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单词 ExamplesOfTraceAndNorm
释义

examples of trace and norm


Let ω be a complex root of unity different than 1. Then ω and ω2 are the conjugatePlanetmathPlanetmathPlanetmath roots of the minimal polynomialPlanetmathPlanetmath x2+x+1.Since (ω) is the splitting fieldMathworldPlanetmath of x2+x+1, it is Galois over . Moreover the Galois groupMathworldPlanetmath Gal((ω)/)) is formed by the identityPlanetmathPlanetmath and the automorphismPlanetmathPlanetmathPlanetmath g(ω)=ω2The elements of (ω) have the form a+bω, a,b.Then we obtain

N(ω)(a+bω)=(a+bω)(a+bω2)=a2-ab+b2,Tr(ω)(a+bω)=(a+bω)+(a+bω2)=2a-b
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更新时间:2025/5/4 23:43:04