Hilbert's tenth problem asked for an algorithm to determine whether a multivariate polynomial equation with integer coefficients has a solution in the integers.
32.
The theorem above holds for complex vector bundles and integer coefficients or for real vector bundles with \ mathbb { Z } _ 2 coefficients.
33.
Macdonald conjectured that they are polynomials in " q " and " t ", with non-negative integer coefficients.
34.
It states that every irreducible character on " G " is a linear combination with integer coefficients of characters induced from elementary subgroups.
35.
A monomial of variables in this semiring is a linear map, represented in classical arithmetic as a linear function of the variables with integer coefficients.
36.
In computer algebra, the polynomials have commonly integers coefficients, and this way of normalizing the greatest common divisor introduces too many fractions to be convenient.
37.
The problem was that the cohomology of a coherent sheaf over a finite field couldn't capture as much topology as singular cohomology with integer coefficients.
38.
The second result implies that if a polynomial with integer coefficients can be factored over the rational numbers, then there exists a factorization over the integers.
39.
The second way to normalize the greatest common divisor in the case of polynomials with integers coefficients is to divide every output by the primitive greatest common divisor.
40.
One of these first results was irreducible polynomial " f " with integer coefficients such that " f " ( ? ) = 0.
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