To suppress the output, enter a colon (:) at the end of the input.

You can also insert input using 1-D Math mode.  The input is entered as a one-dimensional sequence of characters. 1-D Math input is red.

To enter input using 1-D Math:

$\frac{1785623}{120}$

As with 2-D math, in 1-D math, if you use a colon, Maple suppresses the output.

To set the default input mode at a prompt to 1-D Math:

To convert between 2-D Math input and 1-D Math input:

In 1-D and 2-D Math input, you can use a semicolon or colon to separate multiple inputs in the same input line.

$2.097617696$

$0.05847385446$

If you do not specify a semicolon or colon, Maple interprets it as a single input. This can either give unexpected results or an error.  Notice that the following example gives an error in 1-D math but in 2-D math this is interpreted as multiplication.

$0.1226557919$

Maple's commands are contained in the Maple library.  There are two types of commands: top-level commands and package commands.

For a complete list of packages and commands, refer to the index/help help pages. For information on the Maple Help System, see The Maple Help System.

To use a top-level command, enter its name followed by parentheses (( )) containing any parameters. This is referred to as a calling sequence for the command.

Note: In 1-D Math input, include a semicolon or colon at the end of the calling sequence.

For example, to differentiate an expression, use the diff command. The required parameters are the expression to differentiate, which must be specified first, and the independent variable.

$\left(1+{\tan \left(x\right)}^2\right)\sin \left(x\right)+\tan \left(x\right)\cos \left(x\right)$

Mathematical Functions

For a complete list of commands that implement mathematical functions, such as BesselI and AiryAi, available in the library, refer to the initialfunctions help page. >  $\frac{\mathrm{BesselI}\left(0.1\,1\right)}{\mathrm{AiryAi}\left(2.2\right)}$ $47.53037086$ For detailed information on the properties of a function, use the FunctionAdvisor command. >  $\mathrm{FunctionAdvisor}\left(\'\mathrm{definition}\'\,\mathrm{BesselI}\right)$ $\left[I_a\left(z\right)=\frac{z^a{}_{0}F_1\left(;a+1;\frac{z^2}{4}\right)}{\mathrm{\Gamma }\left(a+1\right)2^a}\,\mathrm{with\; no\; restrictions\; on}\left(a\,z\right)\right]$ This definition is displayed using the typeset form of the BesselI function, the hypergeometric function (hypergeom) and the Gamma function (GAMMA).  To see the function names rather than the typeset form, use lprint: >  $\mathrm{lprint}\left(\%\right)$ [BesselI(a, z) = z^a*hypergeom([], [a+1], (1/4)*z^2)/(GAMMA(a+1)*2^a), `with no restrictions on `(a, z)] For detailed information on how to use a function in Maple, refer to its help page. For example: >  $\?\mathrm{Bessel}$ Another way to access help is to select the word for which you want help and use the shortcut key for context help, F2 (Control + Shift + ?, for Mac).

Top Commands

Here are a few of the most frequently used Maple commands. A complete list of top-level commands is available on the index/function help page. Table 3.1: Top Commands Command Name Description plot and plot3d Create a two-dimensional and three-dimensional plot of functions. solve Solve one or more equations or inequalities for their unknowns. fsolve Solve one or more equations using floating-point arithmetic. eval Evaluate an expression at a given point. evalf Numerically evaluate expressions. dsolve Solve ordinary differential equations (ODEs). int Compute an indefinite or definite integral. diff Compute an ordinary or partial derivative, as the context dictates. limit Calculate the limiting value of a function. sum For symbolic summation. It is used to compute a closed form for an indefinite or definite sum. assume/is Set variable properties and relationships between variables. Similar functionality is provided by the assuming command. assuming Compute the value of an expression under assumptions. simplify Apply simplification rules to an expression. factor Factor a polynomial. expand Distribute products over sums. normal Normalize a rational expression. convert Convert an expression to a different type or form. type Type-checking command. In many contexts, it is not necessary to know the exact value of an expression; it suffices to know that an expression belongs to a broad class, or group, of expressions that share some common properties. These classes or groups are known as types. series Generalized series expansion. map Apply a procedure to each operand of an expression.

To use a package command, the calling sequence must include the package name, and the command name enclosed in square brackets ([ ]).

If you are frequently using the commands in a package, load the package.

To load a package:

The with command displays a list of the package commands loaded (unless you suppress the output by entering a colon at the end of the calling sequence).

After loading a package, you can use the short form names of its commands.  That is, you can enter the commands without specifying the package name.

For example, use the NLPSolve command from the Optimization package to find a local minimum of an expression and the value of the independent variable at which the minimum occurs.

$\left[\mathrm{-0.0913252028230577}\,\left[x=10.9041216489198\right]\right]$

$\left[\mathrm{ImportMPS}\,\mathrm{Interactive}\,\mathrm{LPSolve}\,\mathrm{LSSolve}\,\mathrm{Maximize}\,\mathrm{Minimize}\,\mathrm{NLPSolve}\,\mathrm{QPSolve}\right]$

$\left[-0.0913252028230576718\,\left[x\=10.9041216700744900\right]\right]$

For more information on optimization, see Optimization.

To unload a package:

Alternatively, use the restart command.  The restart command clears Maple's internal memory. The effects include unassigning all names and unloading all packages. For more information, refer to the restart help page.

Some packages contain commands that have the same name as a top-level command. For example, the plots package contains a changecoords command. Maple also contains a top-level changecoords command.

After the plots package is loaded, the name changecoords refers to the plots[changecoords] command. To use the top-level changecoords command, unload the package or use the restart command. (For alternative methods of accessing the top-level command, see the rebound help page.)

