Some decision problems for polynomial mappings
نویسندگان
چکیده
منابع مشابه
Some combinatorial questions about polynomial mappings
The purpose of this note is to show how recent progress in non-commutative combinatorial algebra gives a new input to Jacobian-related problems in a commutative situation. @ 1997 Elscvier Science B.V. 1991 Math. Subj. Class.: 13B2.5, 13810, 14A05
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Some decision problems
Given a finite set of matrices with integer entries, consider the question of determining whether the semigroup they generated 1) is free, 2) contains the identity matrix, 3) contains the null matrix or 4) is a group. Even for matrices of dimension 3, questions 1) and 3) are undecidable. For dimension 2, they are still open as far as we know. Here we prove that problems 2) and 4) are decidable ...
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In the convergence theory of Padé approximation, one needs to estimate the size of a set on which a suitably normalized polynomial q is small. For example, one needs to estimate the size of the set of r 2 [0; 1] for which max jtj=1 jq (t)j =min jtj=r jq (t)j is not too large. We discuss some old and new problems of this type, and the methods used to solve them. 1. Introduction Let f be a func...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 1978
ISSN: 0304-3975
DOI: 10.1016/0304-3975(78)90010-5