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; # 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.