Advanced Programming Guide

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Type Specification or TestA.2 Internal Representations of Data Types • 347DCOLON ∧ expr ∧ type − exprMaple syntax: expr :: typeExprLength: 3This structure has three interpretations depending on the context inwhich it is used. When it appears in the header of a procedure definition,it is a typed parameter declaration. When it appears in the local sectionof a procedure or on the left side of an assignment, it is a type assertion.When it appears elsewhere (specifically in a conditional expression), it isa type test.DebugMaple syntax: noneLength: 2 or moreDEBUG ∧ expr ∧ expr . . .This is another internal-only structure. It is used by the kernel whenprinting error traceback information to transmit that information up thecall stack.Equation or Test for EqualityMaple syntax: expr = exprLength: 3EQUATION ∧ expr ∧ exprThis structure has two interpretations depending on the context inwhich it is used. It can be either a test for equality, or a statement ofequality (not to be confused with an assignment).Error StatementERROR∧ exprMaple syntax: error "msg", arg, . . . argLength: 2
348 • Appendix A: Internal Representation and ManipulationThis represents the Maple error statement. The expr is either a singleexpression (if only a message was specified in the error statement), or anexpression sequence (if arguments were also specified). The actual internaltag used for the ERROR structure is MERROR, to prevent collision with amacro defined by some C compilers.Expression SequenceMaple syntax: expr, expr, . . .Length: 1 or moreEXPSEQ ∧ expr ∧ expr . . .Expression sequences are available to the user as a data structure, andare also used to pass arguments to procedures. Effectively, procedures takea single argument that is an expression sequence. An expression sequencemay be of length 1 (that is, an empty sequence), which is representedby the Maple symbol NULL, or in some contexts (such as parameters to afunction call) as nothing at all.Floating-Point NumberFLOAT ∧ integer1 ∧ integer2 ∧ attrib − exprMaple syntax: 1.2, 1.2e3, Float(12,34), Float(infinity)Length: 2 (or 3 with attributes)A floating-point number is interpreted as integer1 ∗ 10 integer2 . Afloating-point number may optionally have attributes, in which case thelength of the structure is 3, and the third word points to a Maple expression.This suggests that several floating-point numbers with the samevalue but different attributes can exist simultaneously.The integer2 field can optionally be one of the names undefinedor infinity, in which case the FLOAT structure represents an undefinedfloating-point value (not-a-number, or NaN, in IEEE terminology), or afloating-point infinity. When integer2 is undefined, integer1 can takeon different small integer values, allowing the existence of different NaNs.When integer2 is infinity, integer1 must be 1 or −1.For/While Loop StatementFOR ∧ name ∧ from− ∧ by− ∧ to− ∧ cond− ∧ stat−expr expr expr expr seq
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ii•Waterloo Maple Inc.57 Erb Stre
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Contents • v3.6 Interfaces and Im
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Contents • viiPlotting Gears . .
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Contents • ixForeign Data . . . .
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1 Introduction1.1 Purpose of This B
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2 Procedures, Variables,and Extendi
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2.1 Nested Procedures • 5procedur
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2.1 Nested Procedures • 7> A[j] :
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2.1 Nested Procedures • 9> quicks
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2.1 Nested Procedures • 11> U :=
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2.2 Procedures That Return Procedur
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2.2 Procedures That Return Procedur
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2.3 Local Variables and Invoking Pr
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assign(another_a = a);> eqn;2.3 Loc
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[ seq( s[j][c[j]], j=1..2 ) ];2.3 L
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2.3 Local Variables and Invoking Pr
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2.4 Interactive Input • 25Improve
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2.4 Interactive Input • 27> reads
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2.5 Extending Maple • 29The parse
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2.5 Extending Maple • 31> ‘type
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2.5 Extending Maple • 33The follo
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2.5 Extending Maple • 3556 IIn th
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2.5 Extending Maple • 37Extending
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2.5 Extending Maple • 39The useri
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3 Programming withModulesProcedures
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• 43> gentemp := proc()> count :=
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3.1 Syntax and Semantics3.1 Syntax
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3.1 Syntax and Semantics • 47name
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3.1 Syntax and Semantics • 49> He
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3.1 Syntax and Semantics • 51mode
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3.1 Syntax and Semantics • 53The
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3.1 Syntax and Semantics • 55true
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3.1 Syntax and Semantics • 57modu
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3.1 Syntax and Semantics • 59> m
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This is achieved by the double assi
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3.1 Syntax and Semantics • 63This
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3.1 Syntax and Semantics • 65With
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3.1 Syntax and Semantics • 67> wh
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SpecFuncs := module()> export F; #
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3.2 Records • 71b> evalb( % = b )
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3.3 Packages • 73Packages in the
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3.3 Packages • 751 −1 + 1 21k x
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3.3 Packages • 77> "new types ‘
