refactor(data/polynomial): use monoid_algebra.lift and aeval
#2492
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Some functions and lemmas in `polynomial` now take bundled homomorphisms as arguments.
Don't make `additive` and `multiplicative` irreducible (yet?) because it breaks compilation here and there. Also prove that homomorphisms from `ℕ`, `ℤ` and their `multiplicative` versionsare defined by the image of `1`.
I wonder why it fails to unify instances in `polynomial.algebra`.
jcommelin
reviewed
Apr 28, 2020
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| variables {R A} | ||
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| theorem aeval_def' : | ||
| aeval R A x p = monoid_algebra.lift R (multiplicative ℕ) A (powers_hom A x) p := rfl | ||
| theorem aeval_def' : aeval R A x p = add_monoid_algebra.lift R ℕ A (powers_hom A x) p := rfl |
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The right hand side looks quite intimidating compared to p.eval x. Is this the new simp-normal-form?
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In general there seem to be very few simp-lemmas for aeval. I would expect simp-lemmas for aeval_X and aeval_C.
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This is not a simp lemma. This is a lemma “show me an ugly definition, I want to apply some theorem about add_monoid_algebra.lift”. I'll see if it can be removed. You can find aeval_X and aeval_C below.
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Ok, thanks for explaining. It certainly can stay.
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Thanks for doing all this refactoring work! |
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What happened to this PR? I've lost track of plans to refactor polynomials. |
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monoid_algebrainstead ofadd_monoid_algebra;aevalusingmonoid_algebra.lift;evaletc.