Reduce error results for a polynomial with real (non-integer) coefficients

Question

In Mathematica, I tried to check some condition for a polynomial whose parameters vary in a range. My calculations are the 5th order, but I made it simple to show my needs.

When I create a polynomial that has integers as a parameter, I use Reduce and it gives me the correct answer.

But when I use real numbers in the polynomial, Reduce does not work and gives this error:

Reduce failed to solve the system with inaccurate coefficients. The answer was obtained by solving the corresponding exact system and calculating the result.

Can anyone help?

Answer 1

The Reduce::ratnz does not contain an error, but a warning. If you click on the More or >> link, regardless of what is displayed on your system, it will lead you to documentation that states:

This message is often generated when the first argument in Reduce contains inaccurate numbers. [...] A warning message can be avoided by using only the exact numbers at the input of Reduce

Now, if the message annoys you, you can turn off this message using

 Off[Reduce::ratnz] 

which will turn off the warning for all further applications of Reduce , or you can simply turn off this operation using

 Quiet@Reduce [...] 

If you want to avoid the message, then, as the documentation says, you will need to use exact numbers. One way is to use Rationalize . For instance:

 x = 1.391 + 0.771 a; Reduce[Rationalize[x] > 0 && 1 <= a <= 80, {a}] Out[1]= 1 <= a <= 80 

It gives you the desired result without warning. There may be other ways depending on what exactly you are doing, but it’s hard to say without knowing your exact expression. Hope this helps.