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The actual values are only computed when needed. For example, one could create a function that creates an infinite list (often called a stream) of Fibonacci numbers. The calculation of the n-th Fibonacci number would be merely the extraction of that element from the infinite list, forcing the evaluation of only the first n members of the list.
Let C be a category with finite products and a terminal object 1. A list object over an object A of C is: an object L A, a morphism o A : 1 → L A, and; a morphism s A : A × L A → L A; such that for any object B of C with maps b : 1 → B and t : A × B → B, there exists a unique f : L A → B such that the following diagram commutes:
A number that has the same number of digits as the number of digits in its prime factorization, including exponents but excluding exponents equal to 1. A046758 Extravagant numbers
Python supports most object oriented programming (OOP) techniques. It allows polymorphism, not only within a class hierarchy but also by duck typing. Any object can be used for any type, and it will work so long as it has the proper methods and attributes. And everything in Python is an object, including classes, functions, numbers and modules.
two different references to the same object, e.g., two nicknames for the same person; In many modern programming languages, objects and data structures are accessed through references. In such languages, there becomes a need to test for two different types of equality: Location equality (identity): if two references (A and B) reference the same ...
A matrix with all entries equal to one. a ij = 1. Pascal matrix: A matrix containing the entries of Pascal's triangle. Pauli matrices: A set of three 2 × 2 complex Hermitian and unitary matrices. When combined with the I 2 identity matrix, they form an orthogonal basis for the 2 × 2 complex Hermitian matrices. Redheffer matrix
The data from these papers is summarized in the following table, where the dispatch ratio DR is the average number of methods per generic function; the choice ratio CR is the mean of the square of the number of methods (to better measure the frequency of functions with a large number of methods); [2] [3] and the degree of specialization DoS is ...
This order theoretic duality is in turn a special case of the construction of opposite categories as every ordered set can be understood as a category. Given a semigroup (S, ·), one usually defines the opposite semigroup as (S, ·) op = (S, *) where x*y ≔ y·x for all x,y in S. So also for semigroups there is a strong duality principle.