[kaushikgunasekaren]

Ellipse.polynomial documents coefficients of an equation equal to zero, but its constant term omits the ellipse's unit level. For a unit circle it returns [1, 1, 0, 0, 0, 0], describing x**2 + y**2 = 0 instead of x**2 + y**2 - 1 = 0. Every perimeter point evaluates to 1 rather than 0.

Subtract 1 from the constant coefficient when expanding (x-centre).T @ E @ (x-centre) = 1.

Validation on current master 25b19b3, Python 3.10:

• 12 regression configurations span two radii pairs, translated/origin centres and three rotations. Independently constructed perimeter points evaluate to 0, the centre to -1 and a point at twice the radius to 3. All 12 configurations fail before the fix and pass after it.
• Full local suite: 567 passed, 3 skipped, 111 subtests passed; 29 existing warnings. Pristine baseline: 566 passed, 3 skipped, 99 subtests passed with the same warnings.
• Black 23.10.0, fatal-error flake8 checks on changed files, and git diff --check pass.

This fixes coefficient export only, independently of #290's coefficient-import normalization. AI assistance was used for investigation, implementation and tests. Validated locally without robot hardware.