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Jason moorepants.info +01 530-601-9791 On Sun, Mar 20, 2016 at 2:35 PM, SAMPAD SAHA <sampadsa...@gmail.com> wrote: > Is there any thing called *DirectDelta ?* > > Or here > <https://github.com/sympy/sympy/blob/master/sympy/functions/special/delta_functions.py#L97> > is this a typo? > > > > > Regards > Sampad Kumar Saha > Mathematics and Computing > I.I.T. Kharagpur > > On Mon, Mar 21, 2016 at 2:29 AM, SAMPAD SAHA <sampadsa...@gmail.com> > wrote: > >> Hi, >> >> I might not be able to code for the full time form 25 May - 29 May (max >> 4 days) as I have to go for a family vacation . I will be compensating the >> work during the commmunity bonding period as well as in the other weeks, >> since I will be free for the whole summer break and I will not have any >> commitments other than GSoC. >> >> Would it be fine? >> >> >> --------------------------- >> *Regards,* >> *Sampad* >> >> >> >> >> Regards >> Sampad Kumar Saha >> Mathematics and Computing >> I.I.T. Kharagpur >> >> On Sat, Mar 19, 2016 at 11:28 PM, SAMPAD SAHA <sampadsa...@gmail.com> >> wrote: >> >>> Jason, >>> >>> Actually I have misunderstood earlier. >>> >>> I have updated my proposal here >>> <https://github.com/sympy/sympy/wiki/GSoC-2016-Application-Sampad-Kumar-Saha-:-Singularity-Functions> >>> . >>> Can you please review it and suggest me to improve it. >>> >>> >>> >>> Regards >>> Sampad Kumar Saha >>> Mathematics and Computing >>> I.I.T. Kharagpur >>> >>> On Sat, Mar 19, 2016 at 9:14 PM, Jason Moore <moorepa...@gmail.com> >>> wrote: >>> >>>> I don't think we should do "a hack". If we follow the patterns in the >>>> integration code, we should leave the constants of integration off. But in >>>> the Beam classes you can have them manage the constants of integration. >>>> What you show above looks fine. >>>> >>>> I didn't mean to use dsolve in any way. I just meant to have a look at >>>> that code because they include constants of integration when you solve the >>>> ode. You can also set the boundary conditions in the constructor. It can >>>> give you ideas of how to design your api. >>>> >>>> >>>> Jason >>>> moorepants.info >>>> +01 530-601-9791 >>>> >>>> On Sat, Mar 19, 2016 at 8:27 AM, SAMPAD SAHA <sampadsa...@gmail.com> >>>> wrote: >>>> >>>>> Jason, >>>>> >>>>> I went through the ode package. I felt that it would be difficult to >>>>> use boundary condition to solve for the constants of integration using the >>>>> exisiting *dsolve() *method. It seems that it is still under >>>>> development. >>>>> >>>>> So I thought of implementing that functionality explicitly for solving >>>>> beam problems. >>>>> >>>>> I would be taking Boundary conditions as input as: >>>>> >>>>> *bcs = Beam.BoundaryCondition( {f(0) : 5, f.diff(0) : 4 } )* and so >>>>> on. >>>>> >>>>> If nothing is provided then *f(0) != 0 , f.diff(0) = 0 *or >>>>> something like this would be assumed. >>>>> >>>>> Depending on this boundary condition I would add the required >>>>> constants by myself while finding the slope and deflection function and >>>>> output the value by solving for those constants. >>>>> >>>>> By this way, the hack would be easier. What do you suggests? >>>>> >>>>> >>>>> >>>>> >>>>> >>>>> >>>>> Regards >>>>> Sampad Kumar Saha >>>>> Mathematics and Computing >>>>> I.I.T. Kharagpur >>>>> >>>>> On Sat, Mar 19, 2016 at 7:17 AM, SAMPAD SAHA <sampadsa...