HasRealRoots - Maple Help

RootFinding

 HasRealRoots
 check for real roots

 Calling Sequence HasRealRoots(sys) HasRealRoots(sys, vars)

Parameters

 sys - list or set of polynomial equations with rational coefficients vars - list of names; the indeterminates

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{RootFinding}\right):$
 > $\mathrm{HasRealRoots}\left(\left[{x}^{2}+{y}^{2}+2\right]\right)$
 ${\mathrm{false}}$ (1)
 > $\mathrm{HasRealRoots}\left(\left[{x}^{2}+{y}^{2},z-{x}^{3}\right],\left[x,y,z\right]\right)$
 ${\mathrm{true}}$ (2)
 > $\mathrm{HasRealRoots}\left(\left[{\left({x}^{2}+{\left(y-1\right)}^{2}\right)}^{2}\right]\right)$
 ${\mathrm{true}}$ (3)
 > $\mathrm{HasRealRoots}\left(\left[{x}^{4}-4{x}^{2}+4=-1\right]\right)$
 ${\mathrm{false}}$ (4)