“ElementarySymmetricPolynomial”的概念、定义、习题解题方法及翻译-数学辞典

单词	ElementarySymmetricPolynomial
释义	elementary symmetric polynomial The coefficient of $x^{n-k}$ in the polynomial $(x+t_{1})(x+t_{2})\\cdots(x+t_{n})$ is called the $k^{\\mathrm{th}}$ elementary symmetric polynomial in the $n$ variables $t_{1},\\dots,t_{n}$ . The elementary symmetric polynomials can also be constructed by taking the sum of all possible degree $k$ monomials in $t_{1},\\dots,t_{n}$ having distinct factors. The first few examples are: $n=1$ : $\\begin{array}[]{l}t_{1}\\end{array}$ $n=2$ : $\\begin{array}[]{l}t_{1}+t_{2}\\\\t_{1}t_{2}\\end{array}$ $n=3$ : $\\begin{array}[]{l}t_{1}+t_{2}+t_{3}\\\\t_{1}t_{2}+t_{2}t_{3}+t_{1}t_{3}\\\\t_{1}t_{2}t_{3}\\end{array}$
随便看	ProofOfWhenIsAPointInsideATriangle proof of when is a point inside a triangle ProofOfWielandtHoffmanTheorem proof of Wielandt-Hoffman theorem ProofOfWilsonsTheorem ProofOfWilsonsTheoremResult ProofOfWilsonsTheoremUsingTheWilsonQuotient proof of Wilson’s theorem proof of Wilson’s theorem result proof of Wilson’s theorem using the Wilson quotient ProofOfYoungInequality proof of Young Inequality ProofOfYoungsInequalityByPicture proof of Young’s inequality by picture ProofOfZermelosPostulate ProofOfZermelosWellorderingTheorem proof of Zermelo’s postulate proof of Zermelo’s well-ordering theorem proof of ◇ is equivalent to ♣ and continuum hypothesis ProofThat3IsTheOnlyPrimePerfectTotientNumber proof that 3 is the only prime perfect totient number ProofThat4xExceedsTheProductOfThePrimesUpToX proof that 4^x exceeds the product of the primes up to x ProofThatACompactSetInAHausdorffSpaceIsClosed proof that a compact set in a Hausdorff space is closed

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elementary symmetric polynomial