The BASIC programming language was developed in 1965 by John G. Kemeny and Thomas E. Kurtz as a language for introductory courses in computer science. In 1988 they extended the language to make it modular and portable.

**1. Introduction**

True BASIC, C, Fortran, and Pascal are examples of *procedural
languages.* Procedural languages change the state or memory of the machine by a sequence of statements. True BASIC is similar to F
(a subset of Fortran 90) and has excellent graphics capabilities which
are
hardware independent. True BASIC programs can run without change on
computers running the Macintosh, Unix, and Windows operating systems.
We will consider version 3.0 (2.7 on the Macintosh) of True BASIC.
Version 5 includes the ability to build objects such as buttons, scroll
bars, menus, and dialog boxes. However, because we wish to emphasize
the similarity between True BASIC and other
procedural languages such as C, F, and Java, we do not consider these
features.

There is no perfect programming language (or operating system) and users should be flexible and choose the appropriate language to accomplish their goals. Former students who were well grounded in True BASIC have had no trouble learning C, F, and Java quickly.

This tutorial is based on the text, Introduction to Computer Simulation Methods, by Harvey Gould and Jan Tobochnik. The features of True BASIC which are common to other procedural languages are emphasized.

To illustrate the nature of True BASIC, we first give a program that multiplies two numbers and prints the result:

The features of True BASIC included in the above program include:PROGRAM product ! taken from Chapter 2 of Gould & Tobochnik LET m = 2 ! mass in kilograms LET a = 4 ! acceleration in mks units LET force = m*a ! force in Newtons PRINT force END

The first statement is an optional **PROGRAM** header. The inclusion of a program header is good programming style.

Comment statements begin with **!** and can be included anywhere in the program.

PROGRAM, LET, PRINT, and END are **keywords**
(words that are part of the language and cannot be redefined) and are
given in upper case. The case is insignificant (unlike C, F, and Java).
The **DO FORMAT** command converts keywords to upper case.

The **LET** statement causes the expression to the right of the = sign to be evaluated and then causes the result to be *assigned* to the left of the = sign. (The LET statement reminds us that the meaning of the **=**
symbol is not the same as equals.) It is not necessary to type LET,
because the DO FORMAT command automatically inserts LET where
appropriate. The LET statement can be omitted if the OPTION NOLET
statement is included.

True BASIC does not distinguish between integer numerical variables and floating point numerical variables and recognizes only two types of data: numbers and strings (characters). The first character of a variable must be a letter and the last must not be an underscore.

The PRINT statement displays output on the screen.

The last statement of the program must be **END**.

We next introduce syntax that allows us to enter the desired values of m and a from the keyboard.

Note the difference between thePROGRAM product2 INPUT m INPUT prompt "acceleration a (mks units) = ": a LET force = m*a ! force in Newton's PRINT "force (in Newtons) ="; force END

**2. Loop structures**

True BASIC uses a **FOR** or a **DO** construct to execute the same statements more than once. An example of a FOR loop follows:

The use of thePROGRAM series ! add the first 100 terms of a simple series ! True BASIC automatically initializes variables to zero, ! but other languages might not. LET sum = 0 FOR n = 1 to 100 LET sum = sum + 1/(n*n) PRINT n,sum NEXT n END

The block of statements inside the loop is indented for clarity. Use the DO FORMAT command to indent loops automatically.

The order of evaluation follows the mathematical conventions shared by all computer languages. Exponentiations are performed first, followed by multiplications and divisions from left to right. Parentheses should be used whenever the result might be ambiguous to the reader. The parentheses in the statement, LET sum = sum + 1/(n*n), are included for clarity.

All unassigned variables are automatically initialized to zero. Because C, F, and Java do not, it is recommended that variables such as sum in Program series be initialized explicitly.

