From: Dieter Kaiser <crategus@us...>  20091129 23:49:43

Update of /cvsroot/maxima/maxima/doc/info In directory sfpcvsdas1.v30.ch3.sourceforge.com:/tmp/cvsserv23944/doc/info Modified Files: Simplification.texi Log Message: Cutting out the description of the option variables $radexpand and %e_to_numlog from the documentation of the function radcan. Both variables have no effect on radcan. Adding examples to the documentation of radcan. Related bug report: ID: 1977146  radexpand does not work as explained in documentation Index: Simplification.texi =================================================================== RCS file: /cvsroot/maxima/maxima/doc/info/Simplification.texi,v retrieving revision 1.23 retrieving revision 1.24 diff u d r1.23 r1.24  Simplification.texi 29 Nov 2009 22:36:22 0000 1.23 +++ Simplification.texi 29 Nov 2009 23:49:24 0000 1.24 @@ 700,34 +700,55 @@ @closecatbox @end defvr +@c  @deffn {Function} radcan (@var{expr}) Simplifies @var{expr}, which can contain logs, exponentials, and radicals, by converting it into a form which is canonical over a large class of expressions and a given ordering of variables; that is, all functionally equivalent forms are mapped into a unique form. For a somewhat larger class of expressions, @code{radcan} produces a regular form. Two equivalent expressions in this class do not necessarily have the same appearance, but their difference can be simplified by @code{radcan} to zero. +Simplifies @var{expr}, which can contain logs, exponentials, and radicals, by +converting it into a form which is canonical over a large class of expressions +and a given ordering of variables; that is, all functionally equivalent forms +are mapped into a unique form. For a somewhat larger class of expressions, +@code{radcan} produces a regular form. Two equivalent expressions in this class +do not necessarily have the same appearance, but their difference can be +simplified by @code{radcan} to zero. For some expressions @code{radcan} is quite time consuming. This is the cost of exploring certain relationships among the components of the expression for simplifications based on factoring and partialfraction expansions of exponents. +For some expressions @code{radcan} is quite time consuming. This is the cost +of exploring certain relationships among the components of the expression for +simplifications based on factoring and partialfraction expansions of exponents. @c %e_to_numlog NEEDS ITS OWN @defvar !!! @... DOESN'T APPEAR TO AFFECT radcan !!! When @code{%e_to_numlog} is @code{true}, @...{%e^(r*log(expr))} simplifies to @code{expr^r} if @code{r} is a rational number. When @code{radexpand} is @code{false}, certain transformations are inhibited. @...{radcan (sqrt (1x))} remains @code{sqrt (1x)} and is not simplified to @code{%i sqrt (x1)}. @...{radcan (sqrt (x^2  2*x + 1))} remains @code{sqrt (x^2  2*x + 1)} and is not simplified to @code{x  1}. +@c %e_to_numlog HAS NO EFFECT ON RADCAN. RADCAN ALWAYS SIMPLIFIES +@c exp(a*log(x)) > x^a. Commenting the following out. 11/2009 +@c When @code{%e_to_numlog} is @code{true}, @code{%e^(r*log(expr))} simplifies +@c to @code{expr^r} if @code{r} is a rational number. @... MERGE EXAMPLES INTO THIS FILE @...{example (radcan)} displays some examples. +@c RADEXPAND CONTROLS THE SIMPLIFICATION OF THE POWER FUNCTION, E.G. +@c (x*y)^a > x^a*y^a AND (x^a)^b > x^(a*b), IF RADEXPAND HAS THE VALUE 'ALL. +@c THE VALUE OF RADEXPAND HAS NO EFFECT ON RADCAN. RADCAN ALWAYS SIMPLIFIES +@c THE ABOVE EXPRESSIONS. COMMENTING THE FOLLOWING OUT. 11/2009 +@c When @code{radexpand} is @code{false}, certain transformations are inhibited. +@c @code{radcan (sqrt (1x))} remains @code{sqrt (1x)} and is not simplified +@c to @code{%i sqrt (x1)}. @code{radcan (sqrt (x^2  2*x + 1))} remains +@c @code{sqrt (x^2  2*x + 1)} and is not simplified to @code{x  1}. + +Examples: + +@c ===beg=== +@c radcan((log(x+x^2)log(x))^a/log(1+x)^(a/2)); +@c radcan((log(1+2*a^x+a^(2*x))/log(1+a^x))); +@c radcan((%e^x1)/(1+%e^(x/2))); +@c ===end=== +@example +(%i1) radcan((log(x+x^2)log(x))^a/log(1+x)^(a/2)); + a/2 +(%o1) log(x + 1) + +(%i2) radcan((log(1+2*a^x+a^(2*x))/log(1+a^x))); +(%o2) 2 + +(%i3) radcan((%e^x1)/(1+%e^(x/2))); + x/2 +(%o3) %e  1 +@end example @opencatbox @category{Simplification functions} 