@gmail.com> >>>>> wrote: >>>>> >>>>>> Yah, you are right . We should not have the name simplify() as a >>>>>> method since it have already created some issues in #7716 >>>>>> <https://github.com/sympy/sympy/issues/7716> and #8798 >>>>>> <https://github.com/sympy/sympy/issues/8798>. So i will keep it as >>>>>> *to_piecewise()* . it would be fine then. >>>>>> >>>>>> As you suggested I will be look at ode package for this constant of >>>>>> integration thing. >>>>>> >>>>>> Thank You... >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> Regards >>>>>> Sampad Kumar Saha >>>>>> Mathematics and Computing >>>>>> I.I.T. Kharagpur >>>>>> >>>>>> On Sat, Mar 19, 2016 at 7:07 AM, Jason Moore <moorepa...@gmail.com> >>>>>> wrote: >>>>>> >>>>>>> Simplification means something very specific in SymPy, see the >>>>>>> simplify() function. I think you need to choose a different method name >>>>>>> for >>>>>>> converting to piecewise continuous. Maybe: .to_piecewise()? >>>>>>> >>>>>>> You will need to implement some method for dealing with the >>>>>>> constants of integration and boundary conditions. Maybe you should have >>>>>>> a >>>>>>> look at the ordinary differential equations package in SymPy to get some >>>>>>> ideas about that. >>>>>>> >>>>>>> >>>>>>> Jason >>>>>>> moorepants.info >>>>>>> +01 530-601-9791 >>>>>>> >>>>>>> On Fri, Mar 18, 2016 at 4:04 PM, SAMPAD SAHA <sampadsa...@gmail.com> >>>>>>> wrote: >>>>>>> >>>>>>>> Thank You Jason for the appreciation. >>>>>>>> >>>>>>>> Yah, that *Simplify * method would convert into continous >>>>>>>> piecewise. Like this :- >>>>>>>> >>>>>>>> In [ ] : F = singularityFunc(x, 0, 1) + singularityFunc(x, 3, 2) >>>>>>>> >>>>>>>> In [ ] : F >>>>>>>> Out [ ] : >>>>>>>> 2 >>>>>>>> <x> + <x - 3> >>>>>>>> >>>>>>>> In [ ] : F.simplify() >>>>>>>> Out [ ] : >>>>>>>> >>>>>>>> 0 for x < 0 >>>>>>>> x for 0 <= x < 3 >>>>>>>> x + (x-3)^2 for x >= 3 >>>>>>>> >>>>>>>> >>>>>>>> As you have suggested earlier, I have solved some examples by hand >>>>>>>> and then tried to implement a desired api. From that I came to this >>>>>>>> conclusion that if we implement Addition, Substraction, >>>>>>>> Integration, Differentiation, Simplify on Singularity Functions then >>>>>>>> we can >>>>>>>> successfully solve out the beam problems. >>>>>>>> >>>>>>>> But i got doubt while implementing the boundary constants. I mean >>>>>>>> to say that sympy dont gives constant of integration while doing >>>>>>>> indefinite >>>>>>>> integration. We can take boundary conditions as input from users that >>>>>>>> is >>>>>>>> not a problem, but we cant use it since there will be no constant of >>>>>>>> integration. >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> Regards >>>>>>>> Sampad Kumar Saha >>>>>>>> Mathematics and Computing >>>>>>>> I.I.T. Kharagpur >>>>>>>> >>>>>>>> On Sat, Mar 19, 2016 at 4:07 AM, Jason Moore <moorepa...