In many cases the number of repetitions is not known in advance. An example of a **DO** loop follows:

Note the use of thePROGRAM series_do ! illustrate use of DO LOOP structure LET sum = 0 LET n = 0 LET relative_change = 1 ! choose large value DO while relative_change > 0.0001 LET n = n + 1 LET newterm = 1/(n*n) LET sum = sum + newterm LET relative_change = newterm/sum PRINT n,relative_change,sum LOOP END

ThePROGRAM decision1 LET x = 0 DO while x < 20 LET x = x + 1 IF x <= 10 then LET f = 1/x ELSE LET f = 1/(x*x) END IF PRINT x,f LOOP END

Any number of ELSEIF statements may be used in an IF structure, and IF statements may be nested.PROGRAM decision2 LET x = 0 DO while x <= 30 IF x = 0 then LET f = 0 ELSEIF x <= 10 then LET f = 1/x ELSEIF x <= 20 then LET f = 1/(x*x) ELSE LET f = 1/(x*x*x) END IF PRINT x,f LET x = x + 1 LOOP END

relation | operator |
---|---|

equal | = |

less than | < |

less than or equal | <= |

greater than | > |

greater than or equal | >= |

not equal | <> |

If all the choices in the decision structure are based on the value of a single expression, it is sometimes convenient to use a SELECT CASE structure.

Although True BASIC explicitly recognizes only two kinds of variables, numeric and string, it implicitly distinguishes between floating point (real) and integer numeric variables. For example, the variable x in Program decision2 is treated as an integer variable and hence stored with infinite precision; the variable f is treated as a real variable and stored to 14 to 16 decimal places depending on the computer. Arithmetic with numbers represented by integers is exact, but arithmetic operations which involve real numbers is not. For this reason, decision statements should involve comparisons of integer variables rather than floating point variables.

C and Fortran 90 support the WHILE statement, but F does not. A program equivalent to Program decision2 is given in the following:

PROGRAM decision3 LET x = 0 DO LET x = x + 1 IF x <= 10 then LET f = 1/x ELSE LET f = 1/(x*x) END IF PRINT x,f IF x = 20 then EXIT DO ! note syntax END IF LOOP END

**4. Subprograms and local and shared variables**

It is convenient to divide a program into smaller units consisting of a main program and subprograms consisting of subroutines and functions. Subprograms are called from the main program or other subprograms. As an example, the following program adds and multiplies two numbers which are inputed from the keyboard.

Program tasks is an example of aPROGRAM tasks ! illustrate use of subroutines ! note how variables are passed CALL initial(x,y) ! initialize variables CALL add(x,y,sum) ! add two variables CALL multiply(x,y,product) PRINT "sum ="; sum, "product ="; product END ! end of main program SUB initial(x,y) INPUT x INPUT y END SUB SUB add(x,y,sum) LET sum = x + y END SUB SUB multiply(x,y,product) LET product = x*y END SUB

A subroutine is defined by a **SUB** statement; the end of a subroutine is denoted by **END SUB**.
We use only external subroutines and functions. External program units
are defined in any order after the END statement of the main program.

A subroutine is a separate program unit with its own *local*
variables, that is, the variables in the main program and in each
external subroutine and function are available only to the program
subunit. A variable name represents a memory location in the computer.
If the same variable name is used in two program units, the name
represents two different memory locations.

The most common method for subroutines to pass information to the main program and to other subroutines is via arguments in the subroutine calls. In Program tasks the variables x, y, sum, and product are passed in this way. (It is a little misleading to say that variable names are passed to a subroutine. More precisely, the variable names are not passed, but rather the memory location in the computer is passed. The variable name is simply a label that identifies the memory location.)

In Program no_pass the variable name x is used in the main program and in SUB add_one, but is not passed. Convince yourself that the result printed for x in the main program is 10. What is the value of x in SUB add_one?

PROGRAM no_pass LET x = 10 ! local variable name x defined in main program CALL add_one PRINT x END SUB add_one ! variable name x not passed LET x = x + 1 ! local variable name defined in subroutine END SUB

What are the values of x and y if SUB add_one in Program pass is written in the following form?

