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PDF-Lecture10TheSylvesterResultantWewanttocomputeintersectionsofalgebraicc PDF document

hf hhg hf hgorfg hf hg0Inotherwordswehavenonzeropolynomialssghandtfhsuchthat0degsdeggand0degtdegfandfsgt01WehavethusprovedonedirectionofthefollowingLemmaLEMMA1Letf2Rxandg2Rx

h=f hhg h=f hgorfg hf hg0:Inotherwords wehavenonzeropolynomialss=g=handt=f=hsuchthat0degsdeggand0degtdegfandfs+gt0:(1)WehavethusprovedonedirectionofthefollowingLemma.LEMMA1.Letf2R[x]andg2R[x

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