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Viewing changes to doc/info/Simplification.texi

  • Committer: Bazaar Package Importer
  • Author(s): Camm Maguire
  • Date: 2010-04-30 13:30:33 UTC
  • mto: This revision was merged to the branch mainline in revision 12.
  • Revision ID: james.westby@ubuntu.com-20100430133033-wtewap0zdnmsix1y
Tags: upstream-5.21.1
Import upstream version 5.21.1

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doc/info/Simplification.texi
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@end defvr
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@c NEEDS WORK
 
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@c -----------------------------------------------------------------------------
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@deffn {Function} expand (@var{expr})
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@deffnx {Function} expand (@var{expr}, @var{p}, @var{n})
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Expand expression @var{expr}.
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@code{(x+1)^n} expanded where @code{n} is greater than @code{expop} then executing
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@code{expand ((x+1)^n)} will work only if @code{maxposex} is not less than @code{n}.
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@code{expand(expr, 0, 0)} causes a resimplification of @code{expr}. @code{expr}
 
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is not reevaluated. In distinction from @code{ev(expr, noeval)} a special 
 
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representation (e. g. a CRE form) is removed. See also @code{ev}.
 
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The @code{expand} flag used with @code{ev} causes expansion.
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The file @file{simplification/facexp.mac}
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Brief function descriptions are available in @file{simplification/facexp.usg}.
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A demo is available by doing @code{demo("facexp")}.
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Examples:
 
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@c ===beg===
 
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@c expr:(x+1)^2*(y+1)^3;
 
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@c expand(expr);
 
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@c expand(expr,2);
 
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@c expr:(x+1)^-2*(y+1)^3;
 
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@c expand(expr);
 
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@c expand(expr,2,2);
 
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@c ===end===
 
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@example
 
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(%i1) expr:(x+1)^2*(y+1)^3;
 
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                                      2        3
 
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(%o1)                          (x + 1)  (y + 1)
 
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(%i2) expand(expr);
 
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       2  3        3    3      2  2        2      2      2
 
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(%o2) x  y  + 2 x y  + y  + 3 x  y  + 6 x y  + 3 y  + 3 x  y
 
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                                                 2
 
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                                + 6 x y + 3 y + x  + 2 x + 1
 
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(%i3) expand(expr,2);
 
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                      2        3              3          3
 
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(%o3)                x  (y + 1)  + 2 x (y + 1)  + (y + 1)
 
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(%i4) expr:(x+1)^-2*(y+1)^3;
 
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                                          3
 
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                                   (y + 1)
 
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(%o4)                              --------
 
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                                          2
 
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                                   (x + 1)
 
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(%i5) expand(expr);
 
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                 3               2
 
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                y             3 y            3 y             1
 
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(%o5)      ------------ + ------------ + ------------ + ------------
 
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            2              2              2              2
 
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           x  + 2 x + 1   x  + 2 x + 1   x  + 2 x + 1   x  + 2 x + 1
 
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(%i6) expand(expr,2,2);
 
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                                          3
 
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                                   (y + 1)
 
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(%o6)                            ------------
 
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                                  2
 
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                                 x  + 2 x + 1
 
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@end example
 
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Resimplify an expression without expansion:
 
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@c ===beg===
 
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@c expr:(1+x)^2*sin(x);
 
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@c exponentialize:true;
 
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@c expand(expr,0,0);
 
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@c ===end===
 
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@example
 
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(%i7) expr:(1+x)^2*sin(x);
 
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                                       2
 
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(%o7)                           (x + 1)  sin(x)
 
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(%i8) exponentialize:true;
 
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(%o8)                                true
 
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(%i9) expand(expr,0,0);
 
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                                   2    %i x     - %i x
 
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                         %i (x + 1)  (%e     - %e      )
 
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(%o9)                  - -------------------------------
 
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                                        2
 
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@end example
 
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@opencatbox
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@category{Expressions}
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@closecatbox