somehow saying, "here are 'some' of > the solutions, but maybe not all of them", and ditto for anything that > uses solve, like singularities)? Maybe Piecewise is sufficient > somehow? We will return a set as a solution if and only if we have found all the solutions in the given domain. For every other case we will be using the unevaluated Solve object. We will have a attribute in the unevaluated solve named "know_solutions" to say "here are some solutions". Yes Picewise might be helpful, but for now I can't think of a clear way to say "assuming this parameter 'a' is positive the solutions are ..." > Do the radical denesting algorithms > work with symbolic entries as well? I don't think so. > - Did you plan to add any new solvers? I think there are still quite a > few cases that we can't solve. Some higher degree irreducible > polynomials for instance (not all higher degree polynomials are > solvable by radicals but some are). There will also be a lot to > implement once we are able to even represent the solutions to > sin(x)=0. There was one algorithm I discussed on the discussion https://github.com/sympy/sympy/pull/2948#issuecomment-36970134. By that algo we will be able to solve some special cases like `sin(x) == x`. I will implement that and we might come up with new algorithm in the process of rewriting current solvers. If time permits I'll surely try to implement new solvers. -- 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. 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/CADN8iuq9aVesJzFFE0wpG9_eJd6C7RW-7Lb%2BRZ3OHA4AXP1yXA%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
