Can you please give a final review.. and i didn't get you by this
comment "*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 Thu, Mar 24, 2016 at 8:16 PM, SAMPAD SAHA <[email protected]> wrote:

>
>
> Can you please give a final review.. and i didn't get you by this comment
> "*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 Thu, Mar 24, 2016 at 8:13 PM, Jason Moore <[email protected]> wrote:
>
>> 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
>>>>>>>>>>>>>>>>>>>>>>>>>> >> > > >>
>>>>>>>>>>>>>>>>>>>>>>>>>> >> > > >> --
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>>>>>>>>>>>>>>>>>>>>>>>>>> >> > > >> Visit this group at
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>>>>>>>>>>>>>>>>>>>>>>>>>> >> > > >> To view this discussion on the web
>>>>>>>>>>>>>>>>>>>>>>>>>> visit
>>>>>>>>>>>>>>>>>>>>>>>>>> https://groups.google.com/d/msgid/sympy/7cbe2101-fd59-484b-9e25-f563636d6366%40googlegroups.com
>>>>>>>>>>>>>>>>>>>>>>>>>> .
>>>>>>>>>>>>>>>>>>>>>>>>>> >> > > >> For more options, visit
>>>>>>>>>>>>>>>>>>>>>>>>>> https://groups.google.com/d/optout.
>>>>>>>>>>>>>>>>>>>>>>>>>> >> > > >
>>>>>>>>>>>>>>>>>>>>>>>>>> >> > > > --
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>>>>>>>>>>>>>>>>>>>>>>>>>> .
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>>>>>>>>>>>>>>>>>>>>>>>>>> >> > >
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>>>>>>>>>>>>>>>>>>>>>>>>>> .
>>>>>>>>>>>>>>>>>>>>>>>>>> >> > > For more options, visit
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>>>>>>>>>>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>>>>>>>>>>> >> > >
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>>>>>>>>>>>>>>>>>>>>>>>>>> .
>>>>>>>>>>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>>>>>>>>>>> >> > > For more options, visit
>>>>>>>>>>>>>>>>>>>>>>>>>> https://groups.google.com/d/optout.
>>>>>>>>>>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>>>>>>>>>>> >> > >
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>>>>>>>>>>>>>>>>>>>>>>>>>> .
>>>>>>>>>>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>>>>>>>>>>> >> > > For more options, visit
>>>>>>>>>>>>>>>>>>>>>>>>>> https://groups.google.com/d/optout.
>>>>>>>>>>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>>>>>>>>>>> >> > >
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>>>>>>>>>>>>>>>>>>>>>>>>>> .
>>>>>>>>>>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>>>>>>>>>>> >> > > For more options, visit
>>>>>>>>>>>>>>>>>>>>>>>>>> https://groups.google.com/d/optout.
>>>>>>>>>>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>>>>>>>>>>> >> > >
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>>>>>>>>>>>>>>>>>>>>>>>>>> >> > > Visit this group at
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>>>>>>>>>>>>>>>>>>>>>>>>>> >> > > 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.
>>>>>>>>>>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>>>>>>>>>>> >> > --
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>>>>>>>>>>>>>>>>>>>>>>>>>> >> > Visit this group at
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>>>>>>>>>>>>>>>>>>>>>>>>>> >> > 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].
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>>>>>>> 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]>*
>>>>>>
>>>>>> --
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>>>>>> To unsubscribe from this group and stop receiving emails from it,
>>>>>> send an email to [email protected].
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>>>>>> <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.
>>>>>>
>>>>>
>>>>>
>>>>
>>>
>>
>

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