solve()-ing Equations in CC

[sagetrac-tux21b]

The following looks like a bug to me, but feel free to correct me if I'm mistaken.

sage: var('z')
sage: g1 = z^5 - (2 - I)*z^4 - (34 + 13*I)*z^3 + (22 - 51*I)*z^2 \
+ (53 - I)*z - 728 - 196*I == 0
sage:
sage: solve([g1], z)
[0 == z^5 + (I - 2)*z^4 - (13*I + 34)*z^3 - (51*I - 22)*z^2 -
(I - 53)*z - 196*I - 728]
sage:
sage: solve([g1, I == I], z)
[[z == (-4.00420663449 - 1.03443096055*I)], [z == (7.03872088238 +
1.11154206861*I)], [z == (1.40276621 - 2.70758376454*I)], [z == (
-3.78854832152 - 0.122376366114*I)], [z == (1.35126786363 +
1.7528490226*I)]]
sage:
sage: solve([g1, z == z], z)
[[z == (-4.00420663449 - 1.03443096055*I)], [z == (7.03872088238 +
1.11154206861*I)], [z == (1.40276621 - 2.70758376454*I)], [z == (
-3.78854832152 - 0.122376366114*I)], [z == (1.35126786363 +
1.7528490226*I)]]

I think the problem is that solve() refuses to solve equation systems with more variables than equations, even if some of the variables are already known.

Regards

Christoph

CC: @sagetrac-tux21b

Component: symbolics

Issue created by migration from https://trac.sagemath.org/ticket/10311

[rbeezer]

comment:1

Yes, that looks suspicious to me. I tried replacing all the instances of I in g1 by imag=CC((0,1)), with no better luck.

This is not really a linear algebra problem, but more of something to do with symbolics (where g1 lives) so I am going to change the component on this so it might get noticed sooner. If you haven't already, you might bring this up on sage-devel or sage-support - somebody might be able to confirm this as undesirable behavior, or offer a workaround.

[kcrisman]

comment:2

This could be related to #10750.

[rwst]

comment:3

Should be addressed by #18900.