assume() not playing well with solve_diophantine()

asked 2023-09-24 23:22:01 +0100

Eric Snyder
53 ●2 ●8

Simple code:

var('n k')
assume(n > 0)
assume(k > 0)
assume(n > k)

eqn = n^2 - (k^2 + k) == 30
print(solve_diophantine(eqn, (n,k)))

This outputs:

[(30, -30), (-6, 2), (-6, -3), (6, 2), (6, -3), (-30, 29), (-30, -30), (30, 29)]

which contains solutions where each of the assumptions is skipped (including at least one where all three assumptions are not met). Can anyone help explain what might be happening here?

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answered 2023-09-27 11:49:41 +0100

rburing

10919 ●4 ●80 ●218 https://www.rburing.nl/

The explanation is that solve_diophantine simply calls sympy's diophantine, which ignores all assumptions.

So you will have to filter manually:

sage: var('n,k')
sage: eqn = n^2 - (k^2 + k) == 30
sage: [(n0, k0) for (n0, k0) in solve_diophantine(eqn, (n,k)) if n0 > 0 and k0 > 0 and n0 > k0]
[(6, 2), (30, 29)]

Filtering could be added as a post-processing step in solve_diophantine, so you could open an issue for that.

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Asked: 2023-09-24 23:22:01 +0100

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Last updated: Sep 27 '23

assume() not playing well with solve_diophantine() edit

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