Tree @debian/3b6-3 (Download .tar.gz)
- debian
- alist.scm
- alist.txi
- alistab.scm
- ANNOUNCE
- array.scm
- array.txi
- arraymap.scm
- arraymap.txi
- batch.scm
- Bev2slib.scm
- bigloo.init
- break.scm
- byte.scm
- byte.txi
- bytenumb.scm
- bytenumb.txi
- ChangeLog
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- chap.txi
- charplot.scm
- chez.init
- cie1931.xyz
- cie1964.xyz
- ciesia.dat
- ciesid65.dat
- clrnamdb.scm
- cltime.scm
- coerce.scm
- coerce.txi
- collect.scm
- collectx.scm
- color.scm
- color.txi
- colornam.scm
- colornam.txi
- colorspc.scm
- comlist.scm
- comparse.scm
- comparse.txi
- configure
- COPYING
- crc.scm
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- dbutil.scm
- dbutil.txi
- debug.scm
- defmacex.scm
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- determ.txi
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- differ.txi
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- fluidlet.scm
- format.scm
- format.texi
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- gambit.init
- genwrite.scm
- getopt.scm
- getparam.scm
- getparam.txi
- glob.scm
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- grapheps.scm
- grapheps.txi
- guile-2.init
- guile.init
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- indexes.texi
- iso8601.scm
- iso8601.txi
- jscheme.init
- kawa.init
- limit.scm
- limit.texi
- lineio.scm
- lineio.txi
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- linterp.txi
- logical.scm
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- macscheme.init
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- math-integer.txi
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- mbe.scm
- minimize.scm
- minimize.txi
- mitscheme.init
- mkclrnam.scm
- mkclrnam.txi
- mklibcat.scm
- mkpltcat.scm
- modular.scm
- modular.txi
- mulapply.scm
- mularg.scm
- mwdenote.scm
- mwexpand.scm
- mwsynrul.scm
- mzscheme.init
- nbs-iscc.txt
- ncbi-dna.scm
- ncbi-dna.txi
- null.scm
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- obj2str.txi
- object.scm
- object.texi
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- priorque.txi
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- queue.txi
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- random.txi
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- README
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- root.scm
- RScheme.init
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- saturate.txt
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- scheme2c.init
- scheme48.init
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- srfi-8.scm
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- srfi.scm
- srfi.txi
- stdio.scm
- STk.init
- strcase.scm
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- syncase.sh
- synchk.scm
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- Template.scm
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- tzfile.scm
- umbscheme.init
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- values.scm
- version.txi
- vet.scm
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- vscm.init
- withfile.scm
- wttree-test.scm
- wttree.scm
- xml-parse.scm
- xml-parse.txi
- yasyn.scm
modular.txi @debian/3b6-3 — raw · history · blame
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 | @code{(require 'modular)} @ftindex modular @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 m For odd positive integer @var{m}, returns an object suitable for passing as the first argument to @code{modular:} procedures, directing them to return a symmetric modular number, ie. an @var{n} such that @example (<= (quotient @var{m} -2) @var{n} (quotient @var{m} 2) @end example @end defun @defun modular:characteristic 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} (modular:characteristic @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: @noindent For all of these functions, if the first argument (@var{modulus}) is: @table @code @item positive? Integers mod @var{modulus}. The result is between 0 and @var{modulus}. @item zero? The arguments are treated as integers. An integer is returned. @end table @noindent Otherwise, if @var{modulus} is a value returned by @code{(symmetric:modulus @var{radix})}, then the arguments and result are treated as members of the integers modulo @var{radix}, but with @dfn{symmetric} representation; i.e. @cindex symmetric @example (<= (quotient @var{radix} 2) @var{n} (quotient (- -1 @var{radix}) 2) @end example @noindent If all the arguments are fixnums the computation will use only fixnums. @defun modular:invertable? modulus k 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}. 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 |