Section2.12

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## 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 Axiom 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.

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