#804 no doc for 'polydecomp':

closed
nobody
None
5
2005-11-09
2005-10-28
No

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

Discussion

  • Stavros Macrakis

    Logged In: YES
    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^3-x-1, x, x^2-a ))
    => x^6-2*x^4-2*x^3+x^2+2*x-a+1
    polydecomp( poly , x) => [ x^2-a, x^3-x-1]

    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 ) $

    Re-express above example using composef:

    polydecomp(compose_ex( [ x^2-a, x^3-x-1 ], x), x)
    => [ x^2-a, x^3-x-1]

    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]

     
  • Stavros Macrakis

    • status: open --> closed
     
  • Robert Dodier

    Robert Dodier - 2005-11-16

    Logged In: YES
    user_id=501686

    Description given by Stavros adapted into r1.18 of
    doc/info/Polynomials.texi.

     

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