特征为2的有理函数域上求二次型的非平凡零

Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation Pub Date : 2022-03-08 DOI:10.1145/3476446.3535485

P. Kutas, Mickaël Montessinos, Gergely Zábrádi, T'imea Csah'ok

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引用次数: 2

摘要

提出了在特征为2的有理函数域上求四变量二次型非平凡零点的多项式时间算法。我们应用这些结果，在由结构常数给出的除法代数上的满矩阵代数$M_2(D)$中，求出四元数除法代数和零除法代数的规定二次子域。我们还提供了一个在MAGMA中实现我们的结果，表明算法是真正实用的。

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Finding Nontrivial Zeros of Quadratic Forms over Rational Function Fields of Characteristic 2

We propose polynomial-time algorithms for finding nontrivial zeros of quadratic forms with four variables over rational function fields of characteristic 2. We apply these results to find prescribed quadratic subfields of quaternion division algebras and zero divisors in $M_2(D)$, the full matrix algebra over a division algebra, given by structure constants. We also provide an implementation of our results in MAGMA which shows that the algorithms are truly practical.

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Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation

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