Distributed Computation For Dixon Resultant On VEGA Grid

Elimination Method is an effective method for solving non-linear polynomialequations. It mainly includes Wu's methods, Grobner base and resultant methods.Resultant method is an important tool in elimination theory. Dixon resultant is themore efficient method among the several resultant methods. Dixon resultant can beestablished by polynomial coefficients from the original equation sets and theircombination. That Dixon resultant equals to zero is the sufficient and necessarycondition that the equation sets have common zero point, and whether there are rootsin the equation sets can be deduced. Application of Dixon resultant to solve polynomial equation sets in normalcomputer algebra system is limited by one computer's processing ability andmemory capacity. The Dixon matrix enlarges greatly when the polynomial sets havehigher rank, and the computer may fail in the Dixon resultant computation. Pro.FuHongguang et al recently work out the recursive algorithm for caculating Dixonresultant polynomial, which open the door to utilize distributed and parallelcomputer system.As the computer technology evolves rapidly, CPU speeds, memory capacity andnetwork bandwith grow a great step. Clusters based on high speed switched networkhave been widely deployed. In the meantime, grid computation oriented next internetservice have been taken seriously into account by developed nations which investquite a lot to research, develop and deploy grid system. Recently, Mathmatic, aworld known computer algebra system provides a grid based symbolic computationfunction, Tsinghua University in cooporation with system institute of Academy ofChina Science have transplanted the Wu' methods to Grid based distributedenvironment. These facts demostrate that under grid environment, the existingcomputer algebra system could be extended via parallel solution to solve theproblems of computer algebra much faster, even to solve a few unsolvable problemsfor present computer system. VEGA is a grid system developed by Xu Zhiwei et al.The focus of this thesis is research on the distributed and parallel computation forDixon resultant under VEGA environment.GiNaC symbolic computation system is a kind of open source computer algebrasystem on the basis of Linux. Firstly, we study in the paper how to transplant GiNaCto VEGA and cluster environment, mainly to solve the key problems such ascommunication and storage etc in distributed symbolic computation system, becausethe Dixon resultant involves polynomial operation. Secondly, the Dixon resultantrecursive algorithm is recalled, the problems which we should face to during theparallelization are analyzed, the model of distributed computation for Dixonresultant under VEGA grid and cluster environment is presented. Lastly, the MPIC++ parallel program for calculating Dixon resultant has been immplemented, andencapsulated into VEGA service. In the end, we implement the Dixon distributedcomputation on VEGA. The calculation results show that distributed computationsolution based on VEGA grid and cluster environment can speed up the Dixonresultant calculation efficiently.