2.12 Commands for Snooping

To conclude this chapter, we introduce you to some system commands that you can use for getting more information about domains, packages, categories, and operations. The most powerful FriCAS facility for getting information about constructors and operations is the Browse component of HyperDoc. This is discussed in Chapter ugBrowse .

Use the )what system command to see lists of system objects whose name contain a particular substring (uppercase or lowercase is not significant). what

Issue this to see a list of all operations with complex in their names. what operation

)what operation complex

Operations whose names satisfy the above pattern(s):
complex                   complex?
complexEigenvalues        complexEigenvectors
complexElementary         complexExpand
complexForm               complexIntegrate
complexLimit              complexNormalize
complexNumeric            complexNumericIfCan
complexRoots              complexSolve
complexZeros              createLowComplexityNormalBasis
createLowComplexityTable  doubleComplex?
drawComplex               drawComplexVectorField
fortranComplex            fortranDoubleComplex
pmComplexintegrate

To get more information about an operation such as
complexZeros, issue the command )display op complexZeros

If you want to see all domains with matrix in their names, issue this. what domain

)what domain matrix

----------------------- Domains -----------------------
Domains with names matching patterns:
     matrix
 DHMATRIX DenavitHartenbergMatrix
 DPMM     DirectProductMatrixModule
 IMATRIX  IndexedMatrix
 LSQM     LieSquareMatrix
 M3D      ThreeDimensionalMatrix
 MATCAT-  MatrixCategory&
 MATRIX   Matrix
 RMATCAT- RectangularMatrixCategory&
 RMATRIX  RectangularMatrix
 SMATCAT- SquareMatrixCategory&
 SQMATRIX SquareMatrix

Similarly, if you wish to see all packages whose names contain gauss, enter this. what packages

)what package gauss

---------------------- Packages -----------------------
Packages with names matching patterns:
     gauss
 GAUSSFAC GaussianFactorizationPackage

This command shows all the operations that Any provides. Wherever $ appears, it means Any. show

)show Any

 Any  is a domain constructor
 Abbreviation for Any is ANY
 This constructor is exposed in this frame.
 Issue )edit /usr/local/axiom/mnt/algebra/any.spad
  to see algebra source code for ANY
--------------------- Operations ----------------------
 ?=? : (%,%) -> Boolean
 any : (SExpression,None) -> %
 coerce : % -> OutputForm
 dom : % -> SExpression
 domainOf : % -> OutputForm
 hash : % -> SingleInteger
 latex : % -> String
 obj : % -> None
 objectOf : % -> OutputForm
 ?~=? : (%,%) -> Boolean
 showTypeInOutput : Boolean -> String

This displays all operations with the name complex. display operation

)display operation complex

There is one exposed function called complex :
 [1] (D1,D1) -> D from D if D has COMPCAT D1 and D1 has COMRING

Let’s analyze this output.

First we find out what some of the abbreviations mean.

)abbreviation query COMPCAT

COMPCAT abbreviates category ComplexCategory

)abbreviation query COMRING

COMRING abbreviates category CommutativeRing

So if D1 is a commutative ring (such as the integers or floats) and D belongs to ComplexCategory D1, then there is an operation called complex that takes two elements of D1 and creates an element of D. The primary example of a constructor implementing domains belonging to ComplexCategory is Complex. See Complex for more information on that and see ugUserDeclare for more information on function types.