The following results which is due to Enestrom and Kakeya [1] is well known in the theory of the location of the zeros of polynomials. The aim of this paper is to prove some extensions of ...

The main purpose of this paper is to extend various results of Eneström-Kakeya type from the complex to quaternionic setting by virtue of a maximum modulus theorem and the structure of the zero sets ...

expected_p = Polynomial([2, 0, 1, 1]).reduced_modulo_scalar(p) expected_q = Polynomial([-3, 7, 3, -6]).reduced_modulo_scalar(q) # Sanity check assert expected_p ...

IN elementary algebra the well-known remainder theorem enables us to determine a polynomial, except for a numerical factor, when all the zeroes are given. If we replace the polynomial by an integral ...

F.<i> = GF((2**31-1,2), modulus=[1,0,1]) R.<x> = F[] f = x^2 + (1196423630*i + 1564527877)*x + 2041534867*i + 2147483645 g = x^3 + x S.<y> = R.quotient_ring(g) print ...

1 Warwick Mathematics Institute, The University of Warwick, Coventry, United Kingdom 2 School of Computer and Information Engineering, Luoyang Institute of Science and Technology, Luoyang, China To ...

If \((x \pm h)\) is a factor of a polynomial, then the remainder will be zero. Conversely, if the remainder is zero, then \((x \pm h)\) is a factor. Often ...