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feat: ordinal powers of a field form a basis for nimbers - #348

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feat: ordinal powers of a field form a basis for nimbers#348
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@vihdzp

@vihdzp vihdzp commented Mar 5, 2026

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@vihdzp vihdzp added the t-nimber This is mainly about nimbers label Mar 5, 2026
@plp127

plp127 commented Mar 5, 2026

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Why do you use AddMonoidAlgebra? You don't need the "algebra" part, right?

@vihdzp

vihdzp commented Mar 5, 2026

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You're right, I've re-stated everything in terms of finsupps.

Comment thread CombinatorialGames/Nimber/Finsupp.lean
Comment thread CombinatorialGames/Nimber/Finsupp.lean
/-- `toFinsupp b hb x e` returns the coefficient of `b ^ e` in `x`. This is a specialization of
`Ordinal.CNF.coeff`. -/
@[pp_nodot]
def toFinsupp (x : Nimber) : Ordinal →₀ hb.toSubfield :=

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Would it be possible to only expose the bundled LinearEquiv? I can't think of a scenario in which having a LinearEquiv instead of a plain function would be bad.

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