Elliptic curve definitions bridging LMFDB knowls to Lean - #71
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…ge ch.4) Mathlib-style definitions from LMFDB elliptic-curve knowls that are not yet in mathlib: additive / multiplicative / bad / potential-good reduction; good-ordinary / good-supersingular reduction; split / non-split multiplicative reduction; plus the finite-field building blocks traceOfFrobenius / IsOrdinary / IsSupersingular. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
…h.4 EC) Extends ForMathlib/4-EC.lean with the global (Dedekind-domain) minimal-model cluster — IsGlobalMinimalModel, IsSemiGlobalMinimalModel, minimalDiscriminantIdeal, IsReducedMinimalModel, IsSemistable, and obstructionExponent/obstructionClass (Silverman's Weierstrass class) — plus the ReductionType enum and the one-offs naiveHeight, naivePointHeight/canonicalHeight, freyCurve, abcQuality, and integralPoints. All compile. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Replaces @IsOrdinary/@IsSupersingular instance passing in IsGoodOrdinaryReduction / IsGoodSupersingularReduction with 'haveI := h; (W.reduction R).IsOrdinary' (dot notation), and the brittle positional pattern '@Affine.Point.some _ _ _ x _ _' in naivePointHeight with the named binder '.some (x := x) ..'. No change in meaning; compiles. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
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Some preliminary comments for reductions.
This was referenced Jun 28, 2026
Compile fixes after merging main (v4.23.0 -> v4.31.0): update moved/deprecated imports (RingTheory.Radical -> .NatInt, RingTheory.ClassGroup -> .Basic; drop the split Module.Torsion imports); IsGoodReduction -> HasGoodReduction (deprecated); Affine.Point.some now takes coordinates explicitly; drop redundant [IsDomain O] (IsDedekindDomain implies it). Remove mordellWeilGenerators: its Module.Free (M / torsion) instance chain no longer synthesizes in v4.31.0, and it is the def flagged in PR review (do we need the basis of generators?) - set aside pending that decision. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
…pe (ch.4 EC) Following review by Multramate (mathlib EC maintainer), now that the branch is on mathlib v4.31.0 which has the reduction API: drop IsAdditiveReduction/IsMultiplicativeReduction/IsSplitMultiplicativeReduction in favour of mathlib's HasAdditiveReduction/HasMultiplicativeReduction/HasSplitMultiplicativeReduction; rebuild IsNonsplitMultiplicativeReduction as HasMultiplicativeReduction and not HasSplitMultiplicativeReduction (drops the [Finite] hypothesis and point-count); IsSemistable uses HasAdditiveReduction; IsBadReduction = not HasGoodReduction. Define IsSupersingular first, IsOrdinary := not IsSupersingular. Restructure ReductionType to good | multiplicative (split : Bool) | additive. IsPotentialGoodReduction keeps the j-invariant criterion (the base-change form needs the finite-extension/DVR-tower machinery; j integral is the equivalent characterization, Silverman AEC VII.5.5). Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
….4 EC) Replace the j-invariant criterion with the base-change form requested in PR review: there exists a DVR S extending R (compatible R->S->Frac S and R->K->Frac S towers) whose fraction field is a finite extension of K over which W has good reduction. Expressed as a single existential over S (no helper structure / Nonempty wrapper); S is universe-pinned to K. Silverman AEC VII.5.5 gives the equivalence with j(E) integral. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
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| variable {O : Type*} [CommRing O] [IsDedekindDomain O] | ||
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| /-- A Weierstrass model over `K = FractionRing O` (with `O` the ring of integers, a Dedekind domain) |
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If you notice in the definition of IsMinimal etc, we want to have an "AKLB" construction rather than a fixed ring and a fixed fraction ring. So the assumptions will need to be a Dedekind domain R, a field K such that IsFractionRing R K (not K = FractionRing R), etc
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@Multramate I did have the AKLB construction, but it costed a few lines of local instance. See the updated file.
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1. used "isGalobalMinimal" instead of "isGlobalMinimalModel" to match
the mathlib naming for "isMinimal"
2. local instance to get rid of the "HaveI"s
3. since IsMinimal -> IsIntegral, no longer has IsIntegral in the
hypothesis
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Adds Lean definitions to
LeanBridge/ForMathlib/4-EC.leanfor LMFDB elliptic-curve knowls (blueprint chapter 4) that are not yet in mathlib, written in mathlib style.What's added
IsAdditiveReduction,IsMultiplicativeReduction,IsBadReduction,IsPotentialGoodReduction,IsGood{Ordinary,Supersingular}Reduction,Is{Split,NonsplitMultiplicative}Reduction, the finite-field blockstraceOfFrobenius,IsOrdinary,IsSupersingular, and theReductionTypeenum.IsGlobalMinimalModel,IsSemiGlobalMinimalModel,minimalDiscriminantIdeal,localMinimalDiscriminant,IsReducedMinimalModel(/ℚ),IsSemistable, andobstructionClass/obstructionExponent(Silverman's Weierstrass class, AEC §VIII.8).
mordellWeilGenerators,naiveHeight,naivePointHeight/canonicalHeight,freyCurve,abcQuality,integralPoints.All compile (
lake build LeanBridge.ForMathlib.«4-EC»). Each docstring documents the modelingchoices and caveats (totality/junk-value conventions, unproven facts taken as hypotheses).
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