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Racket: the built-in exact numbers are of arbitrary precision. Example: (expt 10 100) produces the expected (large) result. Exact numbers also include rationals, so (/ 3 4) produces 3/4. Arbitrary precision floating point numbers are included in the standard library math/bigfloat module.
The JScience library has a Complex number class. The JAS library allows the use of complex numbers. Netlib has a complex number class for Java. javafastcomplex also adds complex number support for Java. jcomplexnumber is a project on implementation of complex number in Java. JLinAlg includes complex numbers with arbitrary precision.
However, since division almost immediately introduces infinitely repeating sequences of digits (such as 4/7 in decimal, or 1/10 in binary), should this possibility arise then either the representation would be truncated at some satisfactory size or else rational numbers would be used: a large integer for the numerator and for the denominator.
Note that C99 and C++ do not implement complex numbers in a code-compatible way – the latter instead provides the class std:: complex. All operations on complex numbers are defined in the <complex.h> header. As with the real-valued functions, an f or l suffix denotes the float complex or long double complex variant of the function.
(A variant of this can also be used to multiply complex numbers quickly.) Done recursively, this has a time complexity of (). Splitting numbers into more than two parts results in Toom-Cook multiplication; for example, using three parts results in the Toom-3 algorithm. Using many parts can set the exponent arbitrarily close to 1, but the ...
Hermes Project: C++/Python library for rapid prototyping of space- and space-time adaptive hp-FEM solvers. IML++ is a C++ library for solving linear systems of equations, capable of dealing with dense, sparse, and distributed matrices. IT++ is a C++ library for linear algebra (matrices and vectors), signal processing and communications ...
Transcendental number: Any real or complex number that is not algebraic. Examples include e and π. Trigonometric number: Any number that is the sine or cosine of a rational multiple of π. Quadratic surd: A root of a quadratic equation with rational coefficients. Such a number is algebraic and can be expressed as the sum of a rational number ...
A real number is computable if its digit sequence can be produced by some algorithm or Turing machine. The algorithm takes an integer as input and produces the -th digit of the real number's decimal expansion as output. (The decimal expansion of a only refers to the digits following the decimal point.)