Hi everyone,
Before continuing further with the Diophantine module development (PR
#2168<https://github.com/sympy/sympy/pull/2168>
)
I thought it would be better for me to get other people's views on the
representation
of solutions returned by diop_solve().
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.
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.
Regards,
Thilina
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