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Algebraic

  

MakeMonic

  

rewrite a RootOf in terms of a monic RootOf

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

MakeMonic(r)

Parameters

r

-

algebraic expression

Description

• 

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.

Examples

Algebraic:-MakeMonic(RootOf(y*x^3-1,x));

RootOf_Z3y2y

(1)

Algebraic:-MakeMonic(1+RootOf(y*x^3-1,x));

1+RootOfy_Z31

(2)

Algebraic:-MakeMonic(RootOf(2*sin(x)-1));

RootOf2sin_Z1

(3)

Algebraic:-MakeMonic(RootOf(y*x^3-1,x,index=1));

RootOfy_Z31,index=1

(4)

Algebraic:-MakeMonic(RootOf(y*x^3-1,x,index=1)) assuming y>0;

RootOf_Z3y2,index=1y

(5)

Algebraic:-MakeMonic(RootOf(y*x^3-1,x,index=1)) assuming y<0;

RootOf_Z3+y2&comma;index=1y

(6)

Algebraic:-MakeMonic(RootOf(5*y^2-RootOf(3*x^2+1,index=1),index=1));

RootOf_Z215RootOf_Z2+3&comma;index=1&comma;index=115

(7)

Note that RootOf itself tries to get rid of non-integral leading coefficients by inverting them:

RootOf(RootOf(_Z^2-2)*_Z^2-2);

RootOf_Z2RootOf_Z22

(8)

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);

fRootOfRootOf_Z2_Z_Z22

(9)

Algebraic:-MakeMonic(f);

RootOf_Z22RootOf_Z2_ZRootOf_Z2_Z

(10)

See Also

Algebraic

RootOf