2.11 Exposing Domains and Packages

In this section we discuss how FriCAS makes some operations available to you while hiding others that are meant to be used by developers or only in rare cases. If you are a new user of FriCAS, it is likely that everything you need is available by default and you may want to skip over this section on first reading.

Every constructor:exposed domain and package in the FriCAS library either exposed (meaning that you can use its operations without doing anything special) or it is hidden (meaning you have to either package call (see ugTypesPkgCall) the operations it contains or explicitly expose it to use the operations). The initial exposure status for a constructor is set in the file exposed.lsp (see the Installer’s Note exposed.lsp for FriCAS if you need to know the location of this file). Constructors are collected together in groups. Categories are all in the exposure group categories and the bulk of the basic set of packages and domains that are exposed are in the exposure group basic. Here is an abbreviated sample of the file (without the Lisp parentheses):


        AlgebraicNumber                          AN
        AlgebraGivenByStructuralConstants        ALGSC
        Any                                      ANY
        AnyFunctions1                            ANY1
        BinaryExpansion                          BINARY
        Boolean                                  BOOLEAN
        CardinalNumber                           CARD
        CartesianTensor                          CARTEN
        Character                                CHAR
        CharacterClass                           CCLASS
        CliffordAlgebra                          CLIF
        Color                                    COLOR
        Complex                                  COMPLEX
        ContinuedFraction                        CONTFRAC
        DecimalExpansion                         DECIMAL

        AbelianGroup                             ABELGRP
        AbelianMonoid                            ABELMON
        AbelianMonoidRing                        AMR
        AbelianSemiGroup                         ABELSG
        Aggregate                                AGG
        Algebra                                  ALGEBRA
        AlgebraicallyClosedField                 ACF
        AlgebraicallyClosedFunctionSpace         ACFS
        ArcHyperbolicFunctionCategory            AHYP

For each constructor in a group, the full name and the abbreviation is given. There are other groups in exposed.lsp but initially only the constructors in exposure groups basic categories naglink and anna are exposed.

As an interactive user of FriCAS, you do not need to modify this file. Instead, use )set expose to expose, hide or query the exposure status of an individual constructor or exposure group. set expose The reason for having exposure groups is to be able to expose or hide multiple constructors with a single command. For example, you might group together into exposure group quantum a number of domains and packages useful for quantum mechanical computations. These probably should not be available to every user, but you want an easy way to make the whole collection visible to FriCAS when it is looking for operations to apply.

If you wanted to hide all the basic constructors available by default, you would issue )set expose drop group basic. set expose drop group We do not recommend that you do this. If, however, you discover that you have hidden all the basic constructors, you should issue )set expose add group basic to restore your default environment. set expose add group

It is more likely that you would want to expose or hide individual constructors. In ugUserTriangle we use several operations from OutputForm, a domain usually hidden. To avoid package calling every operation from OutputForm, we expose the domain and let FriCAS conclude that those operations should be used. Use )set expose add constructor and )set expose drop constructor to expose and hide a constructor, respectively. set expose drop constructor You should use the constructor name, not the abbreviation. The )set expose command guides you through these options. set expose add constructor

If you expose a previously hidden constructor, FriCAS exhibits new behavior (that was your intention) though you might not expect the results that you get. OutputForm is, in fact, one of the worst offenders in this regard. OutputForm This domain is meant to be used by other domains for creating a structure that FriCAS knows how to display. It has functions like + that form output representations rather than do mathematical calculations. Because of the order in which FriCAS looks at constructors when it is deciding what operation to apply, OutputForm might be used instead of what you expect.

This is a polynomial.

x + x
\[2 \ x\]

Type: Polynomial Integer

Expose OutputForm.

)set expose add constructor OutputForm
OutputForm is now explicitly exposed in frame G82322

This is what we get when OutputForm is automatically available.

x + x
\[x + x\]

Type: OutputForm

Hide OutputForm so we don’t run into problems with any later examples!

)set expose drop constructor OutputForm
OutputForm is now explicitly hidden in frame G82322

Finally, exposure is done on a frame-by-frame basis. A frame (see ugSysCmdframe ) is one of possibly several logical FriCAS workspaces within a physical one, each having its own environment (for example, variables and function definitions). If you have several FriCAS workspace windows on your screen, they are all different frames, automatically created for you by HyperDoc. Frames can be manually created, made active and destroyed by the )frame system command. frame They do not share exposure information, so you need to use )set expose in each one to add or drop constructors from view.