ENHANCED ALGORITHM FOR COMPUTING CAYLEY’S FIRST HYPERDETERMINANT

КЭЙЛИ БІРІНШІ ГИПЕРДЕТЕРМИНАНТЫН ЕСЕПТЕУДІҢ ЖЕТІЛДІРІЛГЕН АЛГОРИТМІ
УЛУЧШЕННЫЙ АЛГОРИТМ ВЫЧИСЛЕНИЯ ПЕРВОГО ГИПЕРДЕТЕРМИНАНТА КЭЛИ
Amanov A.
2024 Kazakh-British Technical University

Herald of the Kazakh British Technical UNiversity
2024 #21 Issue 3 58 - 65 pp.

Combinatorial hyperdeterminant – is the homogeneous polynomial in the entries of a hypermatrix of even number of indices, which is also a unique SL-invariant of minimal degree. It was first studied by Cayley in the middle of 19-th century. Given its fundamental nature, the computation of this polynomial is an important task. For fixed and a cubical hypermatrix of length Barvinok introduced an algorithm of computing hyperdeterminant in. Since the problem of deciding whether for the given hypermatrix the hyperdeterminant is equal to zero is NP-hard, it is essential to develop efficient algorithm for computing hyperdeterminant, as the size of problem grows exponentially. We provide enhanced algorithm of computing hyperdeterminant that requires arithmetic operations.

Cayley’s first hyperdeterminant , Laplace expansion , SL-invariant

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Kazakh-British Technical University, Almaty, 050000, Kazakhstan

Kazakh-British Technical University

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