Top Packages

Here are a few of the most frequently used Maple packages. A complete list of packages is available on the index/package help page. Table 3.2: Top Packages Package Name Description CodeGeneration The Code Generation package is a collection of commands and subpackages that enable the translation of Maple code to other programming languages, such as C, C#, Fortran, MATLAB®, Visual Basic®, JavaTM, Julia, Perl, and Python®. LinearAlgebra The Linear Algebra package contains commands to construct and manipulate Matrices and Vectors, and solve linear algebra problems. LinearAlgebra routines operate on three principal data structures: Matrices, Vectors, and scalars. Optimization The Optimization package is a collection of commands for numerically solving optimization problems, which involve finding the minimum or maximum of an objective function possibly subject to constraints. Physics The Physics package implements computational representations and related operations for most of the objects used in mathematical physics computations. RealDomain The Real Domain package provides an environment in which Maple assumes that the basic underlying number system is the field of real numbers instead of the complex number field. ScientificConstants The Scientific Constants package provides access to the values of various physical constants, for example, the velocity of light and the atomic weight of sodium. This package provides the units for each of the constant values, allowing for greater understanding of an equation. The package also provides units-matching for error checking of the solution. ScientificErrorAnalysis The Scientific Error Analysis package provides representation and construction of numerical quantities that have a central value and an associated uncertainty (or error), which is a measure of the degree of precision to which the quantity's value is known. Various first-order calculations of error analysis can be performed with these quantities. Statistics The Statistics package is a collection of tools for mathematical statistics and data analysis. The package supports a wide range of common statistical tasks such as quantitative and graphical data analysis, simulation, and curve fitting. Student The Student package is a collection of subpackages designed to assist with teaching and learning standard undergraduate mathematics. The many commands display functions, computations, and theorems in various ways, including stepping through important computations.   The Student package contains the following subpackages: •  Basics - fundamental math concepts •  Calculus1 - single-variable calculus •  LinearAlgebra - linear algebra •  MultivariateCalculus - multivariate calculus •  NumericalAnalysis - numerical analysis •  Precalculus - precalculus •  Statistics - statistics •  VectorCalculus - multivariate vector calculus Units The Units package contains commands for unit conversion and provides environments for performing calculations with units. It accepts approximately 300 distinct unit names (for example, meters and grams) and over 550 units with various contexts (for example, standard miles and U.S. survey miles). Maple also contains two Units palettes that allow you to enter the unit for an expression quickly. VectorCalculus The Vector Calculus package is a collection of commands that perform multivariate and vector calculus operations. A large set of predefined orthogonal coordinate systems is available. All computations in the package can be performed in any of these coordinate systems. It contains a facility for adding a custom but orthogonal coordinate system and using that new coordinate system for your computations.

Determine the rational expression (fraction) that approximates the floating-point number $0.3463678+1.7643$.

Notice that an equation label reference has been used. For information on equation labels and equation label references, see Equation Labels.

For more information on the Context Panel, see Computing with the Context Panel in Chapter 2.

To launch an assistant or tutor:

For more information on assistants and tutors, see Assistants in Chapter 1.

You can assign any Maple expression to a name: numeric values, data structures, procedures (a type of Maple program), and other Maple objects.

Initially, the value of a name is itself.

$a$

The assignment operator (:=) associates an expression with a name.

$a≔\mathrm{\pi }$

Recall that you can enter $\pi$ using the following two methods.

When Maple evaluates an expression that contains a name, it replaces the name with its value. For example:

$\mathrm{-1}$

For information on Maple evaluation rules, see Evaluating Expressions.

Mathematical Functions

To define a function, assign it to a name. For example, define a function that computes the cube of its argument. >  $\mathrm{cube}:=x\to x^3\:$ For information on creating functions, see Example 2 - Define a Mathematical Function. >  $\mathrm{cube}\left(3\right)\;\mathrm{cube}\left(1.666\right)$ $27$ $4.624076296$ Note: To insert the right arrow, enter the characters ->. In 2-D Math, Maple replaces -> with the right arrow symbol$\to \.$ In 1-D Math, the characters are not replaced. For example, define a function that squares its argument. >  square := x -> x^2: >  square(32); $1024$ For more information on functions, see Functional Operators.

	Protected Names
	Protected names are valid names that are predefined or reserved. If you attempt to assign to a protected name, Maple returns an error. >  $\sin :=2$ Error, attempting to assign to `sin` which is protected.  Try declaring `local sin`; see ?protect for details. For more information, refer to the type/protected and protect help pages.

To unassign a name, reset the value of a name to itsef.  Right single quotes (unevaluation quotes) prevent Maple from evaluating the name.

You can also use the unassign command.  You must enclose the name in right single quotes (' ').

$a$

For more information on the uses of unevaluation quotes, see Delaying Evaluation or refer to the uneval help page.

Unassigning all names:

The restart command clears Maple's internal memory. The effects include unassigning all names. For more information, refer to the restart help page.

A Maple name must be one of the following.

Important: Do not begin a name with an underscore character. Maple reserves names that begin with an underscore for use by the Maple library.

Examples of valid names:

Instead of re-entering previous results in computations, you can use equation label references. Each time you need to refer to a previous result, insert an equation label reference.

You can insert equation labels by:

Insert an equation label reference using the double-click method:

Insert an equation label reference using the Insert menu:

Maple inserts the reference.

To integrate the product of (3.4) and (3.5):

An equation label is associated with the last output within an execution group.

You can number equation labels in two ways:

To change the equation label numbering scheme:

Although equation labels are not descriptive names, labels offer other important features.

For information on assigning to, using, and unassigning names, see Names.

For more information on equation labels, refer to the equationlabels help page.

The following chapters describe how to use Maple to perform tasks such as solving equations, producing plots and animations, and creating mathematical documents. The chapters were created using Worksheet mode. Except where noted, all features are available in both Worksheet mode and Document mode.