Fix missing warning in SplittingAlgebra

[soehms]

📝 Checklist

• The title is concise and informative.
• The description explains in detail what this PR is about.
• I have linked a relevant issue or discussion.
• I have created tests covering the changes.
• I have updated the documentation and checked the documentation preview.

This PR fixes the bug identified at #40213 (comment). In detail:

• The keyword is passed in recursive calls.
• An additional check is added before the warning in recursive calls is raised to avoid unnecessary warnings.

This PR also fixes some optional doctests in src/sage/algebras/hecke_algebras/cubic_hecke_algebra.py that were broken due to changes to polynomial formatting.

⌛ Dependencies

[github-actions]

Documentation preview for this PR (built with commit 3c445f3; changes) is ready! 🎉
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[user202729]

if it defaults to None but is set to True whenever it's None, isn't it simpler to default it to True as before?

[soehms]

if it defaults to None but is set to True whenever it's None, isn't it simpler to default it to True as before?

Yes, you're right! I changed that again (it must have been a relic from a previous attempt). Thanks for watching.

[user202729]

not sure if the following can happen and what's the intended behavior. Let's say you have

def f(warning=True):
	g(warning=warning)
	h(warning=warning)

def g(warning=True):
	if some_condition:
		warn(...)
		warning=False

def h(warning=True):
	if some_condition:
		warn(...)
		warning=False

and both some_condition is True, then the warning=False set in g will not be propagated to h, raising two warnings.
(although having extra warnings doesn't really cause any harm, plus the warning message may be different anyway)

[soehms]

not sure if the following can happen and what's the intended behavior. Let's say you have

def f(warning=True):
	g(warning=warning)
	h(warning=warning)

def g(warning=True):
	if some_condition:
		warn(...)
		warning=False

def h(warning=True):
	if some_condition:
		warn(...)
		warning=False

and both some_condition is True, then the warning=False set in g will not be propagated to h, raising two warnings. (although having extra warnings doesn't really cause any harm, plus the warning message may be different anyway)

I understand your point, but I think it doesn't apply in our cases:

1. Your f is the __init__ of SplittingAlgebra. Then g is its class call, and h = f (recursively). Since the latter is applied to a polynomial of degree one, the warning doesn't occur there.
2. Your f is solve_with_extension, and g and h are both create_roots. Here, g and h are in different conditional branches.