cmMinor44Matrix

The module expands every tetrahedral Cayley–Menger cofactor into an explicit polynomial in the six squared edge coordinates. Downstream dihedral-angle calculus can then name polynomial partials instead of opaque Fréchet derivatives.

SqEdges is the type of squared edge lengths of a tetrahedron, indexed by Fin 6. The classical Cayley–Menger setup borders a matrix of those squared distances by a row and column of ones (with a zero corner) so that a principal minor’s determinant encodes volume data and related geometric invariants.

Cofactor $(4,4)$ of the $5\times 5$ bordered matrix is (up to sign) the determinant of the complementary $4\times 4$ principal minor. This definition freezes that minor in a fixed coordinate normal form so later lemmas can equate it to a submatrix extraction and expand its determinant as a named polynomial.

Pure definition: a matrix literal. The four rows are written with the constant border $(0,1,1,1)$ and $(1,\ldots)$, zeros on the squared-distance diagonal block, and the three relevant squared edges $a(0)$, $a(1)$, $a(3)$ in the off-diagonal slots. No lemmas are applied.

Gives a concrete handle on the $(4,4)$ CM minor so the cofactor can be treated as an ordinary polynomial in squared edges. Immediately used by the equality that identifies this matrix with the submatrix of the full bordered CM matrix after deleting index 4, and by the determinant identity that expands $\det$ of this matrix to the named cofactor polynomial cmCofactor3Poly 4 4. Those steps sit in the cofactor analogue of the Cayley–Menger derivative pipeline: once every cofactor is an explicit polynomial, dihedral-angle formulas can differentiate named partials rather than opaque fderiv terms. Sibling minors (34, 24, 23, …) play the same role for the other cofactor slots.