Bugs item #1340694, was opened at 20051028 07:31
Message generated for change (Comment added) made by robert_dodier
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Category: None
Group: None
Status: Closed
Resolution: Duplicate
Priority: 5
Submitted By: Barton Willis (willisbl)
Assigned to: Nobody/Anonymous (nobody)
Summary: no doc for 'polydecomp':
Initial Comment:
There is no user documentation for 'polydecomp':
(%i1) describe("polydecomp");
(%o1) false
There is such a function:
(%i2) polydecomp(x^2 + 2*x + 1,x);
(%o2) [x^2,x+1]
Barton

>Comment By: Robert Dodier (robert_dodier)
Date: 20051115 23:44
Message:
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user_id=501686
Description given by Stavros adapted into r1.18 of
doc/info/Polynomials.texi.

Comment By: Stavros Macrakis (macrakis)
Date: 20051109 11:07
Message:
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user_id=588346
I already submitted this documentation bug to the
sourceforge bug
database in August 2002: "No describe(polydecomp)", bug
#593531, and
included documentation.
Below please find a second draft of the documentation for
polydecomp
which I included in the followup to the August 2002 bug report.
s

Polydecomp(p,v) considers p as a polynomial in v and
decomposes it into
the functional composition of polynomials in v. A return
value of
[p1,p2,...,pn] denotes
lambda([v],p1) ( lambda([v],p2) ( ... v ... ) )
Degree(pi) > 1 for i<n.
Examples:
polydecomp(x^210,x) => [ x^7, x^5, x^3, x^2 ]
poly: expand( subst( x^3x1, x, x^2a ))
=> x^62*x^42*x^3+x^2+2*xa+1
polydecomp( poly , x) => [ x^2a, x^3x1]
The following function composes [ex1,ex2,...] as functions
in var; it is
the inverse of polydecomp:
/* Computes the functional composition of the expressions in
exlist
as functions in var, returning an expression in var. */
compose_ex(exlist,var):=
block([r:var],
for i in exlist do r: subst(i,var,r),
r ) $
Reexpress above example using composef:
polydecomp(compose_ex( [ x^2a, x^3x1 ], x), x)
=> [ x^2a, x^3x1]
Note that though compose_ex(polydecomp(p,x),x) always returns p
(unexpanded), polydecomp(compose_ex([p1...],x),x) does *not*
necessarily
return [p1...]:
polydecomp(compose_ex( [x^2+2*x+3, x^2] , x), x)
=> [x^2+2, x^2+1]
polydecomp(compose_ex( [x^2+x+1, x^2+x+1], x), x)
=> [(x^2+3)/4, (x^2+5)/2, 2*x+1]

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