Section11.0

]>
Book Contents Previous Section 10.10 Automatic Newton Iteration Formulas Next Section 11.1 Names, Abbreviations, and File Structure Book Index

## 11.0 Packages

Packages provide the bulk of package Axiom's algorithmic library, from numeric packages for computing special functions to symbolic facilities for constructor:package differential equations, symbolic integration, and limits. package:constructor

In Chapter ugIntProg , we developed several useful functions for drawing vector fields and complex functions. We now show you how you can add these functions to the Axiom library to make them available for general use.

The way we created the functions in Chapter ugIntProg is typical of how you, as an advanced Axiom user, may interact with Axiom. You have an application. You go to your editor and create an input file defining some functions for the application. Then you run the file and try the functions. Once you get them all to work, you will often want to extend them, add new features, perhaps write additional functions.

Eventually, when you have a useful set of functions for your application, you may want to add them to your local Axiom library. To do this, you embed these function definitions in a package and add that package to the library.

To introduce new packages, categories, and domains into the system, you need to use the Axiom compiler to convert the constructors into executable machine code. An existing compiler in Axiom is available on an ``as-is'' basis. A new, faster compiler will be available in version 2.0 of Axiom.

C ==> Complex DoubleFloat All constructors used in a file
S ==> Segment DoubleFloat must be spelled out in full
INT ==> Integer unless abbreviated by macros
DFLOAT ==> DoubleFloat like these at the top of
VIEW3D ==> ThreeDimensionalViewport a file
CURVE ==> List List Point DFLOAT
)abbrev package DRAWCX DrawComplex Identify kinds and abbreviations
DrawComplex(): Exports == Implementation where Type definition begins here
Exports == with Export part begins
drawComplex: (C -> C,S,S,Boolean) -> VIEW3D Exported Operations
drawComplexVectorField: (C -> C,S,S) -> VIEW3D
setRealSteps: INT -> INT
setImagSteps: INT -> INT
setClipValue: DFLOAT-> DFLOAT
Implementation == add Implementation part begins
arrowScale : DFLOAT := (0.2)::DFLOAT --relative size Local variable 1
arrowAngle : DFLOAT := pi()-pi()/(20::DFLOAT) Local variable 2
realSteps : INT := 11 --# real steps Local variable 3
imagSteps : INT := 11 --# imaginary steps Local variable 4
clipValue : DFLOAT := 10::DFLOAT --maximum vector length
Local variable 5
setRealSteps(n) == realSteps := n Exported function definition 1
setImagSteps(n) == imagSteps := n Exported function definition 2
setClipValue(c) == clipValue := c Exported function definition 3
clipFun: DFLOAT -> DFLOAT --Clip large magnitudes.
clipFun(x) == min(max(x, -clipValue), clipValue)
Local function definition 1
makeArrow: (Point DFLOAT,Point DFLOAT,DFLOAT,DFLOAT) -> CURVE
makeArrow(p1, p2, len, arg) == ... Local function definition 2
drawComplex(f, realRange, imagRange, arrows?) == ...
Exported function definition 4
The DrawComplex package.
Book Contents Previous Section 10.10 Automatic Newton Iteration Formulas Next Section 11.1 Names, Abbreviations, and File Structure Book Index