* lib/calculus/integration.gel: Add TrapezoidRule, LeftHandRule,

	  RightHandRule

	* help/C/genius.xml: Document the new functions

	* src/geniustests.txt: add some tests

ChangeLog

@@ -1,3 +1,12 @@
+Tue Oct 03 23:23:52 2023  Jiri (George) Lebl <jirka@5z.com>
+
+	* lib/calculus/integration.gel: Add TrapezoidRule, LeftHandRule,
+	  RightHandRule
+
+	* help/C/genius.xml: Document the new functions
+
+	* src/geniustests.txt: add some tests 
+
 Tue Oct 03 22:58:01 2023  Jiri (George) Lebl <jirka@5z.com>
 
 	* src/graphing.c: The shortcut of inputting just the function name

help/C/genius.xml

@@ -7353,6 +7353,14 @@ or <varname>b</varname> can be <constant>null</constant>.</para>
          </listitem>
         </varlistentry>
 
+        <varlistentry>
+         <term><anchor id="gel-function-LeftHandRule"/>LeftHandRule</term>
+         <listitem>
+          <synopsis>LeftHandRule (f,a,b,n)</synopsis>
+          <para>Integration by left hand rule on the interval [a,b] with n subintervals.</para>
+         </listitem>
+        </varlistentry>
+
         <varlistentry>
          <term><anchor id="gel-function-LeftLimit"/>LeftLimit</term>
          <listitem>
@@ -7373,7 +7381,7 @@ or <varname>b</varname> can be <constant>null</constant>.</para>
          <term><anchor id="gel-function-MidpointRule"/>MidpointRule</term>
          <listitem>
           <synopsis>MidpointRule (f,a,b,n)</synopsis>
-          <para>Integration by midpoint rule.</para>
+          <para>Integration by midpoint rule on the interval [a,b] with n subintervals.</para>
          </listitem>
         </varlistentry>
 
@@ -7525,7 +7533,8 @@ computed by numerical integration using
          <term><anchor id="gel-function-NumericalIntegral"/>NumericalIntegral</term>
          <listitem>
           <synopsis>NumericalIntegral (f,a,b)</synopsis>
-          <para>Integration by rule set in NumericalIntegralFunction of f from a to b using NumericalIntegralSteps steps.</para>
+	  <para>Integration by rule set in NumericalIntegralFunction of f from a to b using NumericalIntegralSteps steps.
+By default NumericalIntegralFunction is the CompositeSimpsonsRule.</para>
          </listitem>
         </varlistentry>
 
@@ -7605,6 +7614,14 @@ and has period <userinput>b-a</userinput>.</para>
          </listitem>
         </varlistentry>
 
+        <varlistentry>
+         <term><anchor id="gel-function-RightHandRule"/>RightHandRule</term>
+         <listitem>
+          <synopsis>RightHandRule (f,a,b,n)</synopsis>
+          <para>Integration by right hand rule on the interval [a,b] with n subintervals.</para>
+         </listitem>
+        </varlistentry>
+
         <varlistentry>
          <term><anchor id="gel-function-RightLimit"/>RightLimit</term>
          <listitem>
@@ -7613,6 +7630,14 @@ and has period <userinput>b-a</userinput>.</para>
          </listitem>
         </varlistentry>
 
+        <varlistentry>
+         <term><anchor id="gel-function-TrapezoidRule"/>TrapezoidRule</term>
+         <listitem>
+          <synopsis>TrapezoidRule (f,a,b,n)</synopsis>
+          <para>Integration by trapezoid rule on the interval [a,b] with n subintervals.</para>
+         </listitem>
+        </varlistentry>
+
         <varlistentry>
          <term><anchor id="gel-function-TwoSidedFivePointFormula"/>TwoSidedFivePointFormula</term>
          <listitem>

lib/calculus/integration.gel

@@ -38,7 +38,6 @@ function CompositeSimpsonsRuleTolerance(f,a,b,FourthDerivativeBound,Tolerance) =
 	CompositeSimpsonsRule (f, a, b, n)
 )
 
-# FIXME: reference, though this is really stupid
 SetHelp ("MidpointRule", "calculus", "Integration by midpoint rule")
 function MidpointRule(f,a,b,n) =
 (
@@ -58,10 +57,68 @@ function MidpointRule(f,a,b,n) =
   (s*len)/n
 )
 
