Gauss Lucas theorem：The Gauss–Lucas Theorem
The Gauss–Lucas Theorem
由JCBaez著作·1988—TheGauss–Lucastheoremsaysthatforanycomplexpoly-nomial,therootsofthederivative′lieintheconvexhulloftherootsof.。其他文章還包含有：「Gauss–Lucastheorem」、「Gauss」、「說明」、「Gauss」、「SOMEAPPLICATIONSOFTHEGAUSS」、「UnderstandingaproofofGauss」、「Mathematics」、「ArefinementoftheGauss–Lucastheorem(afterW.P....」、「[2112.00110]TheGauss」
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Gauss–Lucas theorem
https://en.wikipedia.org
Gauss
https://math.stackexchange.com
Gauss-Lucas theorem proof ... The Gauss-Lucas Theorem states that: All the critical points of a non-constant polynomial f (i.e. the roots of f′ ) ...
說明
https://zh.wikipedia.org
Gauss
https://proofwiki.org
Theorem. Let P be a non-constant polynomial in C. Then all zeroes of its derivative P′ belong to the convex hull of the set of zeroes of P.
SOME APPLICATIONS OF THE GAUSS
https://www.e-periodica.ch
series. The Gauss-Lucas Theorem. The zeros of the derivative of a non-constant polynomial P lie in the convex ...
Understanding a proof of Gauss
https://math.stackexchange.com
According to a proof of Gauss-Lucas theorem from wikipedia, a logarithmic derivative of polynomial P(z) is P′(z)P(z)=n∑i=11z−zi=n∑i=1¯z−¯zi| ...
Mathematics
https://skosmos.loterre.fr
The theorem states that the roots of P' all lie within the convex hull of the roots of P, that is the smallest convex polygon containing the ...
A refinement of the Gauss–Lucas theorem (after W.P. ...
https://www.sciencedirect.com
The following theorem by Gauss and rediscovered by Lucas describes a beautiful relationship between the roots of a polynomial and the roots of its derivative.
![[2112.00110] The Gauss](https://i0.wp.com/api.multiavatar.com/%5B2112.00110%5D+The+Gauss-Lucas+Theorem.png?apikey=viVnb6N20jclO8){kind=avatar}
[2112.00110] The Gauss
https://arxiv.org
Abstract:The Gauss-Lucas theorem says that for any complex polynomial P, the roots of the derivative P' lie in the convex hull of the roots ...