On Tue, Jun 18, 2013 at 11:23 PM, Thilina Rathnayake
<thilina.r...@gmail.com> wrote:
>
>
> When we ask the user to specify the parameter to be used, what should
> be the input? should it be a symbol or a string which contain the symbol
> to be used. What I am asking is whether we should use,
>
>>>>var("t")
>>>>diop_solve(3*x*y + 5*y -7, param=t)
Yes, it should be a symbol.
Ondrej
>
> or
>
>>>>diop_solve(3*x*y + 5*y -7, param="t")
>
>
> On Wed, Jun 19, 2013 at 10:35 AM, Thilina Rathnayake
> <thilina.r...@gmail.com> wrote:
>>
>> Thank you Ondrej for the reply.
>>
>> I think that's the way we should go at it. I can implement the
>> moduels to find the solution and return those naturally as a list.
>> Later we consider about the high level API's.
>>
>>
>> On Wed, Jun 19, 2013 at 1:28 AM, Ondřej Čertík <ondrej.cer...@gmail.com>
>> wrote:
>>>
>>> Hi Thilina,
>>>
>>> On Tue, Jun 18, 2013 at 12:39 PM, Thilina Rathnayake
>>> <thilina.r...@gmail.com> wrote:
>>> > Hi everyone,
>>> >
>>> > Before continuing further with the Diophantine module development (PR
>>> > #2168)
>>> > I thought it would be better for me to get other people's views on the
>>> > representation
>>> > of solutions returned by diop_solve().
>>>
>>> Thanks for discussing it.
>>>
>>> >
>>> > The main routine of the module is diop_solve(), which takes a
>>> > Diophantine
>>> > equation
>>> > as an argument and returns the solution of the equation. Currently the
>>> > solution is
>>> > returned as a dictionary. Ex:
>>> >
>>> >> >>>diop_solve(4*x + 6*y - 4)
>>> >> {x: 6*t - 2, y: -4*t + 2}
>>> >> >>>diop_solve(3*x - 5*y + 7*z -5)
>>> >> {x: -25*t - 14*z + 10, y: -15*t - 7*z + 5, z: z}
>>> >
>>> >
>>> > Everything works fine here because the solutions are parametric.
>>>
>>> Right. For these equations I think a dictionary is the best solution,
>>> as it is simple and clear. You should allow the user to specify the
>>> "t" symbol, e.g. something like:
>>>
>>> var("x y z t")
>>> diop_solve(3*x - 5*y + 7*z -5, param=t)
>>>
>>> so that the user can specify other variables names besides "t" as well.
>>>
>>> >
>>> > But when I was trying to solve quadratic Diophantine equation ( this
>>> > has the
>>> > form
>>> > Ax**2 + Bxy + Cy**2 + Dx + Ey + F), they involve solutions which are
>>> > not
>>> > parametric.
>>> > For example, the equation 2*x*y + 5*x + 56*y + 7 = 0 (which is a
>>> > special
>>> > case of the
>>> > quadratic equation) has 8 solution pairs (x, y). (-27, 64), (-29, -69),
>>> > (-21, 7) and five more.
>>> >
>>> > To represent these in a dictionary which has the above form, we have to
>>> > split the solution
>>> > pair and put it in to two lists which are keyed under x and y in the
>>> > dict.
>>> > if the user want
>>> > to retrieve a solution pair he would have to find the x value and the y
>>> > value of the solution
>>> > separately. Returned value would look like,
>>> >
>>> >> {x: [-27, -29, -21, ...], y: [64, -69, 7, ...]}
>>> >
>>> >
>>> > Is this a good way to cope with this situation? I personally feel that
>>> > it is
>>> > not natural to
>>> > split a solution pair and enable the access of it's elements
>>> > separately.
>>> >
>>> > I would like to know what the others have to say on this.
>>>
>>>
>>> So for this I agree with Aaron:
>>>
>>> > You may want to look at
>>> > https://code.google.com/p/sympy/issues/detail?id=3560 and some of the
>>> > ideas for a unified solve object.
>>>
>>> We definitely need a consistent interface to the solve() command.
>>>
>>> > Already you have the issue that you
>>> > are returning a parameter, but there is no easy way to access that
>>> > parameter (and what happens if t is one of the variables?).
>>>
>>> The user can specify his own symbols as "params", as I suggested above.
>>>
>>> I would also look how Mathematica does it:
>>>
>>> http://reference.wolfram.com/mathematica/guide/DiophantineEquations.html
>>>
>>> e.g.:
>>>
>>> http://reference.wolfram.com/mathematica/ref/Reduce.html
>>>
>>>
>>>
>>> In general, I would suggest you simply write the low level modules for
>>> actually solving the equation.
>>> Those can return pretty much any representation that you think is the
>>> best for that particular type of the equation.
>>>
>>> Then we need a consistent high level API, and that will take some time
>>> to get right. But no matter what API we settle on in the end, it
>>> should be quite simple to call the low level solver and convert the
>>> result if needed. What do you think Aaron?
>>>
>>> Ondrej
>>>
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>>
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