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author | Niels Möller <nisse@lysator.liu.se> | 2012-02-08 09:38:00 +0100 |
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committer | Niels Möller <nisse@lysator.liu.se> | 2012-02-08 09:38:00 +0100 |
commit | 35ee5f096c2e9c57e1554094925cf5c69837e71b (patch) | |
tree | 1f2001b6bfce9677c8a932e1b316363be84f4fa1 /doc | |
parent | 64d9495f6b6144601da9ae123e130dfe496710f2 (diff) | |
download | gmp-35ee5f096c2e9c57e1554094925cf5c69837e71b.tar.gz |
Clarified corner cases in cofactor canonicalization.
Diffstat (limited to 'doc')
-rw-r--r-- | doc/gmp.texi | 21 |
1 files changed, 16 insertions, 5 deletions
diff --git a/doc/gmp.texi b/doc/gmp.texi index 2379813e3..59996dde2 100644 --- a/doc/gmp.texi +++ b/doc/gmp.texi @@ -3551,11 +3551,22 @@ Set @var{g} to the greatest common divisor of @var{a} and @var{b}, and in addition set @var{s} and @var{t} to coefficients satisfying @math{@var{a}@GMPmultiply{}@var{s} + @var{b}@GMPmultiply{}@var{t} = @var{g}}. The value in @var{g} is always positive, even if one or both of @var{a} and -@var{b} are negative (or zero if both inputs are zero). The values in @var{s} and @var{t} are chosen such that -normally, @math{@GMPabs{@var{s}} < @GMPabs{@var{b}} / (2 @var{g})} and -@math{@GMPabs{@var{t}} < @GMPabs{@var{a}} / (2 @var{g})}. The exceptional -cases are that @math{@var{s} = sgn(@var{a})} if @math{@var{b} = 0} and -@math{@var{t} = sgn(@var{b})} if @var{a = 0}. +@var{b} are negative (or zero if both inputs are zero). The values in @var{s} +and @var{t} are chosen such that normally, @math{@GMPabs{@var{s}} < +@GMPabs{@var{b}} / (2 @var{g})} and @math{@GMPabs{@var{t}} < @GMPabs{@var{a}} +/ (2 @var{g})}, and these relations define @var{s} and @var{t} uniquely. There +are a few exceptional cases: + +If @math{@GMPabs{@var{a}} = @GMPabs{@var{b}}}, then @math{@var{s} = 0}, +@math{@var{t} = sgn(@var{b})}. + +Otherwise, @math{@var{s} = sgn(@var{a})} if @math{@var{b} = 0} or +@math{@GMPabs{@var{b}} = 2 @var{g}}, and @math{@var{t} = sgn(@var{b})} if +@math{@var{a} = 0} or @math{@GMPabs{@var{a}} = 2 @var{g}}. + +In all cases, @math{@var{s} = 0} if and only if @math{@var{g} = +@GMPabs{@var{b}}}, i.e., if @var{b} divides @var{a} or @math{@var{a} = @var{b} += 0}. If @var{t} is @code{NULL} then that value is not computed. @end deftypefun |