Does this Turing Machine decide
language of polynomials with integer coefficients which have integer roots:
The input represents a polynomial over variables x1, . . . , xn with integer coefficients.
1. Examine all possible integer values of x1, . . . , xn.
2. Evaluate the polynomial on all of them.
3. If any of them evaluates to 0, accept; else reject
From what I know I would say No, since: "M decides a language L iff M accepts all strings in L and reject all strings not in L ". Where L is the language of polynomials. Is this correct?
Any help is appreciated!