On the other hand, the reduced echelon form of a matrix with integer coefficients generally contains non-integer coefficients.
22.
Proved that if the Jacobian conjecture is false, then it has a counterexample with integer coefficients and Jacobian determinant 1.
23.
For example, singular homology ( taken with integer coefficients, as is most common ) has as coefficients the integers.
24.
Schur polynomials can be expressed as linear combinations of monomial symmetric functions with non-negative integer coefficients called Kostka numbers,
25.
If it happens that the \ alpha chosen has half-integer coefficients, it can be replaced by another Hurwitz quaternion.
26.
In 1970, Russian mathematician Yuri Matiyasevich showed that integer roots of a polynomial in any number of variables with integer coefficients.
27.
A Diophantine equation is a ( usually multivariate ) polynomial equation with integer coefficients for which one is interested in the integer solutions.
28.
The term is related to transcendental numbers, which are numbers which are not the solution to an algebraic equation with integer coefficients.
29.
So Hilbert was asking for a general algorithm to decide whether a given polynomial Diophantine equation with integer coefficients has a solution in integers.
30.
Here the fundamental class is taken in homology with integer coefficients if the manifold is orientable, and in coefficients modulo 2, otherwise.
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