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 >>> <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 <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: >>>>> >>>>> 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 <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. >>>>>>>>>>>>> > > To unsubscribe from this group 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