?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=Bases+de+Gr%C3%B6bner+y+aplicaciones&rft.creator=Garc%C3%ADa+de+la+Cruz+Garc%C3%ADa%2C+Juan&rft.contributor=S%C3%A1nchez+Hern%C3%A1ndez%2C+Jonathan&rft.subject=Computer+Science&rft.subject=Mathematics&rft.description=Una+base+de+Gr%C3%B6bner+es+un+tipo+especial+de+conjunto+generador+de+un+ideal+de+un+anillo+de+polinomios+que+cumple+una+serie+de+propiedades+muy+interesantes.+Este+trabajo+tiene+como+objetivo+su+estudio%2C+para+ello+se+realiza+una+aproximaci%C3%B3n+matem%C3%A1tica+a+las+bases+de+Gr%C3%B6bner%2C+desde+los+conceptos+m%C3%A1s+fundamentales+hasta+conocer+algunas+de+sus+aplicaciones.+Adem%C3%A1s+se+implementa+una+biblioteca+en+C%23+que+recoge+toda+la+teor%C3%ADa+vista%2C+junto+una+aplicaci%C3%B3n+gr%C3%A1fica+que+muestra+el+potencial+de+la+biblioteca+y+a+par+que+el+de+las+propias+bases+de+Gr%C3%B6bner.+Todo+esto+ir%C3%A1+acompa%C3%B1ado+de+numerosos+ejemplos+que+pretenden+facilitar+la+comprensi%C3%B3n.---ABSTRACT---A+Gr%C3%B6bner+basis+is+a+special+kind+of+generator+set+of+an+ideal+in+a+polynomial+ring+that+satisfies+a+series+of+very+interesting+properties.+The+current+project+tackles+their+study.+For+this%2C+a+mathematical+approach+is+done+to+the+subject%2C+starting+with+the+most+basic+underlying+ideas%2C+and+walking+the+reader+comprehensively+through+the+not+so+easy+concepts%2C+up+to+some+of+their+applications.+Numerous+original+examples+will+be+given+throughout+the+document+with+the+aim+of+easing+and+helping+with+the+reading+and+understanding+of+the+theory+presented.+Additionaly+a+C%23+library+is+developed%2C+which+implements+all+the+theoretical+concepts+given%2C+this+library+is+accompanied+by+a+graphical+application+that+showcases+the+potential+of+both%2C+the+library+and+Gr%C3%B6bner+bases.&rft.publisher=E.T.S.+de+Ingenieros+Inform%C3%83%C2%A1ticos+(UPM)&rft.rights=https%3A%2F%2Fcreativecommons.org%2Flicenses%2Fby-nc-nd%2F3.0%2Fes%2F&rft.date=2020-07&rft.type=info%3Aeu-repo%2Fsemantics%2FbachelorThesis&rft.type=Final+Project&rft.type=NonPeerReviewed&rft.format=application%2Fpdf&rft.language=spa&rft.rights=info%3Aeu-repo%2Fsemantics%2FopenAccess&rft.identifier=https%3A%2F%2Foa.upm.es%2F63155%2F