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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


The minimum root separation of a polynomial
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by George E. Collins and Ellis Horowitz PDF
Math. Comp. 28 (1974), 589-597 Request permission


The minimum root separation of a complex polynomial A is defined as the minimum of the distances between distinct roots of A. For polynomials with Gaussian integer coefficients and no multiple roots, three lower bounds are derived for the root separation. In each case, the bound is a function of the degree n of A and the sum d of the absolute values of the coefficients of A. The notion of a seminorm for a commutative ring is defined, and it is shown how any seminorm can be extended to polynomial rings and matrix rings, obtaining a very general analogue of Hadamard’s determinant theorem.
    G. E. Collins, "Computing time analyses for some arithmetic and algebraic algorithms," Proc. 1968 Summer Institute on Symbolic Mathematical Computation, IBM Corp., Cambridge, Mass., 1961, pp. 197-231.
  • George E. Collins, The calculation of multivariate polynomial resultants, J. Assoc. Comput. Mach. 18 (1971), 515–532. MR 298921, DOI 10.1145/321662.321666
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Math. Comp. 28 (1974), 589-597
  • MSC: Primary 12D10; Secondary 30A08
  • DOI:
  • MathSciNet review: 0345940