I've put some comments in your proposal.
Jason moorepants.info +01 530-601-9791 On Sat, Mar 19, 2016 at 10:58 AM, SAMPAD SAHA <[email protected]> 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 <[email protected]> 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 <[email protected]> >> 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 <[email protected]> >>> 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 <[email protected]> >>>> 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 <[email protected]> >>>>> 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 <[email protected]> >>>>>> 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 <[email protected] >>>>>>> > 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 <[email protected] >>>>>>>> > 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 <[email protected]> >>>>>>>>> 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 < >>>>>>>>>> [email protected]> 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 < >>>>>>>>>> [email protected]> 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 <[email protected]> >>>>>>>>>> wrote: >>>>>>>>>> > Add the constants when you integrate in your beam class. >>>>>>>>>> > >>>>>>>>>> > >>>>>>>>>> > On 2016-03-18, at 10:12 AM, SAMPAD SAHA <[email protected]> >>>>>>>>>> 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 < >>>>>>>>>> [email protected]> 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 < >>>>>>>>>> [email protected]> 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 < >>>>>>>>>> [email protected]> 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 < >>>>>>>>>> [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 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: >>>>>>>>>> >> > • 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 < >>>>>>>>>> [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 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/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 [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/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 [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/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 [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/CAKgW%3D6KrEOoZ-CvGJ_HTBVSpTLVkW6geUfvXdP8GAiBNO4y8qQ%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 [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/CANzav4EeosCsLaP55dwMpKxOxBkGhW6ZAkeCQiSvQnXtieU6PQ%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 [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/CAP7f1AjHOvGfvxRfOTy2RhRm3YnNc_eJ9OpjBOain6iK15chMA%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 [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/B66DECFB-0205-41DC-A09D-342BBDF6FAC4%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 [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/CAP7f1AgBDnNy--GmH2y%2BoQoynDd-%2B%2BYHz_bK3_93D43vKkCqCQ%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
