FunctionalDecomposition - Maple Help
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PolynomialTools

  

FunctionalDecomposition

  

compute a functional decomposition of a polynomial

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

FunctionalDecomposition(f)

FunctionalDecomposition(f, v)

FunctionalDecomposition(f, v, inert)

Parameters

f

-

multivariate polynomial

v

-

name or list or set of names

Description

• 

This function computes a functional decomposition of the polynomial f. That is, it computes g(x) and h and rewrites the output as a composition f=gx=h|gx=h and the process is repeated on g and h until they can not be functionally decomposed further. This decomposition is not unique.

• 

This function currently just calls compoly repeatedly and constructs the decomposition as a single unexpanded polynomial. If no decomposition is found, f is returned unaltered.

• 

If f is not of type polynom then frontend is used before performing polynomial calculations.

• 

The inert option adds ``() calls around x so that the linear part of the polynomial and pure monomial substitutions will not be expanded by automatic simplification. The output will look like a polynomial, but will not be true polynomial unless expand is called to remove the ``() similar to the output of ifactor.

Examples

withPolynomialTools:

fexpandevalevalx2+2x1,x=x3x,x=x2+3x

fx12+18x11+135x10+540x9+1213x8+1434x7+623x6198x5107x4+60x3+7x26x1

(1)

FunctionalDecompositionf,x

x2+3x3x23x2+2x2+3x32x26x1

(2)

f1expandevalx2+xexpa1,x=x2x

f1x42x3+x2+ⅇax2xⅇa1

(3)

FunctionalDecompositionf1,x

x2x2+x2xⅇa1

(4)

f2expandevalx32x2x+1,x=y2+x1

f2y63xy4+3x2y2+y4x32xy2+x2+1

(5)

FunctionalDecompositionf2

y2+x132y2+x12+y2x+2

(6)

FunctionalDecompositionf2,inert

y2+x132y2+x12y2+x1+1

(7)

Compatibility

• 

The PolynomialTools[FunctionalDecomposition] command was introduced in Maple 2022.

• 

For more information on Maple 2022 changes, see Updates in Maple 2022.

See Also

compoly