Geodesic
Multiple discriminants and extreme values of polynomials of several variables
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Mathematical analysis, Tome 143 (2017), pp. 87-94.

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An extreme value of a function is the value of the function at one of its extremum points. Each extremum point of a differentiable function of several variables is described by the system of equations expressing the vanishing of all partial derivatives. However, in the general case, one cannot obtain equations for extreme values of the function. The case of polynomials significantly differs from the general case, and in this paper we obtain an equation for extreme values of a given polynomial of several variables.
Mots-clés : polynomial, discriminant
Keywords: extremum point, extreme value. 
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     author = {R. A. Sharipov},
     title = {Multiple discriminants and extreme values of polynomials of several variables},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {87--94},
     publisher = {mathdoc},
     volume = {143},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_143_a6/}
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R. A. Sharipov. Multiple discriminants and extreme values of polynomials of several variables. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Mathematical analysis, Tome 143 (2017), pp. 87-94. http://geodesic.mathdoc.fr/item/INTO_2017_143_a6/