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74 lines
3 KiB
TeX
74 lines
3 KiB
TeX
\section{Built-in Module \sectcode{mpz}}
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\bimodindex{mpz}
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This module implements the interface to part of the GNU MP library.
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This library contains arbitrary precision integer and rational number
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arithmetic routines. Only the interfaces to the \emph{integer}
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(\samp{mpz_{\rm \ldots}}) routines are provided. If not stated
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otherwise, the description in the GNU MP documentation can be applied.
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In general, \dfn{mpz}-numbers can be used just like other standard
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Python numbers, e.g.\ you can use the built-in operators like \code{+},
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\code{*}, etc., as well as the standard built-in functions like
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\code{abs}, \code{int}, \ldots, \code{divmod}, \code{pow}.
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\strong{Please note:} the {\it bitwise-xor} operation has been implemented as
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a bunch of {\it and}s, {\it invert}s and {\it or}s, because the library
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lacks an \code{mpz_xor} function, and I didn't need one.
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You create an mpz-number by calling the function called \code{mpz} (see
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below for an exact description). An mpz-number is printed like this:
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\code{mpz(\var{value})}.
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\renewcommand{\indexsubitem}{(in module mpz)}
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\begin{funcdesc}{mpz}{value}
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Create a new mpz-number. \var{value} can be an integer, a long,
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another mpz-number, or even a string. If it is a string, it is
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interpreted as an array of radix-256 digits, least significant digit
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first, resulting in a positive number. See also the \code{binary}
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method, described below.
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\end{funcdesc}
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A number of {\em extra} functions are defined in this module. Non
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mpz-arguments are converted to mpz-values first, and the functions
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return mpz-numbers.
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\begin{funcdesc}{powm}{base\, exponent\, modulus}
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Return \code{pow(\var{base}, \var{exponent}) \%{} \var{modulus}}. If
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\code{\var{exponent} == 0}, return \code{mpz(1)}. In contrast to the
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\C-library function, this version can handle negative exponents.
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\end{funcdesc}
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\begin{funcdesc}{gcd}{op1\, op2}
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Return the greatest common divisor of \var{op1} and \var{op2}.
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\end{funcdesc}
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\begin{funcdesc}{gcdext}{a\, b}
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Return a tuple \code{(\var{g}, \var{s}, \var{t})}, such that
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\code{\var{a}*\var{s} + \var{b}*\var{t} == \var{g} == gcd(\var{a}, \var{b})}.
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\end{funcdesc}
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\begin{funcdesc}{sqrt}{op}
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Return the square root of \var{op}. The result is rounded towards zero.
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\end{funcdesc}
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\begin{funcdesc}{sqrtrem}{op}
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Return a tuple \code{(\var{root}, \var{remainder})}, such that
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\code{\var{root}*\var{root} + \var{remainder} == \var{op}}.
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\end{funcdesc}
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\begin{funcdesc}{divm}{numerator\, denominator\, modulus}
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Returns a number \var{q}. such that
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\code{\var{q} * \var{denominator} \%{} \var{modulus} == \var{numerator}}.
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One could also implement this function in Python, using \code{gcdext}.
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\end{funcdesc}
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An mpz-number has one method:
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\renewcommand{\indexsubitem}{(mpz method)}
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\begin{funcdesc}{binary}{}
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Convert this mpz-number to a binary string, where the number has been
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stored as an array of radix-256 digits, least significant digit first.
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The mpz-number must have a value greater than or equal to zero,
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otherwise a \code{ValueError}-exception will be raised.
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\end{funcdesc}
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