supnorm should accept non-rational polynomials
Currently, supnorm only accepts polynomials whose coefficients can be proven to be rational numbers:
> P = x-x^2/2+x^3/3-x^4/4 + 7205759403792815 * 2^(-55) * x^5 -11728124044213 * 2^(-46) * x^6 + 5146953844507055 * 2^(-55)*x^7;
> f = log(1+x);
> I = [-5.5* 2^(-17) ; 5.625* 2^(-17)];
> midpointmode=on!;
> supnorm(P,f,I,absolute, 1b-20);
0.10057~1/3~e-36
> P = x-x^2/2+x^3/(log(8)/log(2))-x^4/4 + 7205759403792815 * 2^(-55) * x^5 -11728124044213 * 2^(-46) * x^6 + 5146953844507055 * 2^(-55)*x^7;
> supnorm(P,f,I,absolute, 1b-20);
Warning: the coefficients of the given polynomial cannot all be written as ratios of floating-point numbers.
Supremum norm computation is only possible on such polynomials. Try to use roundcoefficients().
Warning: the supremum norm on the error function between the given polynomial and the given function could not be computed.
Warning: the given expression or command could not be handled.
error
There is no real reason to impose this constraint: internally, supnorm uses taylorform polynomials with interval coefficients anyway. I propose that supnorm automatically evaluates the coefficients of its input polynomial by interval arithmetic and includes the corresponding error terms in the global error that the algorithm handles anyway.