While I’m not Jason, there is no physical significance to n < -2 at least in beam bending. It’s possible they might be used in another context that I don’t know about, though. Since n=-2 is the limit of two Dirac delta functions of opposing directions a distance epsilon apart as epsilon goes to zero (which is a force couple and why it can represent a moment), I’m not sure if there’s even a convenient way to think about n<-2.
Personally, I don’t think there’s any real need to handle the n<-2 case. I’d raise an error if an operation was performed that gave it. If there’s a use for singularity functions in another context that requires that case it can be added. Plus, raising an error is useful in the event someone does an operation they shouldn’t for pure beam bending. Cheers, Tim. > On Mar 15, 2016, at 4:40 PM, SAMPAD SAHA <sampadsa...@gmail.com> wrote: > > Jason, > > I was googling about the Singularity Functions with exponents less than -2 , > but I found out that there is no significance of <x - a>^n for n <-2. It > also doesn't signifies anything while solving beam bending problem. > > So, do we need to implement anything for these functions? > > > ----------------- > Regards, > Sampad > > > > > > > > Regards > Sampad Kumar Saha > Mathematics and Computing > I.I.T. Kharagpur > > On Tue, Mar 15, 2016 at 8:57 PM, SAMPAD SAHA <sampadsa...@gmail.com> wrote: > Jason, > > Do we expect `simplify` ( a method under SingularityFunction class) to give > output like this: > > In [ ] : F = singularityFunc(x, 0, 1) + singularityFunc(x, 3, 2) > > In [ ] : F > > 2 > Out [ ] : <x> + <x - 3> > > > In [ ] : simplify(F) > > Out [ ] : > > 0 for x < 0 > x for 0 <= x < 3 > x + (x-3)^2 for x >= 3 > > > I think this would be cool implementation. > > -------------------- > Regards > Sampad > > > > > > Regards > Sampad Kumar Saha > Mathematics and Computing > I.I.T. Kharagpur > > On Mon, Mar 14, 2016 at 12:46 PM, SAMPAD SAHA <sampadsa...@gmail.com> wrote: > > > ---------- Forwarded message ---------- > From: SAMPAD SAHA <sampadsa...@gmail.com> > Date: Monday, March 14, 2016 > Subject: [sympy] GSoC 2016: Singularity Functions > To: sympy@googlegroups.com > > > Hi Jason, > > I have a confusion regarding the user inputs for the beam problems. > > I think that we should take only the Bending Moment Function (in the form of > singularity functions) and the boundary conditions as inputs. > > I mean to say that generally in a given beam bending problem, a diagram of a > beam and distributed loads are provided. So it is not possible to get these > data as an user input. Rather we can expect that the user would formulate the > bending moment function, in the form of Singularity function, and then > provide that function as an input for getting the elastic curve equation. > > Note:- Values of E , I , Boundary Conditions are also expected as an input. > > > I need your suggestions. > > > > ----------------- > Regards, > Sampad > > > > > > Regards > Sampad Kumar Saha > Mathematics and Computing > I.I.T. Kharagpur > > On Sat, Mar 12, 2016 at 11:50 AM, Aaron Meurer <asmeu...@gmail.com> wrote: > It should give (-1)**n*f^(n)(0) (that is, (-1)**n*diff(f(x), x, n).subs(x, > 0)), if I remember the formula correctly. > > Aaron Meurer > > On Fri, Mar 11, 2016 at 9:00 AM, SAMPAD SAHA <sampadsa...@gmail.com> wrote: > Hi Aaron, > > I have a doubt . > > Do we want: > > > integrate(f(x)*DiracDelta(x, n), (x, -oo, oo)) would output as > > <image.png> > > > > > > Regards > Sampad Kumar Saha > Mathematics and Computing > I.I.T. Kharagpur > > On Wed, Mar 9, 2016 at 3:11 AM, Aaron Meurer <asmeu...@gmail.com> wrote: > DiracDelta(x, k) gives the k-th derivative of DiracDelta(x) (or you > can write DiracDelta(x).diff(x, k)). > > It does look like the delta integrate routines could be improved here, though: > > In [2]: integrate(f(x)*DiracDelta(x), (x, -oo, oo)) > Out[2]: f(0) > > In [3]: integrate(f(x)*DiracDelta(x, 1), (x, -oo, oo)) > Out[3]: > ∞ > ⌠ > ⎮ f(x)⋅DiracDelta(x, 1) dx > ⌡ > -∞ > > Since the integration rules for derivatives of delta functions are > simple extensions of the rules for the delta function itself, this is > probably not difficult to fix. > > Aaron Meurer > > On Mon, Feb 29, 2016 at 3:39 AM, Tim Lahey <tim.la...