Avoid ambiguous generators in output saturation

[ChrisRackauckas-Claude]

Ignore this PR until it has been reviewed by @ChrisRackauckas.

Summary

• track the rational-function-field generators locally during output saturation
• add a regression with a rational output whose first Lie derivative is independent

Root cause

AbstractAlgebra 0.50 added an exported generators alias, while
RationalFunctionFields exports a different generators binding. Importing both
leaves the unqualified binding undefined in StructuralIdentifiability, so
saturate_outputs errors when it calls generators(current_y).

The dependency boundary was reproduced locally:

RationalFunctionFields	AbstractAlgebra	Nemo	Result
0.3.1	0.48.6	0.54.2	2 saturated outputs
0.3.3	0.49.0	0.55.1	2 saturated outputs
0.3.3	0.50.0	0.56.1	UndefVarError: generators not defined

RationalFunctionFields 0.3.2 widened compatibility to the failing dependency
combination. Rather than relying on its undocumented generators helper, this
change retains the exact generator vector already supplied to each field
constructor.

This also fixes the downstream failure exposed by
SciML/ModelingToolkit.jl#4845.

Local verification

• Julia 1.10, AbstractAlgebra 0.50.1 / Nemo 0.56.1 /
  RationalFunctionFields 0.3.3: focused rational-output regression returns two
  outputs, including z(t) // a
• Julia 1.12.6, ModelingToolkit 11.37.1 / ModelingToolkitBase 1.57.1:
  downstream reproduction returns two saturated outputs
• GROUP=Core julia +1.10 --startup-file=no --project=. -e 'using Pkg; Pkg.test()'
• GROUP=QA julia +1.10 --startup-file=no --project=. -e 'using Pkg; Pkg.test()'
  (17 passed, 1 pre-existing broken)
• Runic check on both changed files

[pogudingleb]

Thanks!
I will make some modifications.

[sumiya11]

Note this is fixed in #522 .

The fix there is replacing generators with RationalFunctionFields.generators. (Arguably, the latter should be documented in RFF.jl)

[sumiya11]

With this, the qualifier RationalFunctionFields. can be dropped :

pogudingleb/RationalFunctionFields.jl#70

[pogudingleb]

Fixed by #537