Verification scripts for a C2-equivariant polynomial identity over F2 (cases m=3,4)

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Main Author: Wu, Yuchen
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Published: Zenodo 2026
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_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
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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