Implement factorial and combin functions; minor corrections to graph documentation

Author: BruceSherwood

docs/GlowScriptDocs/factorial.html

@@ -37,13 +37,8 @@ <h1 class="Heading-1"> <font color="#0000A0">The factorial and combin Functions<
       </div>
       <div>
         <div>
-          <p class="program"> from visual import *<br />
-          from visual.factorial import * # import after visual<br />
-          print(factorial(4)) # gives 24 <br />
-          print(combin(10,2)) # gives 45</p>
-          <p class="Normal"> </p>
-          <p class="Normal"><em>Note: To avoid confusion between the module named &quot;factorial&quot; 
-            and the function named &quot;factorial&quot;, import the factorial module <strong>after</strong> importing the visual module itself.</em></p>
+          <p class="program">          print(factorial(4)) # gives 24 <br />
+          print(combin(10,2)) # gives 45 </p>
           <p class="Normal"><span class="program">The factorial function factorial(N)
                is N!; 4! is (4)(3)(2)(1) = 24, and 0! is defined to be 1.<br />
 The combin function is combin(a,b) = a!/(b!*(a-b)!)</span>.</p>
@@ -69,7 +64,7 @@ <h1 class="Heading-1"> <font color="#0000A0">The factorial and combin Functions<
 
             numbers. For example, <span class="attribute">combin(5,2)</span> = 5!/(3!*2!) 
 
-            = (5*4)/2 = 10, and we didn't have to evaluate 5! fully.</p>
+          = (5*4)/(2*1) = (2.5*4) = 10, and we didn't have to evaluate any of the factorials fully..</p>
         </div>
       </div>
       <div> </div>

docs/GlowScriptDocs/math.html

@@ -56,12 +56,14 @@ <h1 class="Heading-1"> <font color="#0000A0">Math Functions</font></h1>
         max(x,y,z) # the largest of x,y,z<br />
         min(x,y,z) # the smallest of x,y,z<br />
         random()   &nbsp;&nbsp;# pseudorandom number 0 to 1<br />
-        ceil(x) &nbsp;# integer closest to x, &lt;=x<br />
-        floor(x) # integer closest to x, &gt;=x<br />
-        round(x) # integer closest to x <br />
+        ceil(x) &nbsp;&nbsp;&nbsp;# integer closest to x, &lt;=x<br />
+        floor(x) &nbsp;&nbsp;# integer closest to x, &gt;=x<br />
+        round(x) &nbsp;&nbsp;# integer closest to x<br />
+        factorial(x) &nbsp;# x! = x*(x-1)*(x-2)....(1)<br />
+        combin(x,y)     &nbsp;&nbsp;#  x!/(y!*(x-y)!)<br />
         max(a,b,c,..) # maximum of these<br />
       min(a,b,c,..) # minimum of these</p>
-<p class="Normal">The quantities above are simplified forms of the JavaScript functions Math.abs(x), Math.sqrt(x), etc.</p>
+<p class="Normal">Many of the quantities above are simplified forms of the JavaScript functions Math.abs(x), Math.sqrt(x), etc. <strong><a href="factorial.html">Here are details</a></strong> of the factorial and combin functions.</p>
 <p class="Normal">There are functions for converting between degrees and
         radians, where there are 2*pi radians in 360 degrees: </p>
       <p class="program">radians(360) &nbsp;# equal to 2*pi<br />

docs/GlowScriptDocs/navigation.js

@@ -38,6 +38,7 @@ s += '<option value="math.html">Math Functions</option>'
 s += '<option value="vector.html">Vector Operations </option>'
 s += '<option value="MathJax.html">LaTeX Math Displays</option>'
 s += '<option value="files.html">Libraries &amp; Files</option>'
+s += '<option value="factorial.html">factorial/combin</option>'
 document.getElementById("menu2").innerHTML = s
 
 s = ''

docs/VPythonDocs/factorial.html

@@ -45,16 +45,8 @@ <h1 class="Heading-1"> <font color="#0000A0">The factorial and combin Functions<
       </div>
       <div>
         <div>
-          <p class="program"> from visual import *<br />
-          from visual.factorial import * # import after visual<br />
-          print(factorial(4)) # gives 24 <br />
-          print(combin(10,2)) # gives 45</p>
-          <p class="Normal"> </p>
-          <p class="Normal"><em>Note: To avoid confusion between the module named &quot;factorial&quot; 
-            and the function named &quot;factorial&quot;, import the factorial module <strong>after</strong> importing the visual module itself.</em></p>
-          <p class="Normal">&nbsp;</p>
-          <p class="Normal">This is not yet available in GlowScript.</p>
-          <p class="Normal">&nbsp;</p>
+          <p class="program">          print(factorial(4)) # gives 24 <br />
+          print(combin(10,2)) # gives 45 </p>
           <p class="Normal"><span class="program">The factorial function factorial(N)
                is N!; 4! is (4)(3)(2)(1) = 24, and 0! is defined to be 1.<br />
 The combin function is combin(a,b) = a!/(b!*(a-b)!)</span>.</p>
@@ -80,7 +72,7 @@ <h1 class="Heading-1"> <font color="#0000A0">The factorial and combin Functions<
 
             numbers. For example, <span class="attribute">combin(5,2)</span> = 5!/(3!*2!) 
 
