Yah, you are right multiplication of singularity functions are not needed for solving beam problems. Mathematically, it is also not used that much. So lets leave this multiplication and powers part.
I was thinking about the *integrate *and *diff* methods. I feel that we should define instance methods *diff *and * integrate * in the singularity function module which would internally use the existing *diff *and *integrate* function for Differentiation and Integration respectively. I need your suggestions. Regards Sampad Kumar Saha Mathematics and Computing I.I.T. Kharagpur On Fri, Mar 18, 2016 at 3:14 AM, Jason Moore <[email protected]> wrote: > I think you need to override the operators. I'm not sure if multiplying > singularity functions is needed (at least for beam problems), even if it is > mathematically correct, you don't have to implement it. If it is easy to > implement then, sure, do so. > > > Jason > moorepants.info > +01 530-601-9791 > > On Thu, Mar 17, 2016 at 1:34 PM, SAMPAD SAHA <[email protected]> > wrote: > >> >> Jason, >> >> For implementing Additon , Multiplication Do we need to over ride *__mul__ >> *, *__add__* these methods inside the class *SingularityFunction *or we >> can just use *simplify *for getting the results. >> >> I am really confused. >> >> >> >> Regards >> Sampad Kumar Saha >> Mathematics and Computing >> I.I.T. Kharagpur >> >> On Fri, Mar 18, 2016 at 1:59 AM, SAMPAD SAHA <[email protected]> >> wrote: >> >>> >>> I was thinking about multiplication of two singularity functions. It is >>> possible and it is mathematically significant. We can implement this too in >>> Sympy. Similarly with powers. >>> >>> I need your suggestions. >>> >>> >>> >>> >>> Regards >>> Sampad Kumar Saha >>> Mathematics and Computing >>> I.I.T. Kharagpur >>> >>> On Wed, Mar 16, 2016 at 9:41 PM, SAMPAD SAHA <[email protected]> >>> wrote: >>> >>>> Yah , You are right . A software having good documentations about all >>>> the functionality is preffered more over the others by the users. I will be >>>> spending a good amount of time in preparing the documentation citing plenty >>>> of examples and tutorials. >>>> >>>> Here >>>> <https://github.com/sympy/sympy/wiki/GSoC-2016-Application-Sampad-Kumar-Saha-:-Singularity-Functions> >>>> is >>>> link to my proposal. I have almost added all the things which we have >>>> disscussed. I still need to add the example and many more "TODO"s are left. >>>> I am working on those. >>>> >>>> >>>> Suggestions are welcomed. >>>> >>>> >>>> >>>> >>>> >>>> Regards >>>> Sampad Kumar Saha >>>> Mathematics and Computing >>>> I.I.T. Kharagpur >>>> >>>> On Wed, Mar 16, 2016 at 6:18 AM, Jason Moore <[email protected]> >>>> wrote: >>>> >>>>> Looks good. I think you should have plenty of examples in the docs. >>>>> People tend to use software more if the docs are top notch. So plenty of >>>>> examples and tutorials will really help. >>>>> >>>>> >>>>> Jason >>>>> moorepants.info >>>>> +01 530-601-9791 >>>>> >>>>> On Tue, Mar 15, 2016 at 5:25 PM, SAMPAD SAHA <[email protected]> >>>>> wrote: >>>>> >>>>>> You are right. *delta_function.py *needs to be improved. I will to >>>>>> be using only* DiracDelta* and *Heaviside *for generating almost all >>>>>> the Singularity Functions. >>>>>> >>>>>> I was also thinking to complete this project in four phases: >>>>>> >>>>>> 1. Improving existiing Functions. >>>>>> 2. Creating Singularity Functions module >>>>>> 3. Creating beam Module >>>>>> 4. Documentation >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> Regards >>>>>> Sampad Kumar Saha >>>>>> Mathematics and Computing >>>>>> I.I.T. Kharagpur >>>>>> >>>>>> On Wed, Mar 16, 2016 at 5:44 AM, Jason Moore <[email protected]> >>>>>> wrote: >>>>>> >>>>>>> https://www.python.org/dev/peps/pep-0008/ >>>>>>> >>>>>>> I think you will need a pure singularity function module and then >>>>>>> you will need a beam module that utlizes the singularity function >>>>>>> module. >>>>>>> You will also likely need to improve