Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symbolic computation of the roots of any polynomial with integer
  coefficients   The roots of any polynomial of degree m with integer coefficients, can be
computed by manipulation of sequences made from 2m distinct symbols and
counting the different symbols in the sequences. This method requires only
'primitive' operations like replacement of sequences and counting of symbols.
No calculations using 'advanced' operations like multiplication, division,
logarithms etc. are needed. The method can be implemented as a geometric
construction of roots of polynomials to arbitrary accuracy using only a
straight edge, a compass, and pencils of 2m different colors. In particular,
the ancient problem of the "doubling of cube" is soluble asymptotically by the
above-mentioned construction. This method, by which a cube can be doubled,
albeit, in infinite steps, is probably the closest to the original problem of
construction using only a straight edge and compass in a finite number of
steps.
  Moreover, to every polynomial of degree m over the field of rationals, can be
associated an m-term recurrence relation for generating integer sequences. A
set of m such sequences, which together exhibit interesting properties related
to the roots of the polynomial, can be obtained if the m initial terms of each
of these m sequences is chosen in a special way using a matrix associated with
the polynomial. Only two of these integer sequences need to be computed to
obtain the real root having the largest absolute value. Since this method
involves only integers, it is faster than the conventional methods using
floating-point arithmetic.

18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc