Table of Contents

The second claimed virtue is the GRAPH button, the big cyan button on the right on top. This button is able to save and run and graph the program in just one click of the mouse. Numbers and color names printed by the program are understood as plotting coordinates and colors for the graph. That is, the plotting is independent of language, so even computer languages without graphics can plot mathematical graphs.

The editor knows how to run the program by looking at the top line of the program file. That is, the editor is not specialized for a small set of languages. I hereby place ScaleDownEdit in the public domain. To top

For whom is this editor?

# c:/ruby/bin/ruby.exe demo.rb

x=1.0

	15.times{ |j|
	x=x-( x**5 + x - 17.0 )/( 5.0 * x**4 + 1.0 - 0.0 )
	print j,"\t",x,"\n"
	}

start c:\tcl\bin\wish85.exe ScaleDownEdit.tk %*

ScaleDownEdit.bat demo.rb

To get back to the program area, the user may use the mouse to click on the SEE PROGRAM button. That will close the output area and re-open the program area, so that changes can be made. SAVE AND RUN and SEE PROGRAM are the important buttons. CLEAR OUTPUT will erase the answers in the output area. SEE OUTPUT will close the program area and open the output area. SAVE PROGRAM will save the program without running it.

Of course, I have stolen the idea of using the first line to say how to run the file. The Unix and Linux shells do this with a shebang. I am merely taking advantage of comments. In the case of Ruby (and many other computer languages) the # character begins a comment. The SAVE AND RUN button’s procedure breaks the first line into tokens, using white-space, and then the left-most token is changed into exec. Then the tokens are handed to eval to be evaluated. The reader sees that there must be white-space after the comment token. Also the reader sees that those are forward slashes in the first line of the program, not backslashes, even though the path is in Microsoft Windows.

The program implements the good old Newton-Raphson loop to solve the equation x⁵ + x = 17 for its real root. The loop goes around fifteen times. All my demo and Demo programs implement this same algorithm. To top

Line number, dirty mark, key bindings, and type size

The dirty mark is the asterisk, *. It goes on the left of the title when the file is “dirty,” that is, when the file in the editor is (or may be) different from the file saved in the hard disk. SAVE AND RUN or SAVE PROGRAM will erase the dirty mark.

The four arrow keys or four triangle keys have their usual meanings. The Page Up and Page Down keys have their usual meanings. The control-Home and control-End keys have their usual meanings. Control-x means cut. Control-c means copy. Control-v means paste. All these are done by Tk without any work on my part.

I have bound control-minus to mean reduce the type size. I have bound control-plus to mean increase the type size, and I have bound control-equal to mean increase the type size. (The plus is the shifted equal sign on my keyboard.)

Also, I have bound the keys “F1” through “F6” to do the same work as my buttons. That is:
F1 is like SAVE AND RUN.
F2 is like SEE PROGRAM.
F3 is like CLEAR OUTPUT.
F4 is like SEE OUTPUT.
F5 is like SAVE PROGRAM.
F6 is like GRAPH.

I have bound these six keys to make a musical sound when they are pushed.

I warn everybody against pushing the “F10” key. Tk has bound it to toggle the focus, I think. Users who do push that key ought to push it a second time to come back into focus, or else the other “F” keys might not work. To top

A Java™ example

// ScaleJava.bat Demo

import static java.lang.Math.*;

public class Demo
{

	public static void main( String[] args )
	{
	int n=15;
	double x=1.0;

		for( int j=0; j<n; j++ )
		{
		x=x-( pow(x,5)+x-17.0 )/( 5.0*pow(x,4)+1.0-0.0 );
		System.out.println( j+"\t"+x );
		}

	}

}

ScaleDownEdit.bat Demo.java

@if exist %1.class del %1.class
@"C:\Program Files\Java\jdk1.7.0\bin\javac.exe" %1.java
@if exist %1.class java %1

I respectfully point out that the last token of the first line of the program is merely Demo, without a suffix. To top

Other demo and Demo examples

No, the way to do this is to use Monte Carlo. That is, let us choose points at random in the hypercube and sum the values of the integrand. Then we can just divide the sum by how many values we used and print the quotient. That is all there is to it:

rem ScaleBas.bat sixDims

option explicit
defdbl a-z

dim n,s
dim x,y,z,u,v,w
dim j as integer

n=1e7
randomize timer
s=0

	for j=1 to n
	x=rnd: y=rnd: z=rnd: u=rnd: v=rnd: w=rnd
	s=s+sqr( sin( x*y*z*u*v*w ) )
	next j
 
print "The answer is ", s/n

@if exist %1.exe del %1.exe
@"c:\program files\freebasic\fbc.exe" -lang fblite -exx %1.bas
@if exist %1.exe %1.exe

Now the question arises, “How good is the answer?” The way to find out is to click on the SAVE AND RUN button, wait for an answer, click again on the SAVE AND RUN button, wait for the second answer, and finally click a third time on the SAVE AND RUN button, and wait for the final answer. (Do not clear the output area between runs. It is not necessary to click back to the program each time.) If the three answers look somewhat alike, then maybe the true integral looks somewhat like them. This argument is feeble, but we have little choice.

