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Family: mordell — Mordell equation - #29

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Family: mordell — Mordell equation#29
roed-math wants to merge 1 commit into
DiophantineLibrary:split/09-backbone-deepfrom
roed-math:family/mordell

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@roed-math roed-math commented Aug 8, 2026

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One family: Mordell equation (mordell) — P1, algorithmic.

  • Standard form: y^2 = x^3 + k
  • Parent: elliptic-weierstrass
  • Examples: y^2 = x^3 - 2

Contents: the registry entry, its docs/FAMILIES.md section, its rows in the classification corpus, its solver and solver-layer tests.

References cited (the claim each one supports):

  • GebelPethoZimmer1998 — the method, with tables for |k| <= 10^4
  • BennettGhadermarzi2015 — complete tables for |k| <= 10^7

Independent of every other family PR: it needs only the registry backbone it is based on.

Part of the series that splits #1 into reviewable pieces:

  1. 01-bibliography — packaging, docs, annotated bibliography
  2. 02-parsing — equation strings to a term model
  3. 03-registry — the YAML family registry (3 seed families)
  4. 04-matchers — shape recognizers
  5. 05-classify — the classification pipeline
  6. 06-solvers — solver framework, two seed solvers, and the CLI
  7. 07..09-backbone — the 23 parent families of the DAG, by depth
  8. one PR per remaining family (38 of them, mutually independent)
  9. 99-polish — restore the full doctests and tighten the invariants

One family: **Mordell equation** (`mordell`) — P1, algorithmic.

- Standard form: `y^2 = x^3 + k`
- Parent: `elliptic-weierstrass`
- Examples: `y^2 = x^3 - 2`

Contents: the registry entry, its `docs/FAMILIES.md` section, its rows in the classification corpus, its solver and solver-layer tests.

References cited (the claim each one supports):

- `GebelPethoZimmer1998` — the method, with tables for |k| <= 10^4
- `BennettGhadermarzi2015` — complete tables for |k| <= 10^7

Independent of every other family PR: it needs only the registry backbone it is based on.

Part of the series that splits #1 into reviewable pieces:

1. `01-bibliography` — packaging, docs, annotated bibliography
2. `02-parsing` — equation strings to a term model
3. `03-registry` — the YAML family registry (3 seed families)
4. `04-matchers` — shape recognizers
5. `05-classify` — the classification pipeline
6. `06-solvers` — solver framework, two seed solvers, and the CLI
7. `07..09-backbone` — the 23 parent families of the DAG, by depth
8. one PR per remaining family (38 of them, mutually independent)
9. `99-polish` — restore the full doctests and tighten the invariants
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