Clarify genus 2 minimal/simplified model snippets - #21
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Rename C/X to Cmin/Csim in the genus 2 curve code snippets and add // minimal equation and // simplified equation comments, so it is clear which model each variable refers to; display Csim after defining it. Point the simplified-model rational points snippet at Csim instead of Cmin, and fix simplify_hyperelliptic_point/comp_poly to divide the y-coordinate by sqrt(n/squarefree_part(n)) rather than n, so the displayed simplified-model points (and the snippet) actually lie on the simplified model when h = 0. Mirror the renaming in the Code-to-Magma download and add a Simplified equation step to it. Verified by running the generated Magma snippets for 169.a.169.1, 400.a.409600.1 and 336.a.172032.1 (all pass except pre-existing Magma package issues), the sage snippets in a sage REPL, page renders and the Magma download via the flask test client, and the genus2_curves test suite (42 passed). Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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The genus 2 curve-page snippets defined a
C(minimal model) and anX(simplified model)without saying which was which. Following the suggestion in the issue, the snippets now use
CminandCsimwith// minimal equation/// simplified equationcomments, and thesimplified-model snippet displays the resulting curve. The simplified-model rational points
snippet now constructs points on
Csimrather than on the minimal model, and the download filegains a matching "Simplified equation" step. Along the way this fixes a bug in
simplify_hyperelliptic_point/comp_poly(y-coordinate divided by the content n of 4f+h²instead of sqrt(n/squarefree_part(n))): for the 3160 curves with h = 0 the displayed
simplified-model points were not actually on the curve (e.g.
(0 : -1/2 : 1)on 400.a.409600.1),and the corrected points are needed for the new snippet to run. Verified by running the generated
Magma/Sage snippets for 169.a.169.1, 400.a.409600.1 and 336.a.172032.1, rendering the affected
pages and the Magma download with the test client, and the genus2_curves test suite (42 passed).
Addresses LMFDB#5344.
🤖 Generated with Claude Code