Title  Structure and Efficient Computation of Multiplication Tables and Associated Quadratic Forms 
Author(s)  Hoon Hong, Josef Schicho, Wolfgang Stöcher 
Type  Technical Report, Misc 
Abstract  We characterize the multiplication table of an algebra with a multiplicative unity and derive properties of multiplication tables and associated quadratic forms, which allow efficient computation. We compare several ways of computing a multiplication table and associated quadratic
forms. By index permutation the complexity of the computation time of associated quadratic forms can be reduced. Exploiting the structure concerning equal entries in the multiplication table gives a further speedup. We apply our results to the case of the factor ring K[\bar{x}]/I and give speedups in the appendix. 
Length  8 
File 

Language  English 
Number  9551 
Address  Johannes Kepler University, Linz, Austria 
Year  1995 
Edition  0 
Translation 
No 
Refereed 
No 
Organization 
Johannes Kepler University Linz 
Institution 
RISC (Research Institute for Symbolic Computation) 