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The input to eval is not necessarily a string; it may be structured representation of code, such as an abstract syntax tree (like Lisp forms), or of special type such as code (as in Python). The analog for a statement is exec , which executes a string (or code in other format) as if it were a statement; in some languages, such as Python, both ...
The converse, though, does not necessarily hold: for example, taking f as =, where V is a Vitali set, it is clear that f is not measurable, but its absolute value is, being a constant function. The positive part and negative part of a function are used to define the Lebesgue integral for a real-valued function.
This phenomenon is very frequent, occurring for n th roots, logarithms, and inverse trigonometric functions. To define a single-valued function from a complex multivalued function, one may distinguish one of the multiple values as the principal value, producing a single-valued function on the whole plane which is discontinuous along certain ...
Thus, both the value and the fact that the value was positive are maintained. If ten bits are used to represent the value "11 1111 0001" (decimal negative 15) using two's complement, and this is sign extended to 16 bits, the new representation is "1111 1111 1111 0001". Thus, by padding the left side with ones, the negative sign and the value 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:
In convex analysis, a branch of mathematics, the effective domain extends of the domain of a function defined for functions that take values in the extended real number line [,] = {}. In convex analysis and variational analysis , a point at which some given extended real -valued function is minimized is typically sought, where such a point is ...
In mathematical optimization, the Rosenbrock function is a non-convex function, introduced by Howard H. Rosenbrock in 1960, which is used as a performance test problem for optimization algorithms. [1] It is also known as Rosenbrock's valley or Rosenbrock's banana function. The global minimum is inside a long, narrow, parabolic-shaped flat ...
To apply such a function object, one must use the funcall function: (funcall #'foo bar baz). Python Explicit partial application with functools.partial since version 2.5, and operator.methodcaller since version 2.6. Ruby The identifier of a regular "function" in Ruby (which is really a method) cannot be used as a value or passed.