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3.3 Packages • 79definition. This
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3.3 Packages • 81true> member( 10
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3.3 Packages • 83The display show
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3.3 Packages • 85> end module:How
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3.3 Packages • 87From the output
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3.3 Packages • 89The final output
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3.3 Packages • 91shape-specific f
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3.3 Packages • 93The area Procedu
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"but got %1", shape> end if;>> # Ex
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3.4 The use Statement • 97> circl
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3.4 The use Statement • 99use sta
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3.4 The use Statement • 101C++),
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3.5 Modeling Objects3.5 Modeling Ob
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3.5 Modeling Objects • 10514 πFo
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3.5 Modeling Objects • 107> nitem
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3.5 Modeling Objects • 109> for i
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3.5 Modeling Objects • 111> lengt
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3.6 Interfaces and Implementations
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(−2790 T 6 − 77814+ 1943715124T
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4 Input and OutputAlthough Maple is
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4.1 A Tutorial Example • 157Openi
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4.1 A Tutorial Example • 159xy :=
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Buffered Files:4.2 File Types and M
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4.3 File Descriptors versus File Na
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f := fopen("testFile.txt",WRITE):>
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4.5 Input Commands • 167iostatus(
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4.5 Input Commands • 169otherwise
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4.5 Input Commands • 171y The nex
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4.5 Input Commands • 173various c
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4.5 Input Commands • 175Example T
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4.6 Output Commands • 177One-Dime
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4.6 Output Commands • 179the appr
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4.6 Output Commands • 181Writing
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4.6 Output Commands • 183z format
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4.6 Output Commands • 185• If n
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4.6 Output Commands • 187> writed
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4.7 Conversion Commands • 189Conv
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4.8 Notes to C Programmers • 191(
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5 Numerical Programmingin MapleFloa
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5.1 The Basics of evalf • 1953.14
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5.2 Hardware Floating-Point Numbers
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iterate(f, df, x0, N);> end proc:Us
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5.3 Floating-Point Models in Maple
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5.3 Floating-Point Models in Maple
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5.4 Extending the evalf Command •
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5.4 Extending the evalf Command •
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5.5 Using the Matlab Package • 21
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6 Programming with MapleGraphicsMap
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6.1 Basic Plot Functions • 217If
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6.2 Programming with Plotting Libra
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6.3 Maple Plotting Data Structures
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PLOT( CURVES( points ) );6.3 Maple
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6.4 Programming with Plot Data Stru
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6.5 Programming with the plottools
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6.6 Vector Field Plots • 257Examp
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6.6 Vector Field Plots • 259> end
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6.6 Vector Field Plots • 261input
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6.6 Vector Field Plots • 263> mak
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6.6 Vector Field Plots • 265> vec
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6.7 Generating Grids of Points •
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A := array(1..2, 1..2):> evalgrid(
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6.8 Animation • 271The gridpoints
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6.8 Animation • 2731.00.500. 0. 2
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6.8 Animation • 275> partsum := p
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6.8 Animation • 277Demonstrating
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plot3d( p, -3..3, -3..3, color=q );
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6.9 Programming with Color • 2811
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6.9 Programming with Color • 283>
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6.9 Programming with Color • 2851
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chessplot3d( sin(x)*sin(y), x=-Pi..
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7 Advanced ConnectivityIn This Chap
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7.1 Code Generation • 291Many opt
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7.2 Using Compiled Code in Maple
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7.2 Using Compiled Code in Maple
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Page 384 and 385: Index%, 174&, 31accuracy, 193, 195,
Page 386 and 387: Index • 375SAVE, 362SERIES, 363SE
Page 388 and 389: Index • 377defining numeric, 210n
Page 390 and 391: Index • 379name, 357name table, 3
Page 392 and 393: Index • 381statements, 174strings
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