PROGRAM pass LET x = 10 LET y = 3 CALL add_one(x) CALL add_one(y) PRINT x,y END SUB add_one(s) ! example of the use of dummy arguments LET s = s + 1 END SUB

The variable name in the subroutine declaration need not match the name used in calling the subroutine. We call the declaration variable name a "dummy variable," because it may not actually be used in the program execution. It is only necessary that the number of variables in the declaration equal the number in the calling of a subroutine. Another way of passing information in True BASIC is discussed later.

An example of the use of a function is given in the following:

Note that functions do not change the values of arguments to them. Definitions are not limited to a single line.PROGRAM example_f ! example of use of external function DECLARE DEF f LET delta = 0.01 ! incremental increase LET sigma2 = 1 ! variance LET x = 0 ! initialize variables even though unnecessary DO PRINT x,f(x,sigma2) LET x = x + delta LOOP until key input END DEF f(x,sigma2) ! define Gaussian function with zero mean and variance sigma2 LET f = (2*pi*sigma2)^(-0.5)*exp(-x*x/(2*sigma2)) END DEF

One way to stop a program is to have the user hit any key as shown by the use of the **key input** statement in Program example_f.

The exponentiation operator is **^**.

The quantity pi (the area of a circle with unit radius) is predefined. Its use is illustrated in Program example_f. (Strictly speaking, pi is a function which has no arguments and whose value is pi.)

True BASIC has many intrinsic (built-in) functions. Some of the more frequently used mathematical functions are given in Table 2.

Table 2. Useful mathematical functions.

notation | function |
---|---|

abs(x) | absolute value |

sqr(x) | square root |

exp(x) | exponential function |

log(x) | natural logarithm |

log10(x) | logarithm base 10 |

sin(x) | sine function |

cos(x) | cosine function |

tan(x) | tangent function |

int(x) | integer part |

mod(x,y) | remainder when x is divided by y |

max(x,y) | larger of x and y |

min(x,y) | smaller of x and y |

remainder(x,y) | mod(x,y) - y |

If you are uncertain how a particular function works, write a little program to test it. For example, what is the value of mod(10,3)? What about mod(-10,3)? What is the difference between the MOD and the REMAINDER functions?

Because the effect of thePROGRAM random RANDOMIZE LET N = 100 FOR i = 1 to N LET integer = int(N*rnd) + 1 PRINT integer; NEXT i END

Although it is a good idea to write your own random number generator using an algorithm that you have tested on the particular problem of interest, it is convenient to use the rnd function when you are debugging a program or if accuracy is not important.

The properties of arrays in True BASIC include:PROGRAM vector ! illustrate use of arrays DIM a(3),b(3) ! arrays defined in DIM statement CALL initial(a(),b()) CALL dot(a(),b()) CALL cross(a(),b()) END SUB initial(a(),b()) LET a(1) = 2 LET a(2) = -3 LET a(3) = -4 LET b(1) = 6 LET b(2) = 5 LET b(3) = 1 END SUB SUB dot(a(),b()) LET dot_product = 0 FOR i = 1 to 3 LET dot_product = dot_product + a(i)*b(i) NEXT i PRINT "scalar product = "; dot_product END SUB SUB cross(r(),s()) ! arrays can be defined in main program or subroutine ! note use of dummy variables DIM cross_product(3) FOR component = 1 to 3 LET i = mod(component,3) + 1 LET j = mod(i,3) + 1 LET cross_product(component) = r(i)*s(j) - s(i)*r(j) NEXT component PRINT PRINT "three components of the vector product:" PRINT " x "," y "," z " FOR component = 1 to 3 PRINT cross_product(component), NEXT component END SUB

The same name cannot be used for both an array variable and for another type of variable.

Because the address of the first element of the array is passed, rather than the entire array, there is no memory or speed penalty when arrays are passed to a subroutine. True BASIC has many intrinsic matrix operations which are similar to the operations in F.

