In CRISP, a class (in the set-theoretical sense) is usually represented by an algorithm which decides membership in that class. Wherever this makes sense, sets (see Set) may also be used as classes.
returns true if C is a class object. The category of class objects is a
subcategory of the category
returns a class C. In the first form, rec must be a record having a
\in and an optional component
name. The values of these
components, if present, are bound to the attributes
Name (see Name) of the class created. The value bound to
\in must be a function
func which returns
true if a GAP object belongs to C, and
otherwise; cf. MemberFunction below. The second form is equivalent to
)). It is the user's responsibility to ensure that func returns the same
result for different GAP objects representing the same mathematical object (or
element, in the GAP sense; see Objects and Elements in the GAP
gap> FermatPrimes := Class(p -> IsPrime(p) and p = 2^LogInt(p, 2) + 1); Class(in:=function( p ) ... end)
If the class does not have a name, this produces a brief description of the information defining class which has been supplied by the user. If the class has a name, only its name will be printed.
gap> View(FermatPrimes); Class(in:=function( p ) ... end)
View, except that the defining
information is being printed in a more explicit way if possible.
gap> Print(FermatPrimes); Class(rec( in = function( p ) return IsPrime( p ) and p = 2 ^ LogInt( p, 2 ) + 1; end))
Display works exactly as
returns true or false, depending upon whether obj belongs to class or
not. If obj can store attributes, the outcome of the membership test is
stored in an attribute
ComputedIsMembers of obj.
Since it is not possible to compare classes given by membership algorithms, two classes are equal in GAP if and only if they are the same GAP object (see IsIdenticalObj in the GAP reference manual).
< for classes has no mathematical meaning; it only exists
so that one can form sorted lists of classes.
This property may be set to
false if the class C is empty
resp. not empty.
This attribute, if bound, stores a function with one argument, obj,
which decides if obj belongs to C or not, and returns
If present, this function is called by the default method for
MemberFunction is part of the definition of C and should not be called
directly by the user.
returns the unary complement of the class C, that is, the class consisting of all objects not in C. C may also be a set.
gap> cmpl := Complement([1,2]); Complement([ 1, 2 ]) gap> Complement(cmpl); [ 1, 2 ]
, ...) F
returns the intersection of the groups in list, resp. of the classes
C1, C2, .... If one of the classes is a list with fewer than
INTERSECTION_LIMIT elements, then the result will be
a sublist of that list. By default,
INTERSECTION_LIMIT is 1000.
gap> Intersection(Class(IsPrimeInt), [1..10]); [ 2, 3, 5, 7 ] gap> Intersection(Class(IsPrimeInt), Class(n -> n = 2^LogInt(n+1, 2) - 1)); Intersection([ Class(in:=function( N ) ... end), Class(in:=function( n ) ... end) ])
returns the union of C and D.
gap> Union(Class(n -> n mod 2 = 0), Class(n -> n mod 3 = 0)); Union([ Class(in:=function( n ) ... end), Class(in:=function( n ) ... end) ])
returns the difference of C and D. If C is a list, then the result will be a sublist of C.
gap> Difference(Class(IsPrimePowerInt), Class(IsPrimeInt)); Intersection([ Class(in:=function( n ) ... end), Complement(Class(in:=function( N ) ... end)) ]) gap> Difference([1..10], Class(IsPrimeInt)); [ 1, 4, 6, 8, 9, 10 ]
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