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[genius] Wed Oct 16 00:33:17 2013 Jiri (George) Lebl <jirka 5z com>

commit e426a865c95160ae82494fddf11acb5e4983913d
Author: Jiri (George) Lebl <jirka 5z com>
Date:   Wed Oct 16 00:43:04 2013 -0500

    Wed Oct 16 00:33:17 2013  Jiri (George) Lebl <jirka 5z com>
    
        * src/symbolic.c: add some derivatives for Bessel functions and
          for the Lambert W functions
    
        * help/C/genius.xml: document LambertW, LambertWm1, NewtonsMethod,
          and some other minor improvements
    
        * lib/equation_solving/newton.gel, lib/functions/elementary.gel:
          improve help string for the Newton's method functions
    
        * pixmaps/Makefile.am: pass -t to gtk-update-icon-cache to avoid
          failing if no theme index file

 ChangeLog                       |   14 ++++++
 NEWS                            |    3 +-
 help/C/genius.xml               |   88 +++++++++++++++++++++++++++++++++++++-
 lib/equation_solving/newton.gel |    4 +-
 lib/functions/elementary.gel    |    4 +-
 lib/library-strings.c           |    4 +-
 pixmaps/Makefile.am             |    2 +-
 src/symbolic.c                  |   10 ++++-
 8 files changed, 117 insertions(+), 12 deletions(-)
---
diff --git a/ChangeLog b/ChangeLog
index a42ab7b..d0c8492 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,17 @@
+Wed Oct 16 00:33:17 2013  Jiri (George) Lebl <jirka 5z com>
+
+       * src/symbolic.c: add some derivatives for Bessel functions and
+         for the Lambert W functions
+       
+       * help/C/genius.xml: document LambertW, LambertWm1, NewtonsMethod,
+         and some other minor improvements
+
+       * lib/equation_solving/newton.gel, lib/functions/elementary.gel:
+         improve help string for the Newton's method functions
+
+       * pixmaps/Makefile.am: pass -t to gtk-update-icon-cache to avoid
+         failing if no theme index file
+
 Tue Oct 15 18:17:58 2013  Jiri (George) Lebl <jirka 5z com>
 
        * lib/functions/lambert.gel, lib/equation_solving/newton.gel: Add
diff --git a/NEWS b/NEWS
index 2b31812..0c8f827 100644
--- a/NEWS
+++ b/NEWS
@@ -1,6 +1,7 @@
 Changes to 1.0.18
 
-* Implement KroneckerProduct (alias TensorProduct) for matrices
+* New functions: KroneckerProduct (alias TensorProduct), NewtonsMethod,
+  LambertW, LambertWm1
 * New PlotCanvasFreeze/PlotCanvasThaw functions to improve flicker
   if doing animations with genius.
 * Allow setting color in LinePlotDrawLine with RGB vector.
diff --git a/help/C/genius.xml b/help/C/genius.xml
index e8a7b43..e1cf9dc 100644
--- a/help/C/genius.xml
+++ b/help/C/genius.xml
@@ -7401,7 +7401,8 @@ and has period <userinput>b-a</userinput>.</para>
           <para>The Gamma function.  Currently only implemented for real values.</para>
           <para>
            See
-           <ulink url="http://planetmath.org/encyclopedia/GammaFunction.html";>Planetmath</ulink> for more 
information.
+           <ulink url="http://planetmath.org/encyclopedia/GammaFunction.html";>Planetmath</ulink> or
+           <ulink url="http://en.wikipedia.org/wiki/Gamma_function";>Wikipedia</ulink> for more information.
           </para>
          </listitem>
         </varlistentry>
@@ -7415,6 +7416,45 @@ and has period <userinput>b-a</userinput>.</para>
         </varlistentry>
 