the discontinuous functions that >>>>>>> are >>>>>>> already in sympy. There are at least three layers to this in my eyes. >>>>>>> >>>>>>> >>>>>>> Jason >>>>>>> moorepants.info >>>>>>> +01 530-601-9791 >>>>>>> >>>>>>> On Tue, Mar 15, 2016 at 5:07 PM, SAMPAD SAHA <[email protected]> >>>>>>> wrote: >>>>>>> >>>>>>>> Jason >>>>>>>> >>>>>>>> Pardon please. I couldn't get you by "You will need to follow PEP8 >>>>>>>> for the method and class names". >>>>>>>> >>>>>>>> and yah, i also felt that it would be better if i use the input and >>>>>>>> output values of the example problem done by hand. >>>>>>>> >>>>>>>> So , what do you suggest, Would it be better if we create a >>>>>>>> different module ,other than the singularity function module, for >>>>>>>> solving >>>>>>>> beam problems? That module would import the singularity function >>>>>>>> module >>>>>>>> for using them. >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> Regards >>>>>>>> Sampad Kumar Saha >>>>>>>> Mathematics and Computing >>>>>>>> I.I.T. Kharagpur >>>>>>>> >>>>>>>> On Wed, Mar 16, 2016 at 5:22 AM, Jason Moore <[email protected]> >>>>>>>> wrote: >>>>>>>> >>>>>>>>> I think it is a good start. You will need to follow PEP8 for the >>>>>>>>> method and class names. But I just want to see desired functionality. >>>>>>>>> The >>>>>>>>> more you can think up, the better. I would suggest doing a beam >>>>>>>>> problem by >>>>>>>>> hand and then translating that to a desired API. You can mock up what >>>>>>>>> you >>>>>>>>> think the inputs and outputs should be for that example problem. >>>>>>>>> >>>>>>>>> >>>>>>>>> Jason >>>>>>>>> moorepants.info >>>>>>>>> +01 530-601-9791 >>>>>>>>> >>>>>>>>> On Tue, Mar 15, 2016 at 4:46 PM, SAMPAD SAHA < >>>>>>>>> [email protected]> wrote: >>>>>>>>> >>>>>>>>>> Ok Jason, >>>>>>>>>> >>>>>>>>>> And what about the API I have posted just before the earlier post? >>>>>>>>>> >>>>>>>>>> Any suggestions >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> Regards >>>>>>>>>> Sampad Kumar Saha >>>>>>>>>> Mathematics and Computing >>>>>>>>>> I.I.T. Kharagpur >>>>>>>>>> >>>>>>>>>> On Wed, Mar 16, 2016 at 5:10 AM, Jason Moore < >>>>>>>>>> [email protected]> wrote: >>>>>>>>>> >>>>>>>>>>> The file locations and method class names are just fine details >>>>>>>>>>> that can be worked out later. They are generally not important for >>>>>>>>>>> your >>>>>>>>>>> proposal. Just focus on describing what the future modules should >>>>>>>>>>> do. >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> Jason >>>>>>>>>>> moorepants.info >>>>>>>>>>> +01 530-601-9791 >>>>>>>>>>> >>>>>>>>>>> On Tue, Mar 15, 2016 at 4:36 PM, SAMPAD SAHA < >>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>> >>>>>>>>>>>> Hi Jason, >>>>>>>>>>>> >>>>>>>>>>>> As I am thinking to create a another module for solving >>>>>>>>>>>> especially beam problems (suppose *beambending.py) *, what >>>>>>>>>>>> will be its file location? >>>>>>>>>>>> Similarly for Singularity Functions (suppose >>>>>>>>>>>> singularity_function.py), What will be its location? >>>>>>>>>>>> >>>>>>>>>>>> And what about the names of methods and classes, Can I give any >>>>>>>>>>>> name or we will be discussing it at the time of developing them? >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> --------------------- >>>>>>>>>>>> Regards, >>>>>>>>>>>> Sampad >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> Regards >>>>>>>>>>>> Sampad Kumar Saha >>>>>>>>>>>> Mathematics and Computing >>>>>>>>>>>> I.I.T. Kharagpur >>>>>>>>>>>> >>>>>>>>>>>> On Wed, Mar 16, 2016 at 3:56 AM, SAMPAD SAHA < >>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>> >>>>>>>>>>>>> Thank You Tim and Jason for your suggestions and clearing my >>>>>>>>>>>>> doubts. >>>>>>>>>>>>> >>>>>>>>>>>>> We can also have an another module for solving beam problems. >>>>>>>>>>>>> As Jason Have suggested earlier. >>>>>>>>>>>>> >>>>>>>>>>>>> Some of its classes would be Beam, DistributedLoad, PointLoad, >>>>>>>>>>>>> Moment. >>>>>>>>>>>>> >>>>>>>>>>>>> We