There shouldn't be any external comments in your final submission.
Jason moorepants.info +01 530-601-9791 On Thu, Mar 24, 2016 at 7:30 AM, SAMPAD SAHA <[email protected]> wrote: > While submitting the final pdf, are we supposed to remove the comments? > > > > > Regards > Sampad Kumar Saha > Mathematics and Computing > I.I.T. Kharagpur > > On Wed, Mar 23, 2016 at 5:44 PM, SAMPAD SAHA <[email protected]> > wrote: > >> Jason , >> >> I have almost made all the changes that you have suggested. Here is the >> link >> >> 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 5:11 PM, SAMPAD SAHA <[email protected]> >> wrote: >> >>> >>> Thanks Sartaj. >>> >>> I went through the Expr class and it cleared all my doubts. I actually >>> forgot that Function class is inheriting Expr class. >>> >>> >>> >>> Regards >>> Sampad Kumar Saha >>> Mathematics and Computing >>> I.I.T. Kharagpur >>> >>> On Wed, Mar 23, 2016 at 4:58 PM, Sartaj Singh <[email protected]> >>> wrote: >>> >>>> 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. >>>>>>>>>>>>>>>>>>>>>>>> >> > > > >>>>>>>>>>>>>>>>>>>>>>>> >> > > > -- >>>>>>>>>>>>>>>>>>>>>>>> >> > > > 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/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 >>>> <https://groups.google.com/d/msgid/sympy/CAC%2BH8-H43g%2BrjCZ5Oqv9oghKa9TVXT5goBX_HfaK4gb5L2twzA%40mail.gmail.com?utm_medium=email&utm_source=footer> >>>> . >>>> >>>> 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/CAP7f1Ai5wo%3DBTHMKHR2E%2BdzkAa9i%2BiU4wtiqjcdOU0tj%3DT5GEw%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
