diff options
Diffstat (limited to 'modular.txi')
| -rw-r--r-- | modular.txi | 12 |
1 files changed, 12 insertions, 0 deletions
diff --git a/modular.txi b/modular.txi index d947b35..bf2cd52 100644 --- a/modular.txi +++ b/modular.txi @@ -26,28 +26,33 @@ If @var{x1} and @var{x2} are integers, then @code{mod} behaves like @end format @end defun + @defun extended-euclid n1 n2 Returns a list of 3 integers @code{(d x y)} such that d = gcd(@var{n1}, @var{n2}) = @var{n1} * x + @var{n2} * y. @end defun + @defun symmetric:modulus n Returns @code{(quotient (+ -1 n) -2)} for positive odd integer @var{n}. @end defun + @defun modulus->integer modulus Returns the non-negative integer characteristic of the ring formed when @var{modulus} is used with @code{modular:} procedures. @end defun + @defun modular:normalize modulus n Returns the integer @code{(modulo @var{n} (modulus->integer @var{modulus}))} in the representation specified by @var{modulus}. @end defun + @noindent The rest of these functions assume normalized arguments; That is, the arguments are constrained by the following table: @@ -79,27 +84,32 @@ Returns @code{#t} if there exists an integer n such that @var{k} * n @equiv{} 1 mod @var{modulus}, and @code{#f} otherwise. @end defun + @defun modular:invert modulus n2 Returns an integer n such that 1 = (n * @var{n2}) mod @var{modulus}. If @var{n2} has no inverse mod @var{modulus} an error is signaled. @end defun + @defun modular:negate modulus n2 Returns (@minus{}@var{n2}) mod @var{modulus}. @end defun + @defun modular:+ modulus n2 n3 Returns (@var{n2} + @var{n3}) mod @var{modulus}. @end defun + @defun modular:- modulus n2 n3 Returns (@var{n2} @minus{} @var{n3}) mod @var{modulus}. @end defun + @defun modular:* modulus n2 n3 Returns (@var{n2} * @var{n3}) mod @var{modulus}. @@ -108,7 +118,9 @@ The Scheme code for @code{modular:*} with negative @var{modulus} is not completed for fixnum-only implementations. @end defun + @defun modular:expt modulus n2 n3 Returns (@var{n2} ^ @var{n3}) mod @var{modulus}. @end defun + |