SET CURSOR | PRINT USING | GET KEY | GET MOUSE | Files | READ/DATA statements |

True BASIC prints at the current cursor position. The functionPRINT "x","y","z" PRINT x,y,z PRINT ! skip line PRINT "time ="; t PRINT tab(7);"time";tab(17);"position";tab(28);"velocity"

The cursor may be moved by the SET CURSOR statement

which moves the cursor to row 10 and column 20. SET CURSOR 1,1 moves the cursor to the upper left corner.SET CURSOR 10, 20 ! row, column

Because different computers have different numbers of rows and columns, the statement

setsASK SET CURSOR max_row,max_col

**Formatted output**

If you need to print output to greater accuracy or in a different format than the default used by True BASIC, use the PRINT using statement.

Try various values of t, x, and v to see the nature of the output. For example, try t = 15.5, x = -3.222222, and v = 1.PRINT using "####.###": t,x,v ! output occupies 8 spaces including decimal point PRINT using "----.###": t,x,v ! - prints number with leading space or minus sign PRINT using "--%%.###": t,x,v ! % prints leading zeroes as '0'

We have already given an example of the use of the logical expression key input.PROGRAM space_bar DO GET KEY k PRINT k LOOP until k = 32 ! pressing space bar exits loop END

**Mouse**

The use of the GET MOUSE statement is illustrated in Program mouse:

The variable s is the state of the mouse when the cursor is at position (x,y). The possible values of the status arePROGRAM mouse DO ! return current x and y window coordinates and state of mouse GET MOUSE x,y,s IF s = 1 then PRINT "button down",x,y ELSE IF s = 2 then PRINT "button clicked",x,y ELSE IF s = 3 then PRINT "button released",x,y END IF LOOP END

s = 0 | mouse button not pressed |

s = 1 | mouse button held down while dragging |

s = 2 | mouse button clicked at (x,y) |

s = 3 | mouse button released at (x,y) |

Program single_column uses a string or character variable for the name of the file. The writing of files with multiple columns is more complicated and is illustrated in the following.PROGRAM single_column ! save data in a single column ! file$ example of string variable INPUT prompt "name of file for data? ": file$ ! channel number #1 associated with file and can be passed to ! subroutines ! various options may be specified in OPEN statement ! access output: write to file only ! create newold: open file if exists, else create new file OPEN #1: name file$, access output, create newold ! True BASIC does not overwrite data in a text file ! ERASE #1 ! erase contents of file ! RESET #1: end ! allows data to be added to end of file FOR i = 1 to 4 LET x = i*i PRINT #1: x ! print column of data NEXT i CLOSE #1 ! channel # irrelevant if only one channel open at a time OPEN #2: name file$, access input FOR i = 1 to 4 INPUT #2: y ! print column of data PRINT y NEXT i ! files automatically closed when program terminates CLOSE #2 ! not necessary but good practice END

It is necessary to separate columns by a comma, an annoying feature of True BASIC. There are many variations on the open statement, but the above example is typical.file$ = "config.dat" OPEN #1: name file$,access output,create new PRINT #1: N PRINT #1: L ! comma added between inputs on the same line so that file ! can be read by True BASIC FOR i = 1 to N PRINT #1, using "----.######, ----.######": x(i),y(i) NEXT i CLOSE #1 ! next illustrate how to read file. OPEN #1: name file$, access input INPUT #1: N INPUT #1: L FOR i = 1 to N INPUT #1: x(i),y(i) NEXT i

PROGRAM example_data DIM x(6) DATA 4.48,3.06,0.20,2.08,3.88,3.36 FOR i = 1 to 6 READ x(i) ! reads input from DATA statement NEXT i END

Core statements | Aspect ratio | Multiple windows | Animation |

determines the minimum and maximum x (horizontal) and y (vertical) coordinates. The statementSET WINDOW xmin, xmax, ymin, ymax

draws a point at (x,y) in the current window coordinates. The statementPLOT POINTS: x,y;

draws a line between (x1,y1) and (x2,y2). Program plot_f uses these statements to draw a set of axes and plot the function T(t) = TPLOT LINES: x1,y1; x2,y2;

