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Doctest makes innovative [1] use of the following Python capabilities: [2] docstrings; The Python interactive shell (both command line and the included idle application) Python introspection; When using the Python shell, the primary prompt: >>>, is followed by new commands.
Kummer's theorem states that the number of carries involved in adding two numbers in base is equal to the exponent of the highest power of dividing a certain binomial coefficient. When several random numbers of many digits are added, the statistics of the carry digits bears an unexpected connection with Eulerian numbers and the statistics of ...
Introduced in Python 2.2 as an optional feature and finalized in version 2.3, generators are Python's mechanism for lazy evaluation of a function that would otherwise return a space-prohibitive or computationally intensive list. This is an example to lazily generate the prime numbers:
[52] [53] While Python 2.7 and older versions are officially unsupported, a different unofficial Python implementation, PyPy, continues to support Python 2, i.e. "2.7.18+" (plus 3.10), with the plus meaning (at least some) "backported security updates". [54] Python 3.0 was released on 3 December 2008, with some new semantics and changed syntax.
This creational pattern [1] is frequently used for numbers and strings in different programming languages. In many object-oriented languages such as Python, even primitive types such as integer numbers are objects. To avoid the overhead of constructing a large number of integer objects, these objects get reused through interning. [2]
Here, the list [0..] represents , x^2>3 represents the predicate, and 2*x represents the output expression.. List comprehensions give results in a defined order (unlike the members of sets); and list comprehensions may generate the members of a list in order, rather than produce the entirety of the list thus allowing, for example, the previous Haskell definition of the members of an infinite list.
This is an accepted version of this page This is the latest accepted revision, reviewed on 6 February 2025. Language for communicating instructions to a machine The source code for a computer program in C. The gray lines are comments that explain the program to humans. When compiled and run, it will give the output "Hello, world!". A programming language is a system of notation for writing ...
SymPy is an open-source Python library for symbolic computation.It provides computer algebra capabilities either as a standalone application, as a library to other applications, or live on the web as SymPy Live [2] or SymPy Gamma. [3]