Hi, This comes from Expr class.
On 23 March 2016 at 16:55, SAMPAD SAHA <[email protected]> wrote: > I am having a big confusion over this. > > There is no *integrate()* method defined in *DiracDelta* and* Heaviside. *But > still how can this happen. > > In [ ] : DiracDelta(x).integrate() > Out [ ] : Heaviside(x) > > In [ ] : Heaviside(x).integrate() > Out [ ] : x*Heaviside(x) > > I feel like this should raise error as *AttributeError: 'DiracDelta' > object has no attribute 'integrate'.* > > Please explain how this is happenning. > > > > Regards > Sampad Kumar Saha > Mathematics and Computing > I.I.T. Kharagpur > > On Wed, Mar 23, 2016 at 4:48 AM, SAMPAD SAHA <[email protected]> > wrote: > >> >> Here is my proposal. >> >> https://github.com/sympy/sympy/wiki/GSoC-2016-Application-Sampad-Kumar-Saha:-Singularity-Functions >> >> >> >> Regards >> Sampad Kumar Saha >> Mathematics and Computing >> I.I.T. Kharagpur >> >> On Wed, Mar 23, 2016 at 4:08 AM, SAMPAD SAHA <[email protected]> >> wrote: >> >>> Thanks Jason, I have made some changes. Can you please review those? I >>> have also added some comments along with yours. >>> >>> I didn't get you in this comment. Can you please elaborate it? >>> "*Comment from Jason: You will need to make sure everything is >>> backwards compatible. See the wiki for our policy.*" >>> >>> >>> >>> >>> Regards >>> Sampad Kumar Saha >>> Mathematics and Computing >>> I.I.T. Kharagpur >>> >>> On Tue, Mar 22, 2016 at 8:53 PM, Jason Moore <[email protected]> >>> wrote: >>> >>>> The example you show doesn't seem to reflect what we may actually see >>>> when using this for beams. I'd suggest picking a simple beam problem and >>>> showing what all of your code will look like. You did that pretty well for >>>> the later examples, but this one with the random polynomials wasn't that >>>> clear. >>>> >>>> >>>> Jason >>>> moorepants.info >>>> +01 530-601-9791 >>>> >>>> On Tue, Mar 22, 2016 at 7:43 AM, SAMPAD SAHA <[email protected]> >>>> wrote: >>>> >>>>> Thank You Jason. I will put it. >>>>> >>>>> I have a doubt about this comment in my proposal : >>>>> >>>>> *"Comment from Jason: It would be more informative to show what a beam >>>>> equation would look like in Piecewise form. This is a little abstract." * >>>>> >>>>> Can you explain it a little more? >>>>> >>>>> I have also added some comment next to yours, I am still working on >>>>> some of your comments. >>>>> >>>>> Regards >>>>> Sampad Kumar Saha >>>>> Mathematics and Computing >>>>> I.I.T. Kharagpur >>>>> >>>>> On Tue, Mar 22, 2016 at 8:08 PM, Jason Moore <[email protected]> >>>>> wrote: >>>>> >>>>>> Sounds good, just put it in your proposal. >>>>>> >>>>>> >>>>>> Jason >>>>>> moorepants.info >>>>>> +01 530-601-9791 >>>>>> >>>>>> On Tue, Mar 22, 2016 at 7:32 AM, SAMPAD SAHA <[email protected]> >>>>>> wrote: >>>>>> >>>>>>> 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. >>>>>>>>>>>>>>>>>>>> >> > > > >>>>>>>>>>>>>>>>>>>> >> > > > -- 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>>>>>>>>>>>>>>>>>>>> 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/CANzav4GGN1PyV%2B8ekiPKgEurqCHf15CU3HuoZYS3THoChL54PA%40mail.gmail.com > <https://groups.google.com/d/msgid/sympy/CANzav4GGN1PyV%2B8ekiPKgEurqCHf15CU3HuoZYS3THoChL54PA%40mail.gmail.com?utm_medium=email&utm_source=footer> > . > > For more options, visit https://groups.google.com/d/optout. > -- Regards *Sartaj Singh* *Mathematics and Computing*, Indian Institute of Technology, Varanasi - 221 005 INDIA E-mail: [email protected], *[email protected] <[email protected]>* -- 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/CAC%2BH8-H43g%2BrjCZ5Oqv9oghKa9TVXT5goBX_HfaK4gb5L2twzA%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
