Hi all,
I want to get the roots of a polynomial. I used the allroot funcion
(as I will show with a code below), and then I mapped the same
polynomial using the value of a root returned from allroots, but it
didn't work.
(%i200) g(x) := x^5-x^3-10^(-15);
allroots(%i*g(x));
(%o200) g(x):=x^5-x^3-10^(-15)
(%o201) [x=8.6602540378443868*10^-6*%i+4.9999999996666667*10^-6,x=-4.5460856822775728*10^-22*%i-1.0000000000333334*10^-5,x=4.9999999996666658*10^-6-8.6602540378443851*10^-6*%i,x=1.0-1.8541339457159821*10^-17*%i,x=1.8539432108527007*10^-17*%i-1.0]
(%i202) map(g, [8.6602540378443868*10^-6*%i+4.9999999996666667*10^-6]);
(%o202) [(8.6602540378443868*10^-6*%i+4.9999999996666667*10^-6)^5-(8.6602540378443868*10^-6*%i+4.9999999996666667*10^-6)^3-1/1000000000000000]
The map of a root has to be zero, doesn't it?
I have already tried with allroots(g(X)), but I got some strange
results (can someone explain me why?)
By the way: my work with maxima is to find some polynomials and value
to which some rounding error happends, can someone give me some source
in the literature the approachs this topic (with examples)? I want to
identify interesting polynomials to test my new benchmark for floating
point calculation, which evaluates the quality of the result
(accuracy). I hope someone can help me.
Thank you,
Oscar