The function HasRealRoots tests if the system of equations defined in sys has real roots.

It returns a boolean, $\mathrm{true}$ if sys has real zeroes and $\mathrm{false}$ otherwise.

The equations in sys must be polynomial with rational coefficients. Any polynomial $p$ appearing in sys is interpreted as the equation $p=0$.

When the list of names vars is provided, it must contain all the indeterminates appearing in sys. The order in the list is used for internal computations.

$\mathrm{with}\left(\mathrm{RootFinding}\right)\:$

$\mathrm{HasRealRoots}\left(\left[x^2+y^2+2\right]\right)$

$\mathrm{false}$

$\mathrm{HasRealRoots}\left(\left[x^2+y^2\,z-x^3\right]\,\left[x\,y\,z\right]\right)$

$\mathrm{true}$

$\mathrm{HasRealRoots}\left(\left[{\left(x^2+{\left(y-1\right)}^2\right)}^2\right]\right)$

$\mathrm{true}$

$\mathrm{HasRealRoots}\left(\left[x^4-4x^2+4=-1\right]\right)$

$\mathrm{false}$