I respectfully point out that the first line of the program file refers to sixDims without a suffix. To top

Graph and the Escape key: Cauchy Camel

-- luaJIT graphCauchyCamel.lua

local width=800
local height=600
local edge=5
print( width,height,edge )

local cauchy=function( x,c )return 1/( 1+(x-c)^2 )/math.pi end

local k=100

	for t = -2*k, 2*k
	do
	local product=cauchy( -k,t )*cauchy( k,t )
	print( t,math.log( product ),"purple" )
	end

The second print statement prints a number for x, a number for y, and a color name. The print statement must make white space to separate the three, but no other punctuation marks. The numbers will be rescaled and translated to fit the monitor, so the programmer need not scale them at all. The color name applies to the solid square of pixels to be drawn. To make the program happen, the user may click on the GRAPH button. (I am assuming that luaJIT.exe is in the path.) Then the program area will be covered up by a canvas with a white background and solid purple squares to show the logarithm of the likelihood. The statistical sample has two numbers, k and -k, where k is 100. The user is respectfully invited to change the color name and the value of k.

The graph turns out to look like a two-humped camel, and the humps are sharp and equal in height. Which of these humps is at the maximum likelihood? To ask the question is to answer it. When the user tires of looking at the graph, a push on the Escape key will close the canvas. The Escape key is commonly the leftmost key in the topmost row of the keyboard, and it is often labeled “Esc.”

Instead of clicking on GRAPH, the user may click on SAVE AND RUN, to see the numbers underlying the graph. When things go wrong, this is the right thing to do.

I nearly forgot to mention that Lua and LuaJIT as downloaded have no graphics of their own. That is the reason that I invented the GRAPH button. To top

Graph and the Escape key: Bessel

c scaleF.bat graphBessel

	function besselJ0( x )
	term=1
	sum=term
	k=1

16	continue
	term=-term*x*x/2/2/k/k
	k=k+1
	oldSum=sum
	sum=sum+term
	if( oldSum.ne.sum )goto 16

	besselJ0=sum
	end



	print *,800,600,5
c	print *,1280,1024,15

	do 17 j=-10,250
	x=j/10.0
	y=besselJ0( x )
	print *,0,y," gray"
	print *,x,0," gray"
	print *,x,y," blue"
17	continue

	end

Here is scaleF.bat:

@path=c:\mingw\bin;%path%
@if exist z.exe del z.exe
@g77 -Wall -s %1.f -o z.exe -O3 -fomit-frame-pointer
@if exist z.exe call z.exe
@if exist z.exe del z.exe

rem c:/chipmunk/chipmunk/basic.exe graphEuler.bas
print 800,600,2
rem print 1280,1024,3

x=.01
y=0
t=0
h=.01
a=3

	for j=1 to 3e3
	t=t+h
	x=x+y*h
	y=y-( a*(x*x-1)*y+x )*h
	print t,0,"gray"
	print t,x,"red"
	print t,y,"blue"
	next j

quit

I found out the hard way that the quit at the end of the program is really necessary. To top

Graph and the Escape key: Polar and no

(* ScalePp.bat graphPolar
*)
program graphPolar;

var
theta,r,x,y: double;
n,j: longint;

begin
writeln( 600,' ',600,' ',2 );
n:=1000;

	for j:=1 to n do
	begin
	theta:=2.0*pi*j/n;
	r:=sin(theta+0.4321)-0.5;
	x:=r*cos(theta);
	y:=r*sin(theta);
	writeln( x,' ',0,' lightgray' );
	writeln( 0,' ',y,' lightgray' );
	writeln( x,' ',y,' red' );
	writeln( y,' ',x,' no' );
	end;

end.

@if exist %1.exe del %1.exe
@if exist %1.o del %1.o
@c:\FPC\2.2.2\bin\i386-win32\fpc.exe %1.pp
@if exist %1.exe %1.exe

	writeln( x,' ',y,' red' );
	writeln( y,' ',x,' no' );

The curve is a slightly tilted limaçon, a familiar polar curve from the calculus book. Without some kind of correction, it would have wrong aspect ratio. Readers wishing to see the tranposed curve and how it works are respectfully invited to change the no to pink.

I nearly forgot to mention the (* and *) tokens for a Pascal comment. ScaleDownEdit is not expecting a right-hand token, so the *) must be dropped down to the next line. To top

Graph and the Escape key: Lissajous

// java -jar c:/rhino/rhino1_7R1/js.jar graphLissajous.js
print( 800,600,20 );
var n=5e2;
var kuller=["red","orange","yellow","green","blue","violet"];

	for( var j=0;j<n;j++ )
	{
	var x=Math.PI*2*j/n;
	print( Math.sin(3*x), Math.sin(4*x), kuller[j%6] );
	}

I respectfully suggest that this is the only method that is sure to work. Stopping just the editor or just the program will fail astonishingly. One must stop both on the same occasion of using Windows Task Manager. To top

License, revision date, and e-mail address

       at        dot
smtw2gh  toadmail   com