Polynomial Relations among Principal Minors of a 4x4 Matrix
Polynomial Relations among
Principal Minors of a 4x4 Matrix
Shaowei Lin and
Bernd Sturmfels
Research Paper
Our paper "Polynomial Relations among Principal Minors of a 4x4 Matrix" can be found here.
Affine relations (ideal-theoretic)
65 polynomials f[1], f[2], ..., f[65] of degree 12 in
variables
A1234, A123, A234, A12, A13, A14, A23, A24, A34, A1, A2, A3, A4.
Maple format:
65gens.txt (12.4 MB)
Projective relations (scheme-theoretic)
718 polynomials homogeneous of degree 12 in variables
A1234, A123, A234, A12, A13, A14, A23, A24, A34, A1, A2, A3, A4,
A.
The 14 files below correspond to the 14 irreducible G-modules in
Theorem 3.
In each module, the polynomial f[i,j,k,l] has multidegree [i,j,k,l].
Maple format:
S4555.txt (37.2 MB)
S5455.txt (37.2 MB)
S5545.txt (37.2 MB)
S5554.txt (37.2 MB)
S4466.txt (7.6 MB)
S4646.txt (7.6 MB)
S4664.txt (7.6 MB)
S6446.txt (7.6 MB)
S6464.txt (7.6 MB)
S6644.txt (7.6 MB)
S3666.txt (2.4 MB)
S6366.txt (2.4 MB)
S6636.txt (2.4 MB)
S6663.txt (2.4 MB)
Polynomials D, E, F
The 1st, 5th and 26th polynomials (d, e and f)
in Table 1 are given below in terms of the cycle-sums
C1234, C123, C234, C12, C13, C14, C23, C24, C34, C1, C2, C3, C4.
The polynomials D, E and F in Section 4 are derived from them
by writing the cycle-sums in terms of the principal minors and
homogenizing the polynomials with respect to the 0x0-minor
A.
Maple format:
d.txt (0.9 KB)
e.txt (1.2 KB)
f.txt (2.8 KB)
Last Updated: 02 Dec 2008