Algebraic
MakeMonic
rewrite a RootOf in terms of a monic RootOf
Calling Sequence
Parameters
Description
Examples
MakeMonic(r)
r
-
algebraic expression
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:-MakeMonicRootOfyx3−1,x
RootOf_Z3−y2y
Algebraic:-MakeMonic1+RootOfyx3−1,x
1+RootOfy_Z3−1
Algebraic:-MakeMonicRootOf2sinx−1
RootOf2sin_Z−1
Algebraic:-MakeMonicRootOfyx3−1,x,index=1
RootOfy_Z3−1,index=1
Algebraic:-MakeMonicRootOfyx3−1,x,index=1assuming0<y
RootOf_Z3−y2,index=1y
Algebraic:-MakeMonicRootOfyx3−1,x,index=1assumingy<0
−RootOf_Z3+y2,index=1y
Algebraic:-MakeMonicRootOf5y2−RootOf3x2+1,index=1,index=1
RootOf_Z2−15RootOf_Z2+3,index=1,index=115
Note that RootOf itself tries to get rid of non-integral leading coefficients by inverting them:
RootOfRootOf_Z2−2_Z2−2
RootOf_Z2−RootOf_Z2−2
In the next example, the leading coefficient is not invertible, and after pulling it out there is a zero divisor in the denominator:
f≔RootOfRootOfx2−xy2−2
f≔RootOfRootOf_Z2−_Z_Z2−2
Algebraic:-MakeMonicf
RootOf_Z2−2RootOf_Z2−_ZRootOf_Z2−_Z
See Also
RootOf
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