Yesterday I had a talk with Harsh regarding the Project,
here is the summary:
He suggested me to make a more detailed plan for
implementation of multivariate solver. I am working on that.
(Suggestions from the community are extremely welcome.)
We discussed about a few more things to implement
which would be quite useful, in sympy.calculus:
General Methods in Calculus:
(These methods would be very useful for differential calculus.)
- is_monotonic
- is_increasing
- is_strictly_increasing
- is_decreasing
- is_strictly_decreasing
He also suggested me a couple of things which he (Harsh) planned to
implement last year in his GSoC Project, including singularities, but was
not able to complete, Now I would take that work, as far as Radical
denesting is concerned, I would work on it if time permits. I think It's
not a good idea to work on too many things, as last year we underestimated
the work, that's why we were not able to complete all the things mentioned
in Harsh's proposal.
I would keep this thread updated, parallel to my progress on my proposal.
Thanks,
AMiT Kumar
3rd Year Undergrad
Delhi Technological University
www.iamit.in
On Saturday, February 7, 2015 at 3:00:55 AM UTC+5:30, AMiT Kumar wrote:
>
>
>> The output should rather be a set of ProductSets rather than a set of
>> sets.
>> General FiniteSet is unordered so {(-oo, oo), 2} is same as {2, (-oo,
>> oo)}.
>> This example shows how you can define and use a product set.
>> ```
>> In [9]: s = FiniteSet(2)*Interval(-oo, oo)
>>
>> In [10]: s
>> Out[10]: {2} x (-oo, oo)
>>
>> In [11]: (2, 0) in s
>> Out[11]: True
>> ```
>>
>> Yes, I agree that would be much better.
>
>
>> > Solve System of Equation: (solvesys)
>> > (For system of Equation, we can have this):
>> > ```python
>> > In [0] solveset([x + y == 1, x - y == 0], (x,y))
>> > Out[1] {{1/2, 1/2}}
>> > ```
>>
>> It has the same issue as I mentioned above {1/2, 1/2} is unordered. You
>> can use a FinteSet set of ordered tuple.
>> ```
>> In [14]: FiniteSet((S(1)/2, S(1)/2))
>> Out[14]: {(1/2, 1/2)}
>> ```
>>
>>
> I did gave a thought about returning FiniteSet of
> ordered tuple, I thought It would look like a Set
> of Interval.
> Now since we don't return Interval like this,
> so this should be good. I agree.
>
>
>> > we also need to extend singularities module (though useful in general)
>>
>> +1
>>
>> I suggest that you create a detailed plan of "how" you are going to solve
>> multivariate equations and how will you find a singular point. I did a
>> shallow
>> study of the current multivariate solver in `solve`. The writeup is here:
>> http://hargup.github.io/posts/week-7.html
>>
>
> I have gone through that write up, that looks good to me.
> I will create a detailed plan as soon as things get more clear.
>
>
>
>> Try searching for some literature,
>>
>
> I found this
> http://www.research.ed.ac.uk/portal/files/413486/Solving_Symbolic_Equations_%20with_PRESS.pdf
> on the Mailing list here:
> https://groups.google.com/forum/#!searchin/sympy/PROLOG/sympy/moSEFHop0n4/dRMJJOKVjRwJ
>
> I am not sure how good it is, as Prof. Fateman's comments isn't very
> convincing about it:
>
> You could look at it, but I think that, unless it has been changed since
>> I last looked, it has nothing at all to offer vs. an algorithmic
>> approach.
>>
> And some real problems in that it returns answers that are wrong,
>> sometimes.
>>
>
> Though I am looking for some reasearch papers,
> can you point me to some, which are good enough?
>
>
>> dig into other older CAS
>>
> maybe like maxima?
>
>
>> and probably you should ask professor Fateman for
>> help. He can be harsh but if you have a thick skin he can be a lot of
>> help too.
>>
>
> Sure, I will try to get some help from him.
>
>
> Cheers!
> AMiT Kumar
>
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