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- W2963396993 abstract "Given any fixed integer q ≥ 2, a q-monomial is of the format [Formula: see text] such that 1 ≤ s j ≤ q - 1, 1 ≤ j ≤ t. q-monomials are natural generalizations of multilinear monomials. Recent research on testing multilinear monomials and q-monomials for prime q in multivariate polynomials relies on the property that Z q is a field when q ≥ 2 is prime. When q > 2 is not prime, it remains open whether the problem of testing q-monomials can be solved in some compatible complexity. In this paper, we present a randomized O*(7.15 k ) algorithm for testing q-monomials of degree k that are found in a multivariate polynomial that is represented by a tree-like circuit with a polynomial size, thus giving a positive, affirming answer to the above question. Our algorithm works regardless of the primality of q and improves upon the time complexity of the previously known algorithm for testing q-monomials for prime q > 7." @default.
- W2963396993 created "2019-07-30" @default.
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- W2963396993 date "2014-03-19" @default.
- W2963396993 modified "2023-09-23" @default.
- W2963396993 title "TOWARD RANDOMIZED TESTING OF q-MONOMIALS IN MULTIVARIATE POLYNOMIALS" @default.
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- W2963396993 doi "https://doi.org/10.1142/s1793830914500165" @default.
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