find singularities for any expression #2925
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| singularity in the following even though it is not in the domain of | ||
| the expression (which is {x | x < 1}). | ||
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| >>> singularities(log(1 - x)/(x - 2)) |
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Why you won't count x=1 as well?
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x=1 is not in log's domain
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it's a branch point for log(1-x), right?
| >>> from sympy import Symbol | ||
| >>> x = Symbol('x', real=True) | ||
| >>> from sympy import Symbol, log | ||
| >>> from sympy.abc import x |
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Do we always prefer from sympy.abc import x over x = Symbol('x')? Does it have any particular advantage?
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importing from abc is pretty common and a good visual reminder that you are getting vanilla symbols when you do so
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@smichr We had a more general implementation of singularities at #2723 but then we decided to stick to rational functions because the current solve is not reliable enough. We were using There are a lot of comments in that PR and many of them might not be useful to you. You can see this #2723 (comment) and subsequent comments. I also branched out that implementation of |
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On Tue, Feb 18, 2014 at 08:56:18AM -0800, Harsh Gupta wrote:
The problem was not in the solve, but in this "more general |
| >>> singularities(1/(1/x - 1), strict=True) | ||
| (0, 1) | ||
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| If `poles` is Truen then points at which functions are undefined will |
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@hargup do you think you can support and perhaps work from the changes I have made here? (This PR has been updated since your last comment.) Note, too, that something like the following can help with finding poles: But I think the thing that needs to be done is for all functions to define their poles since I think it's conceivable that finding where the 1/derivative = 0 may lead to a function that can't be solved, e.g. Note that setting check to False can help in finding solutions from solve: |
If `poles` is True and the function is not rational, an error will be raised; if False, all values of `sym` that set any denominator to zero are returned. If `strict` is False (default) then removable singularities are not reported: 1/(1/x - 1) is not defined for x in (0, 1) but only 1 is returned with the default setting for `strict`.
Yes, that was suggested in #2723 (comment). I think - (1) branch points and (2) essential singularities should be defined on a per-function basis. For (3) poles - we can use solve (and, probably, cache this information and represent it as a property of the function). |
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@skirpichev , the default behavior is as it was before. There is now an option to get singularities of non-rational functions and to return removable singularities. Does this look ok now? |
| for d in denoms(expr, [sym]): | ||
| rv.update(solve(d, sym)) | ||
| # XXX add in poles | ||
| if poles and not expr.is_rational_function(sym): |
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You should move this up.
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Good points, @skirpichev . @hargup is probably a better one to make these changes, so feel free to modify and use at will. Regarding the use of together: yes, that is a good way to handle rational functions. |
Yes I'm willing to work on it in future, but for now I want to work on making |
poleswas added as a keyword; when False it allows the singularites of non-rational expressions to be returned.together, rather than simplify, is now used and solve is applied only on extracted denominators