-            = (5*4)/2 = 10, and we didn't have to evaluate 5! fully.</p>
+            = (5*4)/(2*1) = (2.5*4) = 10, and we didn't have to evaluate any of the factorials fully.</p>
         </div>
       </div>
       <div> </div>

docs/VPythonDocs/graph.html

@@ -72,8 +72,7 @@
       <p class="program"> f1.plot(pos=(100,-30)) # add a single point<br />
         f1.plot(pos=[(100,-30),(20,50),(0,-10)]) # add a list<br />
       </p>
-<p class="Normal">When you add points, you can optionally specify a  color for these points that is different from the default color of the object:</p>
-<p class="program"> f1.plot(pos=(100,-30), color=color.red)</p>
+<p class="Normal">In classic VPython, when you add points you can optionally specify a  color for these points that is different from the default color of the object: <span class="program">f1.plot(pos=(100,-30), color=color.red)</span>. However, this is not currently possible in GlowScript VPython. Once you have created a graphing object such as gcurve, its initial color will be used throughout.</p>
 <p class="Normal"> You can plot more than one thing on the same graph:</p>
 <p class="program"> f1 = gcurve(color=color.cyan) <br />
   f2 = gvbars(delta=0.05, color=color.blue)<br />

docs/VPythonDocs/math.html

@@ -72,10 +72,12 @@ <h1 class="Heading-1"> <font color="#0000A0">Math Functions</font></h1>
         random()   &nbsp;&nbsp;# pseudorandom number 0 to 1<br />
         ceil(x) &nbsp;# integer closest to x, &lt;=x<br />
         floor(x) # integer closest to x, &gt;=x<br />
-        round(x) # integer closest to x <br />
+        round(x) # integer closest to x<br />
+        factorial(x) &nbsp;# x! = x*(x-1)*(x-2)....(1)<br />
+        combin(x,y)     &nbsp;&nbsp;#  x!/(y!*(x-y)!) <br />
         max(a,b,c,..) # maximum of these<br />
         min(a,b,c,..) # minimum of these</p>
-      <p class="Normal">The quantities above are simplified forms of the JavaScript functions Math.abs(x), Math.sqrt(x), etc.</p>
+      <p class="Normal">Many of the quantities above are simplified forms of the JavaScript functions Math.abs(x), Math.sqrt(x), etc. <strong><a href="factorial.html">Here are details</a></strong> of the factorial and combin functions.</p>
       <p class="Normal">There are functions for converting between degrees and
         radians, where there are 2*pi radians in 360 degrees: </p>
       <p class="program">radians(360) &nbsp;# equal to 2*pi<br />

lib/glow/api_misc.js

@@ -286,6 +286,45 @@
     function clock() {
     	return 0.001*msclock()
     }
+    
+    function factorial(x) {
+        if (x <= 0) {
+            if (x === 0) return 1
+            else throw new Error('Cannot take factorial of negative number ' + x)
+        }
+        var fact = 1
+        var nn = 2
+        while (nn <= x) {
+            fact = fact*nn
+            nn += 1
+        }
+        if (nn != x+1) throw new Error('Argument of factorial must be an integer, not ' + x)
+        return fact
+    }
+
+    function combin(x, y) {
+        // combin(x,y) = factorial(x)/[factorial(y)*factorial(x-y)]
+        var z = x-y
+        var num = 1
+        if (y > z) {
+            var temp = y
+            y = z
+            z = temp
+        }
+        var nn = z+1
+        var ny = 1
+        while (nn <= x) {
+            num = num*nn/ny
+            nn += 1
+            ny += 1
+        }
+        if (nn != x+1) throw new Error('Illegal arguments ('+x+','+y+') for combin function')
+        return num
+    }
+
+    //console.log('factorial(6) = 6! =', factorial(6)) // should be 720
+    //console.log('combin(6,2) = 6!/(2!(6-2)!) =', combin(6,2)) // should be 15
+    //console.log('combin(1000,500) = 1000!/(500!(1000-500)!) =', combin(1000,500)) // should be 2.70288240945e+299
 
     var exports = {
         // Top-level math functions
@@ -308,6 +347,8 @@
         min: Math.min,
         random: Math.random,
         round: Math.round,
+        factorial: factorial,
+        combin: combin,
         radians: function radians(deg) { return (deg * Math.PI / 180) },
         degrees: function degrees(rad) { return (rad * 180 / Math.PI) },
 

lib/glow/graph.js

@@ -428,6 +428,12 @@
         this.plot = function (data) {
             // Accept plot(x,y) or plot([x,y], [x,y], ...) or plot([[x,y], [x,y], ...]])
             this.__graph.changed = true
+            if (data.color !== undefined) {
+            	throw new Error("Cannot currently change color in a plot statement.")
+            	//this.__color = data.color
+            	//this.options.color = color.to_html(data.color)
+            	//delete data.color
+            }
             if (typeof arguments[0] == 'number') { // x,y
                 this.options.data.push([arguments[0], arguments[1]])
             } else if (typeof arguments[0][0] == 'number') { // [x,y], [x,y], ....
@@ -447,7 +453,7 @@
                     this.options.data.push(xy)
                 }
             } else {
-                throw new Error("must be plot(x,y) or plot([x,y]) or plot([x,y], ...) or plot([ [x,y], ... ])")
+                throw new Error("must be plot(x,y) or plot(pos=(x,y)) or plot([x,y]) or plot([x,y], ...) or plot([ [x,y], ... ])")
             }
         }
     }