11.0 Packages

Packages provide the bulk of package FriCAS’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 FriCAS 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 FriCAS user, may interact with FriCAS. 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 FriCAS 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 FriCAS compiler to convert the constructors into executable machine code. An existing compiler in FriCAS is available on an as-is basis. A new, faster compiler will be available in version 2.0 of FriCAS.

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.