1129
eng
reportzib
0
2009-05-13
2009-05-13
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Hyperdeterminants as integrable discrete systems
We give the basic definitions and some theoretical results about hyperdeterminants, introduced by A.~Cayley in 1845. We prove integrability (understood as $4d$-consistency) of a nonlinear difference equation defined by the $2 \times 2 \times 2$ - hyperdeterminant. This result gives rise to the following hypothesis: the difference equations defined by hyperdeterminants of any size are integrable. We show that this hypothesis already fails in the case of the $2\times 2\times 2\times 2$ - hyperdeterminant.
09-17
1438-0064
1178
10.1088/1751-8113/42/45/454023
0903.3864
urn:nbn:de:0297-zib-11292
Appeared in: J. Phys. A: Math. Theor., 42 (2009), 454023, 9 pages
Sergey Tsarev
unknown unknown
Thomas Wolf
ZIB-Report
09-17
eng
uncontrolled
hyper determinants
eng
uncontrolled
integrable systems
eng
uncontrolled
discrete equations
eng
uncontrolled
large polynomial systems
eng
uncontrolled
computer algebra
eng
uncontrolled
Form
eng
uncontrolled
Reduce
eng
uncontrolled
Singular
Informatik, Informationswissenschaft, allgemeine Werke
Integrable systems
Symbolic computation (computer algebra)
Explicit machine computation and programs (not the theory of computation or programming)
None of the above, but in this section
Digital Data and Information for Society, Science, and Culture
https://opus4.kobv.de/opus4-zib/files/1129/ZR_09_17.pdf
https://opus4.kobv.de/opus4-zib/files/1129/ZR_09_17.ps