منابع مشابه
The Fourier structure of low degree polynomials
We study the structure of the Fourier coefficients of low degree multivariate polynomials over finite fields. We consider three properties: (i) the number of nonzero Fourier coefficients; (ii) the sum of the absolute value of the Fourier coefficients; and (iii) the size of the linear subspace spanned by the nonzero Fourier coefficients. For quadratic polynomials, tight relations are known betwe...
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Every Latin square of prime or prime power order s corresponds to a polynomial in 2 variables over the finite field on s elements, called the local permutation polynomial. What characterizes this polynomial is that its restrictions to one variable are permutations. We discuss the general form of local permutation polynomials and prove that their total degree is at most 2s−4, and that this bound...
متن کاملOn the resultant of degree-deficient polynomials
The resultant is an algebraic expression, computable in a finite number of arithmetic operations from the coefficients of two univariate polynomials, that vanishes if, and only if, the two polynomials have common zeros. The paper considers formal resultant for degree-deficient polynomials (polynomials whose actual degree is lower than their assumed degree). Some key properties of the resultant ...
متن کاملThe Degree of Approximation for Generalized Polynomials
The classical Mu'ntz theorem and the so-called Jackson-Muntz theorems concern uniform approximation on [0,1 ] by polynomials whose exponents are taken from an increasing sequence of positive real numbers A. Under mild restrictions on the exponents, the degree of approximation for A-poly nomials with real coefficients is compared with the corresponding degree of approximation when the coefficien...
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We describe an efficient randomized algorithm to test if a given binary function is a low-degree polynomial (that is, a sum of low-degree monomials). For a given integer and a given real , the algorithm queries at !" # points. If is a polynomial of degree at most , the algorithm always accepts, and if the value of has to be modified on at least an fraction of all inputs in order to transform it...
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ژورنال
عنوان ژورنال: Časopis pro pěstování matematiky
سال: 1965
ISSN: 0528-2195
DOI: 10.21136/cpm.1965.117537