The program uses a separate subroutine to set up the screen and another to plot the function.PROGRAM plot_f ! plot analytical solution CALL initial(t,tmax,r,Ts,T0) CALL set_up_window(t,tmax,Ts,T0) CALL show_plot(t,tmax,r,Ts,T0) END SUB initial(t,tmax,r,Ts,T0) LET t = 0 LET T0 = 83 ! initial coffee temperature (C) LET Ts = 22 ! room temperature (C) INPUT prompt "cooling constant r = ": r INPUT prompt "duration = ": tmax ! time (minutes) CLEAR END SUB SUB set_up_window(xmin,xmax,ymin,ymax) LET mx = 0.01*(xmax - xmin) ! margin LET my = 0.01*(ymax - ymin) SET WINDOW xmin - mx,xmax + mx,ymin - my,ymax + my ! default background color black on all computers except Macintosh PLOT xmin,ymin; xmax,ymin ! abbreviation for PLOT LINES: PLOT xmin,ymin; xmin,ymax END SUB SUB show_plot(t,tmax,r,Ts,T0) DECLARE DEF f ! declare use of external function SET COLOR "red" DO while t <= tmax PLOT t,f(t,r,Ts,T0); ! abbreviation for PLOT LINES LET t = t + 0.1 LOOP END SUB DEF f(t,r,Ts,T0) LET f = Ts - (Ts - T0)*exp(-r*t) END DEF

**PLOT x,y;** is an abbreviation of **PLOT POINT x,y**.

Program simple_map
uses the SET WINDOW, PLOT, BOX LINES and ASK MAX COLOR statements to
help visualize the trajectory of a two-dimensional dynamical system. A
summary of the some of the important graphics statements is given in
Table 3.

SET BACKGROUND COLOR "black" | ||

SET WINDOW xmin,xmax,ymin,ymax | default window coordinates are 0,1,0,1 | |

PLOT POINTS: x,y | abbreviation is PLOT x,y | |

PLOT LINES: x1,y1; x2,y2; | ||

PLOT | start a new curve | |

PLOT AREA: 1,1;2,1;2,2 | draw filled triangle | |

BOX LINES xmin,xmax,ymin,ymax | draw rectangle | |

BOX AREA xmin,xmax,ymin,ymax | draw filled rectangle | |

BOX CLEAR xmin,xmax,ymin,ymax | erase rectangle | |

BOX CIRCLE xmin,xmax,ymin,ymax | draw inscribed circle (or ellipse) | |

ASK MAX COLOR mc | mc is number of foreground colors | |

SET COLOR "red" | colors include green, blue, brown, magenta, and white | |

CLEAR | erase contents of current window | |

FLOOD x,y | fill enclosed region with current foreground color |

**Aspect Ratio**

When is a circle not a circle? Run the following program and find out.

The problem is that few computer screens are square and have the same number of pixels in the horizontal and vertical direction. Moreover, it is possible to define multiple windows whose shape is arbitrary. Sometimes it is essential that a circle really appear circular on the screen. In this case we must correct for thePROGRAM no_circle LET r = 1 ! radius of circle SET WINDOW -r,r,-r,r SET COLOR "blue" BOX CIRCLE -r,r,-r,r ! FLOOD 0,0: start from the point 0,0 and color continuous pixels ! until boundary of region is reached FLOOD 0,0 END

Note the use of thePROGRAM circle LET r = 1 ! radius of circle CALL compute_aspect_ratio(r,xwin,ywin) SET WINDOW -xwin,xwin,-ywin,ywin SET COLOR "blue" BOX CIRCLE -r,r,-r,r ! draw circle END SUB compute_aspect_ratio(r,x,y) LET m = 0.1*r ! margin LET size = r + m ! px, py: # pixels in horizontal and vertical direction ASK PIXELS px,py IF px > py then LET aspect_ratio = px/py LET x = aspect_ratio*size LET y = size ELSE LET aspect_ratio = py/px LET x = size LET y = aspect_ratio*size END IF END SUB

