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Python sets are very much like mathematical sets, and support operations like set intersection and union. Python also features a frozenset class for immutable sets, see Collection types. Dictionaries (class dict) are mutable mappings tying keys and corresponding values. Python has special syntax to create dictionaries ({key: value})
Liskov's notion of a behavioural subtype defines a notion of substitutability for objects; that is, if S is a subtype of T, then objects of type T in a program may be replaced with objects of type S without altering any of the desirable properties of that program (e.g. correctness).
In natural language processing, a word embedding is a representation of a word. The embedding is used in text analysis.Typically, the representation is a real-valued vector that encodes the meaning of the word in such a way that the words that are closer in the vector space are expected to be similar in meaning. [1]
Another method of grouping the data is to use some qualitative characteristics instead of numerical intervals. For example, suppose in the above example, there are three types of students: 1) Below normal, if the response time is 5 to 14 seconds, 2) normal if it is between 15 and 24 seconds, and 3) above normal if it is 25 seconds or more, then the grouped data looks like:
In Python, a metaclass is most easily defined as a subclass of type. class AttributeInitType ( type ): def __call__ ( self , * args , ** kwargs ): """Create a new instance.""" # First, create the object in the normal default way. obj = type . __call__ ( self , * args ) # Additionally, set attributes on the new object. for name , value in kwargs ...
the Schreier–Sims algorithm for finding the order of a permutation group; the Todd–Coxeter algorithm and Knuth–Bendix algorithm for coset enumeration; the product-replacement algorithm for finding random elements of a group; Two important computer algebra systems (CAS) used for group theory are GAP and Magma.
A group may have a small base compared to the set it acts on. In the "best case", a base can have size 1, as in the case of the additive group of the integers . On the other hand, the symmetric groups and alternating groups have large bases (the symmetric group S n has base size n − 1), and there are often specialized algorithms that deal ...
The quotient group is the same idea, although one ends up with a group for a final answer instead of a number because groups have more structure than an arbitrary collection of objects: in the quotient / , the group structure is used to form a natural "regrouping".