ON THE COMPLEXITY OF BILINEAR FORMS OVER ASSOCIATIVE ALGEBRAS
| dc.contributor.author | Bshouty, Nader H. | eng |
| dc.date.accessioned | 2008-05-26T20:40:33Z | |
| dc.date.available | 2008-05-26T20:40:33Z | |
| dc.date.computerscience | 1999-05-27 | eng |
| dc.date.issued | 1989-12-01 | eng |
| dc.description.abstract | Let $F$ be a field and let $Q( alpha )~=~q sub 1 sup {d sub 1} ( alpha )... q sub k sup {d sub k} ( alpha )~\(mo~F[ alpha ]$ be a polynomial of degree $n$ where $q sub 1 ( alpha ),...,q sub k ( alpha )$ are distinct irreducible polynomials. Let $y sub 1 ( alpha ),...,y sub r ( alpha ),~x sub 1 ( alpha ),...,x sub 3 ( alpha )$ be $r~+~s,~n~-~$1-degree polynomials. It is shown that if $Card(F)~>=~max sub {1 <=i<=k}~2deg~q sub i sup d sub i ( alpha )~-~2$ then the number of nonscalar multiplications/divisions required to compute the coefficients of $x sub i ( alpha ) y sub 1 ( alpha )~ mod~Q( alpha ),~i=1,...,s$ by straight line algorithms is $ s(2n~-~k) $. We also prove that if $H$ is an $s~times~r$ matrix with entries from $F$ then the number of nonscalar multiplications/divisions required to compute the coefficients of $(x sub 1 ( alpha ),...,x sub s ( alpha ))H(y sub 1 ( alpha ), ...,y sub r ( alpha )) sup T $ by straight line algorithms is $ rank(H)(2n~-~k)$. All those systems satisfy the direct sum conjecture strongly. For some other algebras that are direct sum of local algebras the above results also hold. | eng |
| dc.description.notes | We are currently acquiring citations for the work deposited into this collection. We recognize the distribution rights of this item may have been assigned to another entity, other than the author(s) of the work.If you can provide the citation for this work or you think you own the distribution rights to this work please contact the Institutional Repository Administrator at digitize@ucalgary.ca | eng |
| dc.identifier.department | 1989-373-35 | eng |
| dc.identifier.doi | http://dx.doi.org/10.11575/PRISM/30484 | |
| dc.identifier.uri | http://hdl.handle.net/1880/46600 | |
| dc.language.iso | Eng | eng |
| dc.publisher.corporate | University of Calgary | eng |
| dc.publisher.faculty | Science | eng |
| dc.subject | Computer Science | eng |
| dc.title | ON THE COMPLEXITY OF BILINEAR FORMS OVER ASSOCIATIVE ALGEBRAS | eng |
| dc.type | unknown | |
| thesis.degree.discipline | Computer Science | eng |