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Diffstat (limited to 'factor.txi')
| -rw-r--r-- | factor.txi | 69 |
1 files changed, 26 insertions, 43 deletions
@@ -1,73 +1,56 @@ - - @defvar prime:prngs - @var{prime:prngs} is the random-state (@pxref{Random Numbers}) used by these - procedures. If you call these procedures from more than one thread - (or from interrupt), @code{random} may complain about reentrant - calls. +@var{prime:prngs} is the random-state (@pxref{Random Numbers}) used by these +procedures. If you call these procedures from more than one thread +(or from interrupt), @code{random} may complain about reentrant +calls. @end defvar +@emph{Note:} The prime test and generation procedures implement (or +use) the Solovay-Strassen primality test. See - - - +@itemize @bullet +@item Robert Solovay and Volker Strassen, +@cite{A Fast Monte-Carlo Test for Primality}, +SIAM Journal on Computing, 1977, pp 84-85. +@end itemize @defun jacobi-symbol p q - Returns the value (+1, @minus{}1, or 0) of the Jacobi-Symbol of - exact non-negative integer @var{p} and exact positive odd integer @var{q}. +Returns the value (+1, @minus{}1, or 0) of the Jacobi-Symbol of +exact non-negative integer @var{p} and exact positive odd integer @var{q}. @end defun - @defvar prime:trials - @var{prime:trials} the maxinum number of iterations of Solovay-Strassen that will - be done to test a number for primality. +@var{prime:trials} the maxinum number of iterations of Solovay-Strassen that will +be done to test a number for primality. @end defvar - - - @defun prime? n - Returns @code{#f} if @var{n} is composite; @code{#t} if @var{n} is prime. - There is a slight chance @code{(expt 2 (- prime:trials))} that a - composite will return @code{#t}. +Returns @code{#f} if @var{n} is composite; @code{#t} if @var{n} is prime. +There is a slight chance @code{(expt 2 (- prime:trials))} that a +composite will return @code{#t}. @end defun - - @defun primes< start count - Returns a list of the first @var{count} prime numbers less than - @var{start}. If there are fewer than @var{count} prime numbers - less than @var{start}, then the returned list will have fewer than - @var{start} elements. +Returns a list of the first @var{count} prime numbers less than +@var{start}. If there are fewer than @var{count} prime numbers +less than @var{start}, then the returned list will have fewer than +@var{start} elements. @end defun - - @defun primes> start count - Returns a list of the first @var{count} prime numbers greater than @var{start}. +Returns a list of the first @var{count} prime numbers greater than @var{start}. @end defun - - - - - - - - - - - @defun factor k - Returns a list of the prime factors of @var{k}. The order of the - factors is unspecified. In order to obtain a sorted list do - @code{(sort! (factor @var{k}) <)}. +Returns a list of the prime factors of @var{k}. The order of the +factors is unspecified. In order to obtain a sorted list do +@code{(sort! (factor @var{k}) <)}. @end defun |