@gmail.com> wrote: > > Hi, > > > > Singularity functions are actually extremely easy to implement given that > > we have a Dirac delta and Heaviside functions. Assuming that the Dirac > > delta and Heaviside functions properly handle calculus, it’s trivial to > > wrap them for use as singularity functions. The only thing that will need > > to be added is the derivative of the Dirac delta (assuming it’s not already > > there). I implemented singularity functions in Maple in less than an > > afternoon. > > > > I was a TA for a Mechanics of Deformable Solids course about 11 or 12 times > > and wrote it to help the students (as we have a site license for Maple). I > > also wrote a set of lecture notes on the topic. > > > > Cheers, > > > > Tim. > > > >> On Feb 26, 2016, at 4:29 PM, SAMPAD SAHA <sampadsa...@gmail.com> wrote: > >> > >> Hi Jason, > >> > >> Thank you for the explanation. It really helped me. > >> > >> So, basically we want to start it, firstly, by creating a module which > >> would deal with the mathematical operations performed on Singularity > >> Functions. After this whole module is prepared, we would focus on how to > >> use this module for solving beam problems. Am I correct? > >> > >> Can you please explain me in brief that what are the mathematical > >> operations we wanted to implement on that module? > >> > >> > >> On Friday, February 26, 2016 at 4:54:59 PM UTC+5:30, SAMPAD SAHA wrote: > >> > >> Hi, > >> > >> I am Sampad Kumar Saha , an Undergraduate Mathematics and Computing > >> Student at I.I.T. Kharagpur. > >> > >> I have gone through the idea page and I am interested in working on the > >> project named Singularity Function. > >> > >> By going through the Idea, I understood that we want to add a package to > >> Sympy which can be used for for solving beam bending stress and deflection > >> problems using singularity function. Am I correct? > >> > >> We can by this way:- > >> While solving we will be having the moment function as an input which we > >> can arrange in the form of singularity functions and then integrate it > >> twice to get the deflection curve and we can give the plot or the equation > >> obtained of deflection curve as an output. > >> > >> I have gone through some documents available on internet which have brief > >> studies on solving beam bending stress and deflection problems using > >> singularity functions. > >> > >> References:- > >> • Beam Deflection By Discontinuity Functions. > >> • Beam Equation Using Singularity Functions. > >> • Enhanced Student Learning in Engineering Courses with CAS > >> Technology. > >> Since there is just a brief idea given in the idea page, I have a doubt > >> that what are the things other than solving beam bending stress and > >> deflection problems to be implemented in the project? > >> > >> Any type of suggestions are welcome. > >> > >> ========================================================================================================================================== > >> Regards > >> Sampad Kumar Saha > >> Mathematics and Computing > >> I.I.T. Kharagpur > >> > >> -- > >> 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 https://groups.google.com/group/sympy. > >> To view this discussion on the web visit > >> https://groups.google.com/d/msgid/sympy/7cbe2101-fd59-484b-9e25-f563636d6366%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. > > 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 https://groups.google.com/group/sympy. > > To view this discussion on the web visit > > https://groups.google.com/d/msgid/sympy/1795A385-4AEA-44FD-BEE8-8115D53DA14B%40gmail.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. > 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 https://groups.google.com/group/sympy. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/CAKgW%3D6JiW6zhx%3DcTahjcugKaR3jOTrYOnFJWYRr-%2BNiS-2zcLQ%40mail.gmail.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. > 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 https://groups.google.com/group/sympy. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/CANzav4HrH7YbrOm4%3D9s2%2BHevCnCv4vz1RbuU%2BZWwLWLnCZpbcw%40mail.gmail.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. > 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 https://groups.google.com/group/sympy. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/CAKgW%3D6KrEOoZ-CvGJ_HTBVSpTLVkW6geUfvXdP8GAiBNO4y8qQ%40mail.gmail.com. > > For more options, visit https://groups.google.com/d/optout. > > > > > -- > Regards > Sampad Kumar Saha > Mathematics and Computing > I.I.T. 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