         <varlistentry>
+         <term><anchor id="gel-function-LambertW"/>LambertW</term>
+         <listitem>
+          <synopsis>LambertW (x)</synopsis>
+         <para>
+                 The principal branch of Lambert W function computed for only
+                 real values greater than or equal to <userinput>-1/e</userinput>.
+                 That is, <function>LambertW</function> is the inverse of
+                 the expression <userinput>x*e^x</userinput>.  Even for
+                 real <varname>x</varname> this expression is not one to one and
+                 therefore has two branches over <userinput>[-1/e,0)</userinput>.
+                 See <link linkend="gel-function-LambertWm1"><function>LambertWm1</function></link> for the 
other real branch.
+         </para>
+          <para>
+           See
+           <ulink url="http://en.wikipedia.org/wiki/Lambert_W_function";>Wikipedia</ulink> for more 
information.
+         </para>
+         </listitem>
+        </varlistentry>
+
+        <varlistentry>
+         <term><anchor id="gel-function-LambertWm1"/>LambertWm1</term>
+         <listitem>
+          <synopsis>LambertWm1 (x)</synopsis>
+         <para>
+                 The minus-one branch of Lambert W function computed for only
+                 real values greater than or equal to <userinput>-1/e</userinput>
+                 and less than 0.
+                 That is, <function>LambertWm1</function> is the second
+                 branch of the inverse of <userinput>x*e^x</userinput>.
+                 See <link linkend="gel-function-LambertW"><function>LambertW</function></link> for the 
principal branch.
+         </para>
+          <para>
+           See
+           <ulink url="http://en.wikipedia.org/wiki/Lambert_W_function";>Wikipedia</ulink> for more 
information.
+         </para>
+         </listitem>
+        </varlistentry>
+
+        <varlistentry>
          <term><anchor id="gel-function-MinimizeFunction"/>MinimizeFunction</term>
          <listitem>
           <synopsis>MinimizeFunction (func,x,incr)</synopsis>
@@ -7506,7 +7546,8 @@ and has period <userinput>b-a</userinput>.</para>
           <para>The Riemann zeta function.  Currently only implemented for real values.</para>
           <para>
            See
-           <ulink url="http://planetmath.org/encyclopedia/RiemannZetaFunction.html";>Planetmath</ulink> for 
more information.
+           <ulink url="http://planetmath.org/encyclopedia/RiemannZetaFunction.html";>Planetmath</ulink> or
+           <ulink url="http://en.wikipedia.org/wiki/Riemann_zeta_function";>Wikipedia</ulink> for more 
information.
           </para>
          </listitem>
         </varlistentry>
@@ -7693,6 +7734,31 @@ and has period <userinput>b-a</userinput>.</para>
         </varlistentry>
 
         <varlistentry>
+         <term><anchor id="gel-function-NewtonsMethod"/>NewtonsMethod</term>
+         <listitem>
+          <synopsis>NewtonsMethod (f,df,guess,epsilon,maxn)</synopsis>
+         <para>Find zeros using Newton's method.  <varname>f</varname> is
+                 the function and <varname>df</varname> is the derivative of
+                 <varname>f</varname>.  <varname>guess</varname> is the initial
+                 guess.  The function returns after two successive values are
+                 within <varname>epsilon</varname> of each other, or after <varname>maxn</varname> tries, in 
which case the function returns <constant>null</constant> indicating failure.
+         </para>
+         <para>
+         See also <link 
linkend="gel-function-NewtonsMethodPoly"><function>NewtonsMethodPoly</function></link> and <link 
linkend="gel-function-SymbolicDerivative"><function>SymbolicDerivative</function></link>.
+         </para>
+         <para>
+           Example to find the square root of 10:
+          <screen><prompt>genius></prompt> 
<userinput>NewtonsMethod(`(x)=x^2-10,`(x)=2*x,3,10^-10,100)</userinput>
+</screen>
+         </para>
+          <para>
+           See
+           <ulink url="http://en.wikipedia.org/wiki/Newtons_method";>Wikipedia</ulink> for more information.
+         </para>
+         </listitem>
+        </varlistentry>
+
+        <varlistentry>
          <term><anchor id="gel-function-PolynomialRoots"/>PolynomialRoots</term>
          <listitem>
           <synopsis>PolynomialRoots (p)</synopsis>
@@ -7981,7 +8047,23 @@ and has period <userinput>b-a</userinput>.</para>
          <term><anchor id="gel-function-NewtonsMethodPoly"/>NewtonsMethodPoly</term>
          <listitem>
           <synopsis>NewtonsMethodPoly (poly,guess,epsilon,maxn)</synopsis>
-         <para>Run newton's method on a polynomial to attempt to find a root, returns after two successive 
values are within epsilon or after maxn tries (then returns <constant>null</constant>).</para>
+         <para>Find a root of a polynomial using Newton's method.  <varname>poly</varname> is
+                 the polynomial as a vector and <varname>guess</varname> is the initial
+                 guess.  The function returns after two successive values are
+                 within <varname>epsilon</varname> of each other, or after <varname>maxn</varname> tries, in 
which case the function returns <constant>null</constant> indicating failure.
+         </para>
+         <para>
+         See also <link linkend="gel-function-NewtonsMethod"><function>NewtonsMethod</function></link>.
+         </para>
+         <para>
+           Example to find the square root of 10:
+          <screen><prompt>genius></prompt> <userinput>NewtonsMethodPoly([-10,0,1],3,10^-10,100)</userinput>
+</screen>
+         </para>
+          <para>
+           See
+           <ulink url="http://en.wikipedia.org/wiki/Newtons_method";>Wikipedia</ulink> for more information.
+         </para>
          </listitem>
         </varlistentry>
 