PROGRAM multiple_windows ! note passing of channel numbers CALL initial(#1,#2) ! initialize windows CALL show(#1) CALL show(#2) END SUB initial(#1,#2) OPEN #1: screen 0,0.5,0,1 ! left-half of screen SET WINDOW 0,1,0,1 SET COLOR "green" OPEN #2: screen 0.5,1,0,1 ! right-half of screen SET COLOR "red" SET WINDOW 0,1,0,1 END SUB SUB show(#9) WINDOW #9 ! note use of dummy variable FOR i = 1 to 100 PLOT rnd,rnd; NEXT i END SUB

**Animation**

To make animations, we can store screen images as a string
variable and display them again without the need for additional
calculation. The following program illustrates the use of the BOX KEEP,
BOX CLEAR, and BOX SHOW statements to create the illustrate the
illusion of motion across the screen.

Another example of the use of animation is shown in Program pendula.PROGRAM animation SET WINDOW 1,10,1,10 SET COLOR "red" BOX AREA 1,2,1,2 ! draw shape BOX KEEP 1,2,1,2 in box$ ! store shape in string variable box$ CLEAR LET x = 1 DO while x < 10 BOX CLEAR x,x+1,5,6 ! erase shape LET x = x + 0.1 BOX SHOW box$ at x,5 ! redraw shape at different location PAUSE 0.01 ! choose delay LOOP END

A program illustrating the most common operations on string variables follows:LET file_name$ = "config.dat"

True BASIC has many useful string handling functions, some which are summarized in Table 4.PROGRAM string LET a$ = " " LET b$ = "good" PRINT b$ LET b$ = b$ & a$ & "morning" ! & for concatenation PRINT b$ LET c$ = b$[1:4] ! extract substring PRINT c$ END

Table 4. Useful string handling functions.

notation | function |
---|---|

len(x$) | number of characters in x$ |

pos(x$,a$,c) | first occurrence of a$ in x$ at or after character number c |

lcase$(x$) | convert letters to lower case |

ucase$(x$) | convert letters to upper case |

trim$(x$) | remove leading and trailing blanks |

ltrim$(x$) | remove leading blanks |

rtrim$(x$) | remove trailing blanks |

PROGRAM read_file ! open n successive files LET n = 20 FOR i = 1 to n LET si$ = str$(i) LET file_name$ = "config" & si$ & ".dat" OPEN #i: name file_name$, access output, create newold PRINT #i: file_name$ PRINT file_name$ CLOSE #i NEXT i END

Recursion | Global variables | Strong typing | modules | Select case | Matrix operations |

**Recursion**

A simple example of a recursive definition is the factorial function

A recursive definition of the factorial isfactorial(n) = n! = n(n-1)(n-2) ... 1

A program that closely parallels the above definition follows.factorial(n) = n factorial(n-1)

PROGRAM n! DECLARE DEF f LET n = 11 PRINT "n! ="; f(n) END PROGRAM DEF f(n) IF n <= 0 then LET f = 1 ELSE LET f = n*f(n-1) END IF END DEF

PROGRAM show_public PUBLIC L,spin(3,3) CALL initial FOR y = 1 to L FOR x = 1 to L PRINT spin(x,y); NEXT x PRINT NEXT y END SUB initial DECLARE PUBLIC L,spin(,) LET L = 3 FOR y = 1 to L FOR x = 1 to L IF rnd < 0.5 then LET spin(x,y) = 1 ELSE LET spin(x,y) = -1 END IF NEXT x NEXT y END SUB

PROGRAM show_public OPTION TYPO PUBLIC L,spin(3,3) LOCAL x,y CALL initial FOR y = 1 to L FOR x = 1 to L PRINT spin(x,y); NEXT x PRINT NEXT y END SUB initial DECLARE PUBLIC L,spin(,) LOCAL x,y LET L = 3 FOR y = 1 to L FOR x = 1 to L IF rnd < 0.5 then LET spin(x,y) = 1 ELSE LET spin(x,y) = -1 END IF NEXT x NEXT y END SUB

**Modules**

A
module is a library of external subprograms. If you are ready to use a
module, you are ready to learn another procedural language such as F which uses modules more effectively. An example of a True BASIC program which uses a module follows.

