compoly
determine a possible composition of a polynomial
Calling Sequence
Parameters
Description
Examples
compoly(r)
compoly(r, x)
compoly(r, {x, ... })
r
-
polynomial
x
variable on which the composition will be made
The function compoly returns a pair px, x=qx such that subs(x=q(x), p(x)) is equal to r, the input polynomial. If such a pair cannot be found, it returns FAIL. px and qx are nonlinear polynomials and qx has a low-degree in x greater or equal to 1.
When compoly is called without additional arguments, it is equivalent to being called with a second argument which is indets(r). When the second argument is a set with more than one variable, then a multivariate composition is attempted. In this case, the result has the same form, but the second polynomial is multivariate, that is, px, x=qx,.... For the multivariate case, the second polynomial, qx, may be of degree 1.
Note that the composition may not be unique. In particular, if px, x=qx,... is a composition, then we can find another px such that replacing qx,... by cqx,…+b will also result in a valid composition. This non-determinacy is eliminated by selecting c and b such that the q polynomial has integer content 1 and its independent term is 0.
compolyx6−9x5+27x4−27x3−2x2y+6xy+1,x
x3−2xy+1,x=x2−3x
compolyx4−3x3−x+5,x
FAIL
compolyx2+2xy−7x+y2−7y+16
x2−7x+16,x=x+y
compolyx4+4x3y3+6x2y6+4xy9+y12+x+y3−1,x,y
x4+x−1,x=y3+x
See Also
indets
polynomials
subs
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