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The parametrizations in shape position are obtained by solving Hankel systems with a Gohberg-Semencul type formula, which requires the constant coefficient of the first generator Z1 to be nonzero. For a random sequence this fails with probability about 1/p, when a sub-block of size dim - 1 of the Hankel matrix is singular. The code handling this case borders the Hankel matrix into one of size dim + 1, for which the formula applies, but it silently returned wrong parametrizations. Fix the three issues of that code: build the bordered sequence from the points after undoing their mirroring, clear the polynomial used as scratch space by nmod_em_gcd_preinstantiated before filling it again, and recover the solutions of the original system from the bordered generators. invert_hankel_matrix now returns 2 in the bordered case so that solve_hankel can apply this correction. This was the cause of the random failure of diff_cyclic5-16.sh seen in CI with SEED=1790795968. Add a regression test with that seed; it exercises the degenerate case with glibc's rand(). Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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It's ok for me but maybe @jerebertho you could also have a look since you know this part better than me
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This PR is entirely prepared by Claude Code. Below is the commit message.
Fixes #331.
Fixes #368.
The parametrizations in shape position are obtained by solving Hankel systems with a Gohberg-Semencul type formula, which requires the constant coefficient of the first generator Z1 to be nonzero. For a random sequence this fails with probability about 1/p, when a sub-block of size dim - 1 of the Hankel matrix is singular. The code handling this case borders the Hankel matrix into one of size dim + 1, for which the formula applies, but it silently returned wrong parametrizations.
Fix the three issues of that code: build the bordered sequence from the points after undoing their mirroring, clear the polynomial used as scratch space by nmod_em_gcd_preinstantiated before filling it again, and recover the solutions of the original system from the bordered generators. invert_hankel_matrix now returns 2 in the bordered case so that solve_hankel can apply this correction.
This was the cause of the random failure of diff_cyclic5-16.sh seen in CI with SEED=1790795968. Add a regression test with that seed; it exercises the degenerate case with glibc's rand().