diff --git a/lib/equation_solving/newton.gel b/lib/equation_solving/newton.gel
index 3975311..34449fa 100644
--- a/lib/equation_solving/newton.gel
+++ b/lib/equation_solving/newton.gel
@@ -1,11 +1,11 @@
 # Newton's method
 
-SetHelp("NewtonsMethod","equation_solving","Run Newton's method on a function to attempt to find a root, 
returns after two successive values are within epsilon or after maxn tries (then returns null)")
+SetHelp("NewtonsMethod","equation_solving","Attempt to find a zero of a functionf with derivative df using 
Newton's method, returning after two successive values are within epsilon or after maxn tries (then returns 
null)")
 function NewtonsMethod(f,df,guess,epsilon,maxn) = (
        guess := float(guess);
        for n=1 to maxn do (
                dfg := df(guess);
-               if dfg == 0 then (
+               if dfg == 0.0 then (
                        error ("NewtonsMethod: division by zero");
                        bailout
                );
diff --git a/lib/functions/elementary.gel b/lib/functions/elementary.gel
index 44d7cb0..9c3a315 100644
--- a/lib/functions/elementary.gel
+++ b/lib/functions/elementary.gel
@@ -263,14 +263,14 @@ erf = ErrorFunction
 SetHelpAlias ("ErrorFunction", "erf");
 