@gmail.com> >>>>>>>> wrote: >>>>>>>> >>>>>>>>> Sounds like a good start. How about a method to convert to >>>>>>>>> continuous piecewise? >>>>>>>>> >>>>>>>>> Like I said earlier, you should pick some examples that you want >>>>>>>>> the software to be able to solve and then implement methods and >>>>>>>>> functionality based on those examples. It's hard to think of all the >>>>>>>>> needed >>>>>>>>> functionality and API without motivating examples first. >>>>>>>>> >>>>>>>>> >>>>>>>>> Jason >>>>>>>>> moorepants.info >>>>>>>>> +01 530-601-9791 >>>>>>>>> >>>>>>>>> On Fri, Mar 18, 2016 at 10:27 AM, SAMPAD SAHA < >>>>>>>>> sampadsa...@gmail.com> wrote: >>>>>>>>> >>>>>>>>>> Jason, >>>>>>>>>> >>>>>>>>>> I have thought of implementing Addition, Substraction, >>>>>>>>>> Integration, Differentiation, Simplify on Singularity Functions. >>>>>>>>>> >>>>>>>>>> What are the other functionalities we should implement? >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> Regards >>>>>>>>>> Sampad Kumar Saha >>>>>>>>>> Mathematics and Computing >>>>>>>>>> I.I.T. Kharagpur >>>>>>>>>> >>>>>>>>>> On Fri, Mar 18, 2016 at 8:16 PM, SAMPAD SAHA < >>>>>>>>>> sampadsa...@gmail.com> wrote: >>>>>>>>>> >>>>>>>>>>> Yah you are correct. Differentiation of heaviside and diracdelta >>>>>>>>>>> also exists. >>>>>>>>>>> >>>>>>>>>>> It was my mistake. Thanks for rectifying me. >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> Regards >>>>>>>>>>> Sampad Kumar Saha >>>>>>>>>>> Mathematics and Computing >>>>>>>>>>> I.I.T. Kharagpur >>>>>>>>>>> >>>>>>>>>>> On Fri, Mar 18, 2016 at 8:02 PM, Tim Lahey <tim.la...@gmail.com> >>>>>>>>>>> wrote: >>>>>>>>>>> >>>>>>>>>>>> For differentiation you’re missing a case, >>>>>>>>>>>> >>>>>>>>>>>> if n = 0 or n = -1 >>>>>>>>>>>> return Singularity(x, a, n-1) >>>>>>>>>>>> else if n < -1 >>>>>>>>>>>> return error >>>>>>>>>>>> >>>>>>>>>>>> In other words, you can still differentiate for the n = 0 and n >>>>>>>>>>>> = -1 cases. >>>>>>>>>>>> >>>>>>>>>>>> Cheers, >>>>>>>>>>>> >>>>>>>>>>>> Tim. >>>>>>>>>>>> >>>>>>>>>>>> > On Mar 18, 2016, at 10:22 AM, SAMPAD SAHA < >>>>>>>>>>>> sampadsa...@gmail.com> wrote: >>>>>>>>>>>> > >>>>>>>>>>>> > And what about the pseudocode of integration and >>>>>>>>>>>> differentiation i have posted earlier , is it alright? >>>>>>>>>>>> > >>>>>>>>>>>> > >>>>>>>>>>>> > >>>>>>>>>>>> > >>>>>>>>>>>> > >>>>>>>>>>>> > Regards >>>>>>>>>>>> > Sampad Kumar Saha >>>>>>>>>>>> > Mathematics and Computing >>>>>>>>>>>> > I.I.T. Kharagpur >>>>>>>>>>>> > >>>>>>>>>>>> > On Fri, Mar 18, 2016 at 7:51 PM, SAMPAD SAHA < >>>>>>>>>>>> sampadsa...@gmail.com> wrote: >>>>>>>>>>>> > Thanks Tim, >>>>>>>>>>>> > >>>>>>>>>>>> > It is really a nice and effective solution. >>>>>>>>>>>> > >>>>>>>>>>>> > >>>>>>>>>>>> > >>>>>>>>>>>> > >>>>>>>>>>>> > >>>>>>>>>>>> > Regards >>>>>>>>>>>> > Sampad Kumar Saha >>>>>>>>>>>> > Mathematics and Computing >>>>>>>>>>>> > I.I.T. Kharagpur >>>>>>>>>>>> > >>>>>>>>>>>> > On Fri, Mar 18, 2016 at 7:46 PM, Tim Lahey < >>>>>>>>>>>> tim.la...@gmail.com> wrote: >>>>>>>>>>>> > Add the constants when you integrate in your beam class. >>>>>>>>>>>> > >>>>>>>>>>>> > >>>>>>>>>>>> > On 2016-03-18, at 10:12 AM, SAMPAD SAHA < >>>>>>>>>>>> sampadsa...