+SetHelp ("TrapezoidRule", "calculus", "Integration by trapezoid rule")
+function TrapezoidRule(f,a,b,n) =
+(
+  local *;
+  if(not IsFunction(f)) then
+	(error("TrapezoidRule: argument 1 must be a function");bailout)
+  else if(not IsReal(a) or not IsReal(b)) then
+	(error("TrapezoidRule: arguments 2, 3 must be real values");bailout)
+  else if(not IsInteger(n)) then
+	(error("TrapezoidRule: argument 4 must be an integer");bailout);
+  ## check bounds
+  if(a>b) then (error("TrapezoidRule: argument 2 must be less than or equal to argument 3");bailout)
+  else if(n<= 0) then (error("TrapezoidRule: argument 4 must be positive");bailout);
+
+  len = float(b-a);
+  s = sum i=1 to (n-1) do float(2*f(a+(len*i)/n));
+  s = s+f(a)+f(b);
+  (s*len)/(2*n)
+)
+
+SetHelp ("LeftHandRule", "calculus", "Integration by left hand rule")
+function LeftHandRule(f,a,b,n) =
+(
+  local *;
+  if(not IsFunction(f)) then
+	(error("LeftHandRule: argument 1 must be a function");bailout)
+  else if(not IsReal(a) or not IsReal(b)) then
+	(error("LeftHandRule: arguments 2, 3 must be real values");bailout)
+  else if(not IsInteger(n)) then
+	(error("LeftHandRule: argument 4 must be an integer");bailout);
+  ## check bounds
+  if(a>b) then (error("LeftHandRule: argument 2 must be less than or equal to argument 3");bailout)
+  else if(n<= 0) then (error("LeftHandRule: argument 4 must be positive");bailout);
+
+  len = float(b-a);
+  s = sum i=0 to (n-1) do float(f(a+(len*i)/n));
+  (s*len)/n
+)
+
+SetHelp ("RightHandRule", "calculus", "Integration by right hand rule")
+function RightHandRule(f,a,b,n) =
+(
+  local *;
+  if(not IsFunction(f)) then
+	(error("RightHandRule: argument 1 must be a function");bailout)
+  else if(not IsReal(a) or not IsReal(b)) then
+	(error("RightHandRule: arguments 2, 3 must be real values");bailout)
+  else if(not IsInteger(n)) then
+	(error("RightHandRule: argument 4 must be an integer");bailout);
+  ## check bounds
+  if(a>b) then (error("RightHandRule: argument 2 must be less than or equal to argument 3");bailout)
+  else if(n<= 0) then (error("RightHandRule: argument 4 must be positive");bailout);
+
+  len = float(b-a);
+  s = sum i=1 to n do float(f(a+(len*i)/n));
+  (s*len)/n
+)
+
 SetHelp ("NumericalIntegralSteps", "parameters", "Steps to perform in NumericalIntegral")
 parameter NumericalIntegralSteps = 1000
 
-SetHelp ("NumericalIntegralFunction", "parameters", "The function used for numerical integration in NumericalIntegral")
+SetHelp ("NumericalIntegralFunction", "parameters", "The function used for numerical integration in NumericalIntegral (by default CompositeSimpsonsRule)")
 parameter NumericalIntegralFunction = `CompositeSimpsonsRule
 
 SetHelp ("NumericalIntegral", "calculus", "Integration by rule set in NumericalIntegralFunction of f from a to b using NumericalIntegralSteps steps")

lib/library-strings.c

@@ -11,7 +11,7 @@ char *fake = N_("How many successive steps to be within tolerance for calculatio
 char *fake = N_("Tolerance for calculating the derivatives of functions");
 char *fake = N_("Tolerance of the ErrorFunction (used for complex values only)");
 char *fake = N_("Tolerance of the GaussDistribution function");
-char *fake = N_("The function used for numerical integration in NumericalIntegral");
+char *fake = N_("The function used for numerical integration in NumericalIntegral (by default CompositeSimpsonsRule)");
 char *fake = N_("Steps to perform in NumericalIntegral");
 char *fake = N_("How many iterations to try for InfiniteSum and InfiniteProduct");
 char *fake = N_("How many successive steps to be within tolerance for InfiniteSum and InfiniteProduct");
@@ -191,6 +191,7 @@ char *fake = N_("Try to calculate an infinite sum for a single parameter functio
 char *fake = N_("Try to calculate an infinite sum for a double parameter function with func(arg,n)");
 char *fake = N_("Try and see if a real-valued function is continuous at x0 by calculating the limit there");
 char *fake = N_("Test for differentiability by approximating the left and right limits and comparing");
+char *fake = N_("Integration by left hand rule");
 char *fake = N_("Calculate the left limit of a real-valued function at x0");
 char *fake = N_("Calculate the limit of a real-valued function at x0.  Tries to calculate both left and right limits.");
 char *fake = N_("Integration by midpoint rule");
@@ -209,7 +210,9 @@ char *fake = N_("Return a function which is the odd periodic extension of f defi
 char *fake = N_("Compute one-sided derivative using five point formula");
 char *fake = N_("Compute one-sided derivative using three-point formula");
 char *fake = N_("Return a function which is the periodic extension of f defined on the interval [a,b]");
+char *fake = N_("Integration by right hand rule");
 char *fake = N_("Calculate the right limit of a real-valued function at x0");
+char *fake = N_("Integration by trapezoid rule");
 char *fake = N_("Compute two-sided derivative using five-point formula");
 char *fake = N_("Compute two-sided derivative using three-point formula");
 char *fake = N_("argument (angle) of complex number");

src/geniustests.txt

@@ -1035,6 +1035,10 @@ EulersMethod (`(x,y)=[(x-y@(1));(x-y@(2))],0,[0;0],3,3)		[2.0;2.0]
 CompositeSimpsonsRule(`(x)=x^2,0,3,100)				9.0
 CompositeSimpsonsRule(`(x)=x^2,3,0,100)				-9.0
 CompositeSimpsonsRule(`(x)=x^2,3,3,100)				0
+LeftHandRule(`(x)=x^2,0,2,4)					1.75
+RightHandRule(`(x)=x^2,0,2,4)					3.75
+MidpointRule(`(x)=x^2,0,2,4)					2.625
+TrapezoidRule(`(x)=x^2,0,2,4)					2.75
 a								a
 a=7;UndefineAll();a						a
 UndefineAll();a							a