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CommAlgebras as CommRingHoms #1145

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This is an experiment to see if algebras work better when they are defined as homomorphisms of rings.

@felixwellen felixwellen force-pushed the fwellen/ring_with_hom_algebras branch 5 times, most recently from 8a04a53 to e997ccd Compare August 2, 2024 16:22
@felixwellen felixwellen force-pushed the fwellen/ring_with_hom_algebras branch 3 times, most recently from 5abb334 to 72226e5 Compare August 7, 2024 15:16
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I did some random benchmarking (this PR is not really about type checking speed, but I made some changes while I rewrote code). In summary, the two modules in CommAlgebra with comparable content have signficantly lower type checking times now, while there is no significant change for the modules in Ring and CommRing I checked.

* Ring/Quotient
*New*

Deserialization            2,471ms (3,109ms)
Typing                         3ms   (580ms)

*master*

Deserialization            2,449ms (3,086ms)
Typing                         5ms   (535ms)


* CommRing/Localisation/PullbackSquare
*New*

Typing                                       1ms (8,193ms)
Deserialization                          4,001ms (5,061ms)

*master*
Typing                                       1ms (7,534ms)
Deserialization                          3,809ms (4,842ms)

* CommAlgebra/Localisation
*New*

Deserialization                         4,537ms (5,754ms)
Typing                                      4ms (1,357ms)

*master*
Deserialization                         4,721ms (5,998ms)
Typing                                      5ms (3,354ms)

* CommAlgebra/QuotientAlgebra
*New* 
Deserialization            3,431ms (4,312ms)
Typing                         4ms   (656ms)

*master*
Deserialization                         3,610ms (4,553ms)
Typing                                      1ms (2,131ms)

@felixwellen felixwellen force-pushed the fwellen/ring_with_hom_algebras branch 2 times, most recently from e3cae56 to 04adbaf Compare September 2, 2024 07:58
@felixwellen felixwellen force-pushed the fwellen/ring_with_hom_algebras branch from 04adbaf to 1cb7ca5 Compare September 30, 2024 12:27
@felixwellen felixwellen force-pushed the fwellen/ring_with_hom_algebras branch from 1cb7ca5 to e62abab Compare September 30, 2024 16:30
@felixwellen felixwellen force-pushed the fwellen/ring_with_hom_algebras branch from e62abab to bc7a252 Compare October 1, 2024 09:13
@felixwellen felixwellen force-pushed the fwellen/ring_with_hom_algebras branch from 8abc7a4 to 7917b85 Compare October 16, 2024 15:29
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