Path: csiph.com!x330-a1.tempe.blueboxinc.net!newsfeed.hal-mli.net!feeder1.hal-mli.net!weretis.net!feeder4.news.weretis.net!eternal-september.org!feeder.eternal-september.org!.POSTED!not-for-mail From: Joe Riel Newsgroups: comp.soft-sys.math.maple Subject: Re: Mod Date: Tue, 31 May 2011 15:26:33 -0700 Organization: A noiseless patient Spider Lines: 41 Message-ID: <874o4aecbq.fsf@san.rr.com> References: <_dudnRR1uL-yX0TQnZ2dnUVZ_oGdnZ2d@wavecable.com> <93ucb2F9lmU1@mid.individual.net> <93v422FtbfU1@mid.individual.net> Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Injection-Info: mx04.eternal-september.org; posting-host="7daQ3AF9ALJlnU9jGWSG5Q"; logging-data="27355"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19YbBusKtK/1Yqu1cJTgkPH" User-Agent: Gnus/5.13 (Gnus v5.13) Emacs/23.3 (gnu/linux) Cancel-Lock: sha1:QeVvHjebrYIFJ2Ycy0e/ZVKUJAo= sha1:J4biGpe6Vnwju5l25cvXdFQd4jo= Xref: x330-a1.tempe.blueboxinc.net comp.soft-sys.math.maple:170 Ilmari Karonen writes: > On 2011-05-23, Axel Vogt <&noreply@axelvogt.de> wrote: >> Peter Pein wrote: >>> >>> so "mod" is not the "mod" I know? I would expect for any x < 14 that mod >>> (x,14)=x and not an error-message. Should my professor for numbertheory >>> be set on fire? >> >> Nice :-) But may be he is faster, if anyone dares to write >> 1/3 over the integers :-)) >> >> Maple is more or less clear in its help: >> >> "The mod operator evaluates the expression e over the integers >> modulo m. It incorporates facilities for doing finite field >> arithmetic and polynomial and matrix arithmetic over finite >> fields, including factorization." >> >> So 'mod' means to work in the ring Z/7Z, being a field here. > > Admittedly, one sometimes _does_ want to work in the ring R/mZ of > reals modulo m. > > Sometimes, one might even find use for the "division" operation in > R/mZ inherited from R by identifying the equivalence classes of R/mZ > with their lowest non-negative members, even if said operation does > not actually always yield a multiplicative inverse in R/mZ. > > Perhaps more to the OP's point, sometimes one, while nominally working > in R, might nonetheless desire an operator which returns the remainder > of dividing x by y. Curiously, I couldn't immediately find such a > function in Maple, although of course it's easy enough to define, e.g. > > fmod := (x,m) -> x - m * floor(x/m); frem is a builtin that is similar, but minimizes the norm, so will return negative values. -- Joe Riel