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In mathematics, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor(x). Similarly, the ceiling function maps x to the least integer greater than or equal to x , denoted ⌈ x ⌉ or ceil( x ) .
Displays the parameter wrapped in ceiling symbols. This template is for display, not calculation. Template parameters [Edit template data] This template prefers inline formatting of parameters. Parameter Description Type Status Operand 1 The operand of the ceiling function Example π Line required Examples {{ceil|45.23}} → ⌈45.23⌉ {{ceil|''x''}} → ⌈ x ⌉ {{ceil|{{sfrac|2''a''|''b ...
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]
For example, the following algorithm is a direct implementation to compute the function A(x) = (x−1) / (exp(x−1) − 1) which is well-conditioned at 1.0, [nb 12] however it can be shown to be numerically unstable and lose up to half the significant digits carried by the arithmetic when computed near 1.0.
Folds can be regarded as consistently replacing the structural components of a data structure with functions and values. Lists, for example, are built up in many functional languages from two primitives: any list is either an empty list, commonly called nil ([]), or is constructed by prefixing an element in front of another list, creating what is called a cons node ( Cons(X1,Cons(X2,Cons ...
In Python, functions are first-class objects that can be created and passed around dynamically. Python's limited support for anonymous functions is the lambda construct. An example is the anonymous function which squares its input, called with the argument of 5:
FatRat [5] data type implements arbitrary-precision rational numbers. Python: The standard library includes a Fraction class in the module fractions. [6] Ruby: native support using special syntax. Smalltalk represents rational numbers using a Fraction class in the form p/q where p and q are arbitrary size integers.
print length([2+1, 3*2, 1/0, 5-4]) fails under strict evaluation because of the division by zero in the third element of the list. Under lazy evaluation, the length function returns the value 4 (i.e., the number of items in the list), since evaluating it does not attempt to evaluate the terms making up the list.