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 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