Prevent race condition in makeMonomialOrdering

[d-torrance]

A number of the variables used in this function are global, so we lock while modifying them so we can construct monomial orders in parallel.

This also gives us a chance to use the new Mutex class!

Before

i1 : unique \\ class \ taskResult \ apply(20, i -> schedule(() -> ZZ[x]))
/usr/share/Macaulay2/Core/engine.m2:103:47:(1):[18]: error: Inverses => true not compatible with GRevLex
/usr/share/Macaulay2/Core/engine.m2:113:15:(1):[17]: --back trace--
/usr/share/Macaulay2/Core/engine.m2:152:45:(1):[16]: --back trace--
/usr/share/Macaulay2/Core/engine.m2:211:51:(1):[14]: --back trace--
/usr/share/Macaulay2/Core/monoids.m2:565:61:(1):[13]: --back trace--
/usr/share/Macaulay2/Core/methods.m2:130:48:(1):[12]: --back trace--
/usr/share/Macaulay2/Core/methods.m2:146:20:(1):[11]: --back trace--
/usr/share/Macaulay2/Core/option.m2:17:14:(1):[10]: --back trace--
/usr/share/Macaulay2/Core/monoids.m2:589:17:(1):[6]: error: degree list should be of length 0
/usr/share/Macaulay2/Core/remember.m2:11:24:(1):[8]: --back trace--
/usr/share/Macaulay2/Core/methods.m2:130:48:(1):[5]: --back trace--
/usr/share/Macaulay2/Core/polyrings.m2:90:31:(1):[7]: --back trace--
/usr/share/Macaulay2/Core/methods.m2:146:20:(1):[4]: --back trace--
/usr/share/Macaulay2/Core/remember.m2:11:24:(1):[7]: --back trace--
/usr/share/Macaulay2/Core/polyrings.m2:138:55:(1):[2]: --back trace--
/usr/share/Macaulay2/Core/monoids.m2:587:62:(1):[6]: --back trace--
/usr/share/Macaulay2/Core/monoids.m2:589:17:(1):[6]: error: degree list should be of length 0
/usr/share/Macaulay2/Core/methods.m2:130:48:(1):[5]: --back trace--
/usr/share/Macaulay2/Core/methods.m2:130:48:(1):[5]: --back trace--
/usr/share/Macaulay2/Core/methods.m2:146:20:(1):[4]: --back trace--
/usr/share/Macaulay2/Core/methods.m2:146:20:(1):/usr/share/Macaulay2/Core/polyrings.m2:138:55:(1):[2]: --back trace--
[4]: --back trace--
/usr/share/Macaulay2/Core/polyrings.m2:138:55:(1):[2]: --back trace--
/usr/share/Macaulay2/Core/monoids.m2:589:17:(1):[6]: error: degree list should be of length 0
/usr/share/Macaulay2/Core/methods.m2:130:48:(1):[5]: --back trace--
/usr/share/Macaulay2/Core/methods.m2:146:20:(1):[4]: --back trace--
/usr/share/Macaulay2/Core/polyrings.m2:138:55:(1):[2]: --back trace--

o1 = {Nothing, PolynomialRing}

o1 : List

After

i1 : unique \\ class \ taskResult \ apply(20, i -> schedule(() -> ZZ[x]))

o1 = {PolynomialRing}

o1 : List

Closes: #3239 (one of our greatest hits of GitHub workflow build failures!)

AI Disclosure

Claude Code zeroed in on what was causing check(6, "NumericalImplicitization") to fail frequently and wrote an early draft of this commit.

[mahrud]

I was planning on using this as an exercise in debugging :)
That whole section of code should be refactored to be re-entrant IMO.

[mahrud]

On my system, I've added a handy unlock(Mutex, Thing) := (M, x) -> ( unlock M; x ), so I can write:

     unlock(makeMonomialOrderingMutex, (t,t',value logmo, logmo)))

[d-torrance]

Ooh, that's slick! Want to submit a PR to add it for everyone?