Fix a bug with diophantine() when cornacchia() is not called properly

[zylipku]

Occasionally diophantine() and diop_quadratic() result in a DN form $X^2 - DY^2 = N$ which cannot be handled by the current cornacchia() properly. For example, previously the diophantine solver will miss some solutions:

>>> eq1 = x**2 - 15*x + y**2 - 8*y # also mentioned in #18628
>>> diophantine(eq1)
{(0, 0), (15, 0), (15, 8), (0, 8)}
>>> eq1.subs({x: 16, y: 4})
0

>>> eq2 = 2*x**2 - 9*x + 4*y**2 - 8*y + 14
>>> diophantine(eq2)
set()
>>> eq2.subs({x: 2, y: 1})
0

Both the two examples lead to a function call of cornacchia(1, X, 1) with X > 1, which incorrrectly turns out to have no solution by using cornacchia(). The solver can only be applied when $a+b\le m$. See reference from docs:
http://www.numbertheory.org/php/cornacchia.html
An additional check has been added before the algorithm based on the fact that $ax^2 + by^2 = m$ admits a solution for $a + b > m$ only if $x = 0$ or $y = 0$. A test function including both the two examples has been appended as well.

References to other Issues or PRs

Fixes #18628

Brief description of what is fixed or changed

An additional check has been added before the cornacchia algorithm body based on the fact that $ax^2 + by^2 = m$ admits a solution for $a + b > m$ only if $x = 0$ or $y = 0$.

Other comments

Release Notes

• solvers
  • Fix a bug with cornacchia(). Formerly diophantine() and diop_quadratic() may miss some solutions for quadratic equations.

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• solvers
  • Fix a bug with cornacchia(). Formerly diophantine() and diop_quadratic() may miss some solutions for quadratic equations. (#26780 by @zylipku)

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Occasionally diophantine() and diop_quadratic() result in a DN form $X^2 - DY^2 = N$ which cannot be handled by the current cornacchia() properly. For example, previously the diophantine solver will miss some solutions:
```
>>> eq1 = x**2 - 15*x + y**2 - 8*y # also mentioned in #18628
>>> diophantine(eq1)
{(0, 0), (15, 0), (15, 8), (0, 8)}
>>> eq1.subs({x: 16, y: 4})
0
```
```
>>> eq2 = 2*x**2 - 9*x + 4*y**2 - 8*y + 14
>>> diophantine(eq2)
set()
>>> eq2.subs({x: 2, y: 1})
0
```
Both the two examples lead to a function call of cornacchia(1, X, 1) with X > 1, which incorrrectly turns out to have no solution by using cornacchia(). The solver can only be applied when $a+b\le m$. See reference from docs:
http://www.numbertheory.org/php/cornacchia.html 
An additional check has been added before the algorithm based on the fact that $ax^2 + by^2 = m$ admits a solution for $a + b > m$ only if $x = 0$ or $y = 0$. A test function including both the two examples has been appended as well.

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#### References to other Issues or PRs
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Fixes #18628 

#### Brief description of what is fixed or changed
An additional check has been added before the cornacchia algorithm body based on the fact that $ax^2 + by^2 = m$ admits a solution for $a + b > m$ only if $x = 0$ or $y = 0$.

#### Other comments


#### Release Notes

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* solvers
  * Fix a bug with cornacchia(). Formerly diophantine() and diop_quadratic() may miss some solutions for quadratic equations.
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Update

The release notes on the wiki have been updated.

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[haru-44]

thanks! looks good.

[oscarbenjamin]

Thanks