I will start coding along with community bonding. I will spend 3-4 hours extra in the last week of the community bonding period in order to achieve the proposed target in my proposal. I will have no problem managing with those extra hours since I will be having Summer break at that time and along with that I have no other commitments. And I will also have fun working those extra hours.
Regards Sampad Kumar Saha Mathematics and Computing I.I.T. Kharagpur On Tue, Mar 22, 2016 at 4:13 AM, Jason Moore <[email protected]> wrote: > No need to cancel your vacation. Just give a plan for how you will make up > the days. > > > Jason > moorepants.info > +01 530-601-9791 > > On Mon, Mar 21, 2016 at 2:52 PM, SAMPAD SAHA <[email protected]> > wrote: > >> Thank You Jason for the suggestions in my proposal. I will work on those >> and let you know as soon as possible. >> >> I have mentioned in my proposal about the days of the vacation and how >> can I compensate the work. If this vacation raises any problem, I can >> cancel it . That will not be a problem for me. I don't want to let anything >> ruin the progess of the project as this Summer of Code will become an >> integral part of all my learning throughout the summer. >> >> ---------------- >> Regards >> Sampad >> >> >> Regards >> Sampad Kumar Saha >> Mathematics and Computing >> I.I.T. Kharagpur >> >> On Tue, Mar 22, 2016 at 2:33 AM, Jason Moore <[email protected]> >> wrote: >> >>> 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. 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