 #FIXME: Should probably be in a separate source file
-SetHelp("NewtonsMethodPoly","polynomial","Run newton's method on a polynomial to attempt to find a root, 
returns after two successive values are within epsilon or after maxn tries (then returns null)")
+SetHelp("NewtonsMethodPoly","polynomial","Attempt to find a root of a polynomial using Newton's method, 
returning after two successive values are within epsilon or after maxn tries (then returns null)")
 function NewtonsMethodPoly(poly,guess,epsilon,maxn) = (
        pf := PolyToFunction (poly);
        pdf := PolyToFunction (PolyDerivative (poly));
        guess := float(guess);
        for n=1 to maxn do (
                pdfg := pdf(guess);
-               if pdfg == 0 then (
+               if pdfg == 0.0 then (
                        error ("NewtonsMethodPoly: division by zero");
                        bailout
                );
diff --git a/lib/library-strings.c b/lib/library-strings.c
index 0f5d62d..103df5f 100644
--- a/lib/library-strings.c
+++ b/lib/library-strings.c
@@ -237,7 +237,7 @@ char *fake = N_("Find root of a function using the bisection method to within TO
 char *fake = N_("Find root of a function using the method of false position to within TOL tolerance in up to 
N iterations.  f(a) and f(b) must have opposite signs.");
 char *fake = N_("Find root of a function using the Muller's method");
 char *fake = N_("Find root of a function using the secant method to within TOL tolerance in up to N 
iterations.  f(a) and f(b) must have opposite signs.");
-char *fake = N_("Run Newton's method on a function to attempt to find a root, returns after two successive 
values are within epsilon or after maxn tries (then returns null)");
+char *fake = N_("Attempt to find a zero of a functionf with derivative df using Newton's method, returning 
after two successive values are within epsilon or after maxn tries (then returns null)");
 char *fake = N_("Find roots of a polynomial (given as vector of coefficients)");
 char *fake = N_("Find roots of a quartic polynomial (given as vector of coefficients)");
 char *fake = N_("Use classical non-adaptive Runge-Kutta of fourth order method to numerically solve 
y'=f(x,y) for initial x0,y0 going to x1 with n increments, returns y at x1");
@@ -252,7 +252,7 @@ char *fake = N_("Calculate median of each row in a matrix");
 char *fake = N_("Calculate the population standard deviations of rows of a matrix and return a vertical 
vector");
 char *fake = N_("Calculate the standard deviations of rows of a matrix and return a vertical vector");
 char *fake = N_("Calculate the standard deviation of a whole matrix");
-char *fake = N_("Run newton's method on a polynomial to attempt to find a root, returns after two successive 
values are within epsilon or after maxn tries (then returns null)");
+char *fake = N_("Attempt to find a root of a polynomial using Newton's method, returning after two 
successive values are within epsilon or after maxn tries (then returns null)");
 char *fake = N_("Returns a set where every element of X appears only once");
 char *fake = N_("Returns a set theoretic union of X and Y (X and Y are vectors pretending to be sets)");
 char *fake = N_("For a Hilbert function that is c for degree d, given the Macaulay bound for the Hilbert 
function of degree d+1 (The c^<d> operator from Green's proof)");
diff --git a/pixmaps/Makefile.am b/pixmaps/Makefile.am
index 4f0d7fc..0b937dd 100644
--- a/pixmaps/Makefile.am
+++ b/pixmaps/Makefile.am
@@ -9,4 +9,4 @@ EXTRA_DIST = \
        $(image_DATA)
 
 install-data-hook:
-       $(GTK_UPDATE_ICON_CACHE) -q $(datadir)/icons/hicolor
+       $(GTK_UPDATE_ICON_CACHE) -q -t $(datadir)/icons/hicolor
diff --git a/src/symbolic.c b/src/symbolic.c
index 604b74a..531e325 100644
--- a/src/symbolic.c
+++ b/src/symbolic.c
@@ -1,5 +1,5 @@
 /* GENIUS Calculator
- * Copyright (C) 1997-2012 Jiri (George) Lebl
+ * Copyright (C) 1997-2013 Jiri (George) Lebl
  *
  * Author: Jiri (George) Lebl
  *
@@ -125,6 +125,14 @@ gel_differentiate_func1_expr (GelToken *tok)
 
        DERIVATIVE_ENTRY ("sinc", "cos(x)*x^(-1)-sinc(x)*x^(-1)");
 
+       DERIVATIVE_ENTRY ("BesselJ0", "-BesselJ1(x)");
+       DERIVATIVE_ENTRY ("BesselJ1", "(1/2)*(BesselJ0(x)-BesselJn(2,x))");
+       DERIVATIVE_ENTRY ("BesselY0", "-BesselY1(x)");
+       DERIVATIVE_ENTRY ("BesselY1", "(1/2)*(BesselY0(x)-BesselYn(2,x))");
+
+       DERIVATIVE_ENTRY ("LambertW", "LambertW(x)/(x*(1+LambertW(x)))");
+       DERIVATIVE_ENTRY ("LambertWm1", "LambertWm1(x)/(x*(1+LambertWm1(x)))");
+
        /* FIXME: check these, I don't trust the CRC handbook */
        DERIVATIVE_ENTRY_ALIAS ("asin", "arcsin", "1/sqrt(1-x^2)");
        DERIVATIVE_ENTRY_ALIAS ("asinh", "arcsinh", "1/sqrt(1+x^2)");
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