We might try to a rule based system to determine the points of possible discontinuity. For example the poles can occur only on roots of f(x) for a given function log(f(x)), and roots of g(x) if the given function is f(x)/g(x) and for all those points we might test the continuity using limits. For piecewise functions we should also test at the boundaries of the intervals of definition. Unless the function is bizarrely defined we will only have finite points to check for discontinuity.
> On Friday, 3 May 2013 06:29:58 UTC+5:30, Paanini Navilekar wrote: > Hi, > > Since I haven't formally introduced myself, I'm Paanini Navilekar, a final > year student of Electrical Engineering at BITS-Pilani, Goa Campus in India. > I've been using Python for small scripts and automation tasks around my > computer, but I've never worked on a large-scale project before. > > While trying to implement an algorithm for solving ODE's by separating > them into functions of its variables ( > http://webs.uvigo.es/angelcid/Archivos/Papers/IJMEST.pdf), I came across > an idea for an enhancement: a feature that lets you *find the domain and > range of a given function*. This would need to handle a lot of edge > cases, mainly for the different types of functions, such as polynomial, > exponential, transcendental, logarithmic etc. > > Since this may or may not be enough for a summer's worth of coding, I'd > like to suggest a related idea, from the 'Ideas' section of the Ideas Page: > Singularity Analysis and Continuity Tests. This would entail, > > 1. Finding and classifying all points of singularity in the graph of the > function (not necessarily *using* the graph, though) > > 2. Finding all points of continuity in the function (if any), and checking > if the function is continuous at a given point or a given interval. > > I'd like to make it a comprehensive project, that covers as many cases as > possible, so it should be easy to retrieve basic information about a > function such as its domain/range and information about the nature of the > graph of the function with regards to continuity and singularity. This > information may turn out to be of use in other areas of Sympy. > > Any feedback on the idea would be greatly appreciated. > > Thanking You, > > Paanini Navilekar > BITS-Pilani, Goa Campus > > -- 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sympy. For more options, visit https://groups.google.com/groups/opt_out.
