Gosper表示及其應(yīng)用.pdf

1、南開大學(xué)碩士學(xué)位論文Gosper表示及其應(yīng)用姓名：霸志輝申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：侯慶虎20080501AbstractAbstractGosper’SalgorithmisoneofthelandmarksinthehistoryofcomputerizationoftheproblemofclosedformsummationOnekeyideainthisalgorithmistowritearationalfun

2、ctioninitsGosperrepresentationThestandardmethodtocomputetheGosperrepresentationinvolvescoinputingtheresultantoftwopolynomialswithanadditionalparameterandfindingnonnegativeintegerrootsoftheresultantThesetwostepsarethemost

3、timecostpartofthecomputationInthisthesis，weprovideanalternativemethodtoavoidsuchcomputationsNoticethattheintegerrootofapolynomialwithintegercoefficientsmustdividetheconstanttermofthepolynomialWecomputetheconstanttermdire

4、ctlyinsteadofcomputingtheresultantwithparametersThisreducesthecomputationtimesharplyasindicatedbytherealexperimentWealsoprovideexamplesfromitsimplementationthatillustratetheadvantagesovertheuseofresultantwithanadditional

5、parameterGosper’SrepresentationplaysanimportantroleinmanyproblemsinsymboliccomputationsInthefollowingpartofthethesis，wereviewseveralclassicalapplicationsoftherepresentation，includingGosper’Salgorithmanditsexten‘1’’1，一一1一

6、一～slon，Zellberger7Salgorithm，closedtormsolutionoflineardifferenceequationsFinallyweprovideanexampletoillustratehowtoapplythesealgorithmstofindtheformalpowerseriesofsomespecialfunctionsKeywords：Gosper’Salgorithm，Zeilberge