Calculator Examples
# Mouse position, copy, paste work as expected.
# Some keys to use for typing:
# ctrl-z Undo last change. Repeat to undo previous changes.
# ctrl-k Insert a command line prompt, above.
# ctrl-J Insert a command line prompt, below.
# Backspace Delete character left.
# Delete Delete character right.
# Return Execute current group [blue printout]
# Arrows Move the cursor.
# := Keys : and = assign a variable: x:=1;
# : = Common error. No space allowed.
# ; Key semicolon ends a line.
# : Key colon ends a line no echo (no blue print).
# Let's get started!
# Go ahead and type along in maple with these examples.
2 + 2; 3*5; 6-2:
# All three computations were done, although only two results are shown
# (the colon : at the end of a command suppresses the output). If you
# forget the semicolon, go ahead and put it on the next line:
6-2
;
# Basic Math Operations
Addition +, subtraction -, and division / are standard, and parentheses
# are used as in algebra. However, brackets [, ] and braces {, } are used
# for maple engine list and set delimiters, and not for math. An asterisk * means
# math multiplication and a caret ^ is used for powers. The dot (.) is used for
# decimals, ranges (double dot ..), dot product and matrix multiply. Format
# carefully when using a dot.
(1 + 2) * (6 + 7) - 12 / 7;
3^(2.1);
# Computer Algebra and Decimals
Maple by default computes exact quantities. Decimals will not appear
# in an answer unless they appeared in the problem (e.g., 2.1).
# To give decimals in the answer (floating point), use Maple's evalf:
Pi; # The constant 3.1415727... prints as a Greek letter. Must
# be entered as uppercase P and lowercase i.
pi; # Symbol, not 3.14. Prints as a Greek letter (confusing isn't it?)
evalf(Pi); # Print PI to 10 digits default
exp(1); # the number e=2.818... prints as lowercase italic e
evalf(%); # The % sign stands for the most recently computed quantity.
e; E; # symbol e prints in lowercase italic
evalf(e); # decimal conversion of a symbol does nothing
evalf(Pi, 50); # Compute Pi to 50 digits.
Pi^(1/2); # Print symbolic answer
evalf(%); # Print decimal answer 1.77245385
Upper and Lower Case Madness.
Maple code distinguishes upper-case letters from lower-case. Thus
evalf(pi) is not the same as evalf(Pi).
#Spacing
# For the most part, spacing is unimportant in Maple. In the code lines
# above, spaces could be omitted or added without causing any problems.
# Thoughtful use of spacing makes Maple code easier to read, easier to
# understand, and easier to edit.
# Standard Mathematical Functions
# Maple uses naming conventions of computer languages Fortran and C. To
# find out a name, use maple help (?initialfunctions). A short list:
# sin, cos, tan, csc, sec, cot
# sinh, cosh, tanh, csch, sech, coth
# arcsin, and so on. Use prefix arc on the previous for inverses.
# sqrt, ln, log, log10, exp, round, trunc, ceil, floor, max, min
# Re(z) and Im(z) for real and imaginary parts of a complex number a+b*I
# I is a reserved symbol for the square root of minus one.
# Example.
# Let's compute the absolute value of -14 plus the sine of 1 minus the
# square root of 2 plus the base-e (natural logarithm base) power of
# cos(1.6 Pi) plus the arctangent of 3.
abs(-14) + sin(1) - sqrt(2) + exp( cos(1.6*Pi) ) + arctan(3);
evalf(%);
#Degrees and radians.
tan(45); # Surprised? Trig functions use radians only.
tan(45*Pi/180); # Convert 45 degrees to radians
# Maple expression syntax can often be found by intelligent guessing. Thus
# tan(45) does indeed compute the tangent, and 20! computes a factorial.
# If your first guess doesn't work, then use Maple help or switch to a
# browser search engine, looking for sample code.
#Algebraic Variables
# Maple code uses variables and algebra. Consider, for example,
# the square of the sum (a + b) with variables a,b.
(a + b)^2;
expand (%);
factor (%);
p := (a + b)^2; b := 1; p;j
# Expand gives the expanded form, and factor brings us back
# to our starting point. To make long computations easier and
# more intelligible, we can assign values to variables using ":="
# Other Variables.
# In the previous examples, variables store an expression or a number. Variables
# can also store a list of points, a set, a string, an equation, a piece of text, or a function:
pts := [ [1,2], [3,4] ]; # a double-list or list-of-lists
eqn := 2*x - 3*y = 5; # eqn abbreviates equation 2x+3y=5
eqns := { 2*x - 3*y = 5, 5*x - 3*y = 1 }; # A set of two equations
tag := "The nth partial sum is"; # string delimiter is a double quote
print (pts, eqn, eqns, tag); # check
f := x -> x^2; # Defines a function. Use 2 keys, MINUS and GREATER-THAN
f(2); f(3); # Evaluate function f at x=2 and x=3
g:=unapply(x^2,x); # defines a function, with recursive symbol evaluation
g(Pi); g(exp(1.1)); # Evaluate function g at x=3.14159 and x=exp(1.1)=3.004
# Assignment typos.
# Anything we can define or compute in Maple can be assigned to a variable
# for future reference using ":=". The symbol = by itself is used to test
# equality. A space is NOT allowed between the : and the = in an
# assignment statement. Beware of using equal only when you meant
# colon-equal. Such typos are maddening to discover, because they generate
# no maple error message.
# Getting rid of variable definitions.
b := 'b'; # same as unassign('b'); Removes b:=1; assignment made above to symbol b.
p; # re-execute formula for p, with b:=1 replaced by symbol b
# Similarly, clears the variables assigned above using unassign():
unassign ( 'pts', 'eqn', 'eqns', 'tag');
print (pts, eqn, eqns, tag);
restart; # A drastic way to clear variables and computer memory
# Also got rid of library loads for linalg and LinearAlgebra
#The restart command clears ALL variables and unloads all packages.
#So, if you need a package later, then you must reload it anew.
# Quotes.
# Pay special attention to the kind of quotes used in examples. The
# possibilities are the single quote ', the left quote ` (back-quote),
# and the double quote ".
# Here is an extended example of how to use variables, quote and assignment
# statements:
F := m*a; # Newton's formula for force
m := 2.1; # set the mass
a := 5; # set the acceleration
F; # compute the force
a := 21.9; # reset the acceleration
F; # recompute force
a := 'a'; # clear a with single quotes
s:="a"; # make a one-character string, no substitution of symbol a
s:="m"; # one-character string, no substitution of symbol m (m equals 2.1)
F; # recompute F, symbol a was restored
# Substitutions.
# The subs command lets us make temporary substitutions in an expression
# as opposed to assigning values. For example, try these examples:
g := (a+1)^2 / (b-1)^3 + a / (b-1);
simplify (g);
subs( a=3, b=2, g);
subs( a = x+y, b = x+1, g); # x,y can be symbols or := assigned values or constants
simplify(%); # Do all normal algebraic simplifications to last answer %
a; b; # The variables a and b were not permanently assigned a value.