rewrite a RootOf in terms of a monic RootOf
MakeMonic expresses a RootOf in terms of a monic RootOf. It pulls the leading coefficient of the defining polynomial out of the RootOf and into the denominator.
MakeMonic only works on indexed, labeled, or one-argument RootOfs. For RootOfs with a numerical approximation or a range as selector, MakeMonic returns the input unchanged.
Nested RootOfs that are indexed, labeled, or one-argument, are handled recursively.
If r is not a RootOf or not of type algext, it is returned unchanged.
For indexed RootOfs, the leading coefficient is pulled out only if its signum is 1 or −1.
Algebraic:-MakeMonic(RootOf(y*x^3-1,x,index=1)) assuming y>0;
Algebraic:-MakeMonic(RootOf(y*x^3-1,x,index=1)) assuming y<0;
Note that RootOf itself tries to get rid of non-integral leading coefficients by inverting them:
In the next example, the leading coefficient is not invertible, and after pulling it out there is a zero divisor in the denominator:
f := RootOf(RootOf(x^2-x)*y^2-2);
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