The module "common" is in a separate file with the same name. PUBLIC statements determine which variables may be accessed from outside the module. SHARE statements determine the variables that are available to all subprograms within the module, but not outside the module.PROGRAM cool ! numerical solution of Newton's law of cooling LIBRARY "common" DECLARE PUBLIC r,t,dt,tmax,nshow,T_coffee CALL output LET counter = 0 DO IF (t >= tmax) then EXIT DO END IF CALL Euler LET counter = counter + 1 ! number of iterations IF (mod(counter,nshow) = 0) then CALL output END IF LOOP DO LOOP until key input END

MODULE common PUBLIC r,t,dt,tmax,nshow,T_coffee SHARE T_room ! initialize variables LET t = 0.0 ! time LET T_coffee = 82.3 ! initial coffee temperature (C) LET T_room = 17.0 ! room temperature (C) LET r = 0.2 LET dt = 0.01 LET tmax = 1 LET tshow = 0.1 LET nshow = int(tshow/dt) SUB Euler LET change = -r*(T_coffee - T_room)*dt LET T_coffee = T_coffee + change LET t = t + dt END SUB SUB output IF t = 0 then PRINT PRINT "time","T_coffee","T_coffee - T_room" PRINT END IF PRINT t,T_coffee,T_coffee - T_room END SUB END MODULE

LET direction = int(4*rnd) + 1 SELECT CASE direction CASE 1 LET x = x + 1 CASE 2 LET x = x - 1 CASE 3 LET y = y + 1 CASE 4 LET y = y - 1 CASE else PRINT "error" END SELECT

Matrix arithmetic such as adding matrices and dot products can be done as illustrated in the following program. Add some MAT PRINT statements to check the results.DIM usave(0:21) MAT usave = 1.0

True BASIC also allows arrays to be redimensioned in a way similar to the use of thePROGRAM example_matrix ! illustrate simple matrix arithmetic DIM A(4),B(4),C(4),S(2,2),T(2,2),SI(2,2) MAT A = 1 MAT B = 2*A MAT C = A + B MAT PRINT A,B,C LET dot_product = dot(A,B) ! dot product of A and B MAT C = A*B ! matrix product DATA 1,3,4,8 MAT READ S MAT PRINT C,S MAT T = Trn(S) ! transposed matrix MAT SI = Inv(S) ! inverse matrix MAT PRINT T,SI ! check that matrix of most recently inverted matrix is not too small print det END

John G. Kemeny and Thomas E. Kurtz, *True BASIC Reference Manual,* True BASIC (1990).

Harvey Gould and Jan Tobochnik, *Introduction to Computer Simulation Methods,* second edition, Addison-Wesley (1996).

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abs | ASK MAX COLOR | ASK PIXELS | BOX AREA |

BOX CIRCLE | BOX CLEAR | BOX KEEP | BOX LINES |

BOX SHOW | CALL | channel number | CLEAR |

CLOSE | comments | concatenation | DATA |

DECLARE | PUBLIC | DIM | DRAW |

DO while | DO until | END | ERASE |

FLOOD | FOR loops | FUNCTION | GET KEY |

GET MOUSE | GET POINT | IF | INPUT |

INPUT prompt | int | key input | LET |

LOCAL | library | MAT | mod |

OPEN | OPTION TYPO | PAUSE | PICTURE |

PLOT | PLOT LINES | PLOT POINTS | |

PRINT using | PROGRAM (header) | PUBLIC | RANDOMIZE |

READ | RESET | round | rnd |

SET CURSOR | SET COLOR | SET WINDOW | sgn |

string | SUB | tab | truncate |

WINDOW |