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Unformatted text preview: n. You may choose to access these pages during a Maple session. To use the help command, at the Maple prompt enter a question mark (?) followed by the name of the command or topic for which you want more information. ?command 2.1 Introduction This section introduces the following concepts in Maple. • Semicolon (;) usage 5 6• Chapter 2: Mathematics with Maple: The Basics • Representing exact expressions The most basic computations in Maple are numeric. Maple can function as a conventional calculator with integers or ﬂoating-point numbers. Enter the expression using natural syntax. A semicolon (;) marks the end of each calculation. Press enter to perform the calculation.
> 1 + 2; 3
> 1 + 3/2; 5 2
> 2*(3+1/3)/(5/3-4/5); 100 13
> 2.8754/2; 1.437700000 Exact Expressions
Maple computes exact calculations with rational numbers. Consider a simple example.
> 1 + 1/2; 3 2 The result of 1 + 1/2 is 3/2 not 1.5. To Maple, the rational number 3/2 and the ﬂoating-point approximation 1.5 are distinct objects. The ability to represent exact expressions allows Maple to preserve more information about their origins and structure. Note that the advantage is greater with more complex expressions. The origin and structure of a number such as 0.5235987758 2.2 Numerical Computations •7 are much less clear than for an exact quantity such as 1 π 6 Maple can work with rational numbers and arbitrary expressions. It can manipulate integers, ﬂoating-point numbers, variables, sets, sequences, polynomials over a ring, and many more mathematical constructs. In addition, Maple is also a complete programming language that contains procedures, tables, and other programming constructs. 2.2 Numerical Computations This section introduces the following concepts in Maple. • Integer computations • Continuation character (\) • Ditto operator (%) • Commands for working with integers • Exact and ﬂoating-point representations of values • Symbolic representation • Standard mathematical constants • Case sensitivity • Floating-point approximations • Special numbers • Mathematical functions Integer Computations
Integer calculations are straightforward. Terminate each command with a semicolon.
> 1 + 2; 8• Chapter 2: Mathematics with Maple: The Basics 3
> 75 - 3; 72
> 5*3; 15
> 120/2; 60 Maple can also work with arbitrarily large integers. The practical limit on integers is approximately 228 digits, depending mainly on the speed and resources of your computer. Maple can calculate large integers, count the number of digits in a number, and factor integers. For numbers, or other types of continuous output that span more than one line on the screen, Maple uses the continuation character (\) to indicate that the output is continuous. That is, the backslash and following line ending should be ignored.
> 100!; 933262154439441526816992388562667004907\ 15968264381621468592963895217599993229\ 91560894146397615651828625369792082722\ 37582511852109168640000000000000000000\ 00000
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