Fast Multiplication of Polynomials over Arbitrary Rings*

نویسندگان

  • David G. Cantor
  • Erich Kaltofen
چکیده

An algorithm is presented that allows to multiply two univariate polynomials of degree no more than n with coefficients from an arbitrary (possibly non-commutative) ring in O(n log(n) log(log n)) additions and subtractions and O(n log(n)) multiplications. The arithmetic depth of the algorithm is O(log(n)). This algorithm is a modification of the Schönhage-Strassen procedure to arbitrary radix fast Fourier transforms, and division by the radix is circumvented. By a Kronecker homomorphism the method can be extended to multivariate polynomials. * This material is based upon work supported by the National Science Foundation under Grant Nos. DCR-85-04391 and CCR-87-0563 and by an IBM Faculty Development Award (second author).

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تاریخ انتشار 2015