can have the API as:- >>>>>>>>>>>>> >>>>>>>>>>>>> from sympy import >>>>>>>>>>>>> SingularityFunction,Beam,DistributedLoad,PointLoad,Moment >>>>>>>>>>>>> b = Beam(length = 1, E = 1.87, I = 12) >>>>>>>>>>>>> Load1 = DistrubutedLoad(start=l/2, end=l, value= 50) >>>>>>>>>>>>> Load2 = PointLoad(location=l/3, value=60) >>>>>>>>>>>>> Load3 = Moment(locaton = 1, value = 40, anticlockwise = True) >>>>>>>>>>>>> b.apply(Load1,Load2,Load3) >>>>>>>>>>>>> b.loadDistribution # Outputs the loading function in the >>>>>>>>>>>>> form of singularity function >>>>>>>>>>>>> b.shearForce # Outputs the Shear Force Function >>>>>>>>>>>>> b.bendingMoment # Outputs the bending Moment Function >>>>>>>>>>>>> b.slope # Outputs the Slope Function >>>>>>>>>>>>> b.deflection # Outputs the deflection Function >>>>>>>>>>>>> >>>>>>>>>>>>> b.plotLoadDistribution # Outputs the plot of load >>>>>>>>>>>>> Distribution Curve >>>>>>>>>>>>> b.plotBendingMoment # Outputs the plot of Bending Moment >>>>>>>>>>>>> Curve >>>>>>>>>>>>> b.plotDeflection # Outputs the plot of Deflection >>>>>>>>>>>>> Curve >>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> Regards >>>>>>>>>>>>> Sampad Kumar Saha >>>>>>>>>>>>> Mathematics and Computing >>>>>>>>>>>>> I.I.T. Kharagpur >>>>>>>>>>>>> >>>>>>>>>>>>> On Wed, Mar 16, 2016 at 2:45 AM, Tim Lahey < >>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>> >>>>>>>>>>>>>> I agree. One should start directly from the loading function >>>>>>>>>>>>>> q(x). The general steps are: >>>>>>>>>>>>>> >>>>>>>>>>>>>> 1. Start with the loading function q(x) >>>>>>>>>>>>>> 2. Integrate to get the shear function V(x). >>>>>>>>>>>>>> 3. Integrate again to get the bending moment function M(x). >>>>>>>>>>>>>> 4. Integrate to get the slope function E*I*v’(x). >>>>>>>>>>>>>> 5. Integrate to get the displacement function E*I*v(x). >>>>>>>>>>>>>> >>>>>>>>>>>>>> Note that the singularity functions can be multiplied by >>>>>>>>>>>>>> arbitrary functions of x as well. This allows for varied loads >>>>>>>>>>>>>> and cases >>>>>>>>>>>>>> where E and I vary too. To be strictly correct one should >>>>>>>>>>>>>> include the >>>>>>>>>>>>>> integration constants as well and then solve for the reaction >>>>>>>>>>>>>> forces and >>>>>>>>>>>>>> the constants. >>>>>>>>>>>>>> >>>>>>>>>>>>>> You’ll need to carefully consider how you handle evaluating >>>>>>>>>>>>>> at transition points, especially the beam boundaries. >>>>>>>>>>>>>> >>>>>>>>>>>>>> Cheers, >>>>>>>>>>>>>> >>>>>>>>>>>>>> Tim. >>>>>>>>>>>>>> >>>>>>>>>>>>>> > On Mar 15, 2016, at 4:53 PM, Jason Moore < >>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>> > >>>>>>>>>>>>>> > I think you'd want the user to input the loads on the beam >>>>>>>>>>>>>> as singularity functions or some higher level abstraction. If >>>>>>>>>>>>>> you require >>>>>>>>>>>>>> them to manually compute the bending moment then you are >>>>>>>>>>>>>> defeating the >>>>>>>>>>>>>> purpose of having a CAS do it for you. >>>>>>>>>>>>>> > >>>>>>>>>>>>>> > >>>>>>>>>>>>>> > Jason >>>>>>>>>>>>>> > moorepants.info >>>>>>>>>>>>>> > +01 530-601-9791 >>>>>>>>>>>>>> > >>>>>>>>>>>>>> > On Sun, Mar 13, 2016 at 2:25 PM, SAMPAD SAHA < >>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>> > 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 < >>>>>>>>>>>>>> [email protected]> 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 < >>>>>>>>>>>>>> [email protected]> 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 < >>>>>>>>>>>>>> [email protected]> 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 < >>>>>>>>>>>>>> [email protected]> 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 < >>>>>>>>>>>>>> [email protected]> 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 [email protected]. >>>>>>>>>>>>>> > >> To post to this group, send email to >>>>>>>>>>>>>> [email protected]. >>>>>>>>>>>>>> > >> 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 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