@gmail.com> wrote: >>>>>>>>>>>> > >>>>>>>>>>>> >> Thanks TIm, >>>>>>>>>>>> >> >>>>>>>>>>>> >> Integration and Differentiation are really very straight >>>>>>>>>>>> forward that is why i am thinking to add diff and integrate method >>>>>>>>>>>> to the >>>>>>>>>>>> Singularity function class itself. >>>>>>>>>>>> >> >>>>>>>>>>>> >> For integrate the pseuesocode will be :- >>>>>>>>>>>> >> >>>>>>>>>>>> >> if(n<0) >>>>>>>>>>>> >> return SingularityFunction(x , a, n+1) >>>>>>>>>>>> >> else >>>>>>>>>>>> >> return (1/n+1 * SingularityFunction(x , a, n+1)) >>>>>>>>>>>> >> >>>>>>>>>>>> >> Similarly for differentiation: >>>>>>>>>>>> >> >>>>>>>>>>>> >> if (n>0) >>>>>>>>>>>> >> return n * SingularityFunction(x , a, n - 1) >>>>>>>>>>>> >> else >>>>>>>>>>>> >> Error message >>>>>>>>>>>> >> >>>>>>>>>>>> >> >>>>>>>>>>>> >> My doubt regarding Boundary condition was actually was that >>>>>>>>>>>> since sympy don't provide constant of integration while performing >>>>>>>>>>>> indefinite integration on any expression, how to use the boundary >>>>>>>>>>>> conditions to find the exact values of constant of integration? >>>>>>>>>>>> >> >>>>>>>>>>>> >> >>>>>>>>>>>> >> >>>>>>>>>>>> >> >>>>>>>>>>>> >> >>>>>>>>>>>> >> Regards >>>>>>>>>>>> >> Sampad Kumar Saha >>>>>>>>>>>> >> Mathematics and Computing >>>>>>>>>>>> >> I.I.T. Kharagpur >>>>>>>>>>>> >> >>>>>>>>>>>> >> On Fri, Mar 18, 2016 at 6:09 PM, Tim Lahey < >>>>>>>>>>>> tim.la...@gmail.com> wrote: >>>>>>>>>>>> >> Hi, >>>>>>>>>>>> >> >>>>>>>>>>>> >> Do you know the integration and differentiation rules for >>>>>>>>>>>> singularity functions? They’re pretty straightforward. >>>>>>>>>>>> >> >>>>>>>>>>>> >> As for boundary conditions, the beam will have supports (or >>>>>>>>>>>> a free end) at each end of the beam and as part of the beam >>>>>>>>>>>> creation each >>>>>>>>>>>> end type is specified. Each type corresponds to a specific set of >>>>>>>>>>>> conditions on that end (either at x=0 or x=L). You substitute those >>>>>>>>>>>> conditions in the appropriate equation and solve for the >>>>>>>>>>>> integration >>>>>>>>>>>> constant as necessary. All of the conditions should be in any >>>>>>>>>>>> decent >>>>>>>>>>>> mechanics of deformable solids text book. >>>>>>>>>>>> >> >>>>>>>>>>>> >> You’ll want to do sums of forces and moments as well to >>>>>>>>>>>> solve for reaction forces as well. >>>>>>>>>>>> >> >>>>>>>>>>>> >> The only trick is making sure you don’t double count things. >>>>>>>>>>>> If you have a step function due to a reaction force at the start >>>>>>>>>>>> of the >>>>>>>>>>>> beam and assume it’s zero at x=0 (effectively the limit at x=0^-) >>>>>>>>>>>> you can >>>>>>>>>>>> get a non-zero integration constant that can be double counting >>>>>>>>>>>> that >>>>>>>>>>>> reaction since at x=0^+ that reaction force is non-zero. Note that >>>>>>>>>>>> you can >>>>>>>>>>>> get a non-zero integration constant (even when including reaction >>>>>>>>>>>> forces in >>>>>>>>>>>> the loading function) for shear and moment equations if you have >>>>>>>>>>>> non-polynomial loads (e.g., sine and cosine). You’ll also have to >>>>>>>>>>>> think >>>>>>>>>>>> about the other end as well. I leave it up to you to reason that >>>>>>>>>>>> out. Make >>>>>>>>>>>> sure you completely document how you’ve implemented it for the >>>>>>>>>>>> user (and >>>>>>>>>>>> why). >>>>>>>>>>>> >> >>>>>>>>>>>> >> Beam coordinate systems must start at the left end and >>>>>>>>>>>> increase to the right. The definition of the singularity functions >>>>>>>>>>>> require >>>>>>>>>>>> this. >>>>>>>>>>>> >> >>>>>>>>>>>> >> I hope this helps. >>>>>>>>>>>> >> >>>>>>>>>>>> >> Cheers, >>>>>>>>>>>> >> >>>>>>>>>>>> >> Tim. >>>>>>>>>>>> >> >>>>>>>>>>>> >> > On Mar 18, 2016, at 8:17 AM, SAMPAD SAHA < >>>>>>>>>>>> sampadsa...