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Occasionally, when you make an error, Mathematica will beep or the cell will change color. If you are not sure what you did to cause this, you can get a clue by going to Help Why The Beep or Help Why The Coloring
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EXAMPLE 20
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Suppose you know that the command Plot graphs a function, but you cannot remember its
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syntax. Plot
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Plot[ f, {x, xmin, xmax}] generates a plot of f as a function of x from xmin to xmax. Plot[{ f1, f2,...}, {x, xmin, xmax}] plots several functions fi.
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If information is needed about attributes or optional settings (and their defaults), can be used. Plot
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Plot[ f, {x, xmin, xmax}] generates a plot of f as a function of x from xmin to xmax. Plot[{ f1, f2,...}, {x, xmin, xmax}] plots several functions fi.
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Attributes[Plot]={HoldAll,Protected} Options[Plot]={AlignmentPoint Center, AspectRatio 1 , GoldenRatio Axes True, AxesLabel None,AxesOrigin Automatic,AxesStyle {}, Background None,BaselinePosition Automatic, BaseStyle {}, ClippingStyle None, ColorFunction Automatic, ColorFunctionScaling True, ColorOutput Automatic, ContentSelectable Automatic, DisplayFunction $DisplayFunction, Epilog {}, Evaluated System`Private`$Evaluated, EvaluationMonitor None, Exclusions Automatic, ExclusionsStyle None, Filling None, FillingStyle Automatic, FormatType TraditionalForm, Frame False, FrameLabel None, FrameStyle {},FrameTicks Automatic, FrameTicksStyle {}, GridLines None, GridLinesStyle {}, Imagemargins 0., ImagePadding All, ImageSize Automatic, LabelStyle {}, MaxRecursion Automatic, Mesh None, MeshFunctions {#1 &}, MeshShading None, MeshStyle Automatic, Method Automatic, PerformanceGoal $PerformanceGoal, PlotLabel None, PlotPoints Automatic,PlotRange {Full, Automatic}, PlotRangeClipping True, PlotRangePadding Automatic, PlotRegion Automatic, PlotStyle Automatic, PreserveImageOptions Automatic, Prolog {}, RegionFunction (True &), RotateLabel True, Ticks Automatic, TicksStyle {}, WorkingPrecision MachinePrecision}
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Options can also be obtained using the Options command. This is useful if you want to specify an option but cannot remember its name.
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EXAMPLE 21
Options[Solve] {InverseFunctions Automatic, MakeRules False, Method 3, Mode Generic, Sort True, VerifySolutions Automatic, WorkingPrecision }
Very often you may remember part of a symbol name, but not the whole name. If you know the beginning is Arc, for example, type in the part you know and then press [CTRL] + [K]. This will generate a menu of all commands and functions beginning with Arc. Then click on the one you want. If you are using a Macintosh computer, use [COMMAND] + [K]. (The [COMMAND] key is the key with the apple on it.)
Getting Acquainted
EXAMPLE 22 Type Arc and then press [CTRL] + [K] or [COMMAND] + [K] .
Another way of determining symbol names is to use together with wildcards. The character * acts as a wildcard and takes the place of any sequence of characters. Wildcards can be used anywhere, at the beginning, middle, or end of a symbol.
EXAMPLE 23 Output may vary depending upon your version of Mathematica
(a) Find all commands beginning with Inv. Inv*
Getting Acquainted
(b) Find all commands ending with in. *in
(c) Find all commands with our in the middle. *our*
Wildcards can also be used to determine which symbols have been used thus far by the kernel. Typing ` * returns a list of all symbols that have been defined during your Mathematica session. The character ` (backquote) stands for global you want a list of all global symbols. (See the appendix for a discussion of global symbols.)
EXAMPLE 24 Note: The results of this example may be slightly different on your computer, depending upon the
symbols you have defined. a = 3; b2xy = 4; xyz7 = 5; ` *
Global`
a b2xy xyz7
Clear["` * "] will clear all global symbols. Remove["`*"] will remove all global symbols.
EXAMPLE 25
Remove["`*"] ` *
Check to see if any symbols remain.
Remove rmnsm : There are no symbols matching "`*" .
Getting Acquainted
SOLVED PROBLEMS
1.28 Obtain basic information about the Mathematica command Simplify.
SOLUTION
Simplify
Simplify[expr] performs a sequence of algebraic and other transformations on expr, and returns the simplest form it finds. Simplify[expr, assum] does simplification using assumptions.
1.29 Obtain extended information about the Mathematica command Simplify including default settings for options.
SOLUTION
Simplify
Simplify[expr] performs a sequence of algebraic and other transformations on expr, and returns the simplest form it finds. Simplify[expr, assum] does simplification using assumptions.
Attributes[Simplify]={Protected} Options[Simplify]={Assumptions $Assumptions, ComplexityFunction Automatic,ExcludedForms {},TimeConstraint 300, TransformationFunctions Automatic,Trig True}
1.30 Obtain help on the Mathematica command Factor and then factor x3 6 x2 + 11 x 6.
SOLUTION
Factor
Factor[ poly] factors a polynomial over the integers.
Factor[ poly, Modulus p] factors a polynomial modulo a prime p.
Factor[ poly, Extension {a1, a2,...}] factors a polynomial allowing coefficients that are rational combinations of the algebraic numbers ai.
Factor[x3 6 x2 + 11 x 6] ( 3 + x)( 2 + x)( 1 + x)
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