| _version_ | 1866901846152445952 |
|---|---|
| author | Wu, Yuchen |
| author_facet | Wu, Yuchen |
| contents | <p>This upload contains two Python/SymPy scripts (m = 3 and m = 4) that construct an explicit homogeneous polynomial c and verify, over the field F2, a C2-equivariant polynomial identity of the form</p> <p> t1 * v_{2m-1} + b * g(b) = Tr(c) = c + g(c),</p> <p>in a suitable quotient of a polynomial ring with a C2-action (g swaps the indicated generators). Each script implements the transfer map Tr(c)=c+g(c) using simultaneous substitution, constructs c by solving a linear system over F2 in a fixed homogeneous degree, and verifies the identity via reduction using Grobner bases in the eliminated presentation.</p> <p>Files:<br> - verify_m=3.py<br> - verify_m=4.py</p> <p>Run:<br> python3 verify_m=3.py<br> python3 verify_m=4.py</p> <p>Dependency:<br> sympy</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18373311 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Verification scripts for a C2-equivariant polynomial identity over F2 (cases m=3,4) Wu, Yuchen <p>This upload contains two Python/SymPy scripts (m = 3 and m = 4) that construct an explicit homogeneous polynomial c and verify, over the field F2, a C2-equivariant polynomial identity of the form</p> <p> t1 * v_{2m-1} + b * g(b) = Tr(c) = c + g(c),</p> <p>in a suitable quotient of a polynomial ring with a C2-action (g swaps the indicated generators). Each script implements the transfer map Tr(c)=c+g(c) using simultaneous substitution, constructs c by solving a linear system over F2 in a fixed homogeneous degree, and verifies the identity via reduction using Grobner bases in the eliminated presentation.</p> <p>Files:<br> - verify_m=3.py<br> - verify_m=4.py</p> <p>Run:<br> python3 verify_m=3.py<br> python3 verify_m=4.py</p> <p>Dependency:<br> sympy</p> |
| title | Verification scripts for a C2-equivariant polynomial identity over F2 (cases m=3,4) |
| url | https://doi.org/10.5281/zenodo.18373311 |