@gmail.com> wrote: >>>>>>>>>>>> >> > >>>>>>>>>>>> >> > I am also confused about implementing the boundary >>>>>>>>>>>> conditions for getting the deflection curve. >>>>>>>>>>>> >> > >>>>>>>>>>>> >> > Any suggestions on how to implement it. >>>>>>>>>>>> >> > >>>>>>>>>>>> >> > >>>>>>>>>>>> >> > >>>>>>>>>>>> >> > >>>>>>>>>>>> >> > >>>>>>>>>>>> >> > Regards >>>>>>>>>>>> >> > Sampad Kumar Saha >>>>>>>>>>>> >> > Mathematics and Computing >>>>>>>>>>>> >> > I.I.T. Kharagpur >>>>>>>>>>>> >> > >>>>>>>>>>>> >> > On Fri, Mar 18, 2016 at 5:36 PM, SAMPAD SAHA < >>>>>>>>>>>> sampadsa...@gmail.com> wrote: >>>>>>>>>>>> >> > 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 < >>>>>>>>>>>> moorepa...@gmail.com> 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 < >>>>>>>>>>>> sampadsa...@gmail.com> 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 < >>>>>>>>>>>> sampadsa...@gmail.com> 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 < >>>>>>>>>>>> sampadsa...@gmail.com> 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 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 < >>>>>>>>>>>> moorepa...@gmail.com> 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 < >>>>>>>>>>>> sampadsa...@gmail.com> 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: >>>>>>>>>>>> >> > • Improving existiing Functions. >>>>>>>>>>>> >> > • Creating Singularity Functions module >>>>>>>>>>>> >> > • Creating beam Module >>>>>>>>>>>> >> > • Documentation >>>>>>>>>>>> >> > >>>>>>>>>>>> >> > >>>>>>>>>>>> >> > >>>>>>>>>>>> >> > >>>>>>>>>>>> >> > >>>>>>>>>>>> >> > Regards >>>>>>>>>>>> >> > Sampad Kumar Saha >>>>>>>>>>>> >> > Mathematics and Computing >>>>>>>>>>>> >> > I.I.T. Kharagpur >>>>>>>>>>>> >> > >>>>>>>>>>>> >> > On Wed, Mar 16, 2016 at 5:44 AM, Jason Moore < >>>>>>>>>>>> moorepa...@gmail.com> 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 < >>>>>>>>>>>> sampadsa...@gmail.com> 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 < >>>>>>>>>>>> moorepa...@gmail.com> 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 < >>>>>>>>>>>> sampadsa...@gmail.com> 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 < >>>>>>>>>>>> moorepa...@gmail.com> 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 < >>>>>>>>>>>> sampadsa...@gmail.com> 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 < >>>>>>>>>>>> sampadsa...@gmail.com> 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 < >>>>>>>>>>>> tim.la...@gmail.com> 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 < >>>>>>>>>>>> moorepa...@gmail.com> 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 < >>>>>>>>>>>> sampadsa...@gmail.com> 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 < >>>>>>>>>>>> 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. 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