Hi, This time it seems that there are = more failed regression tests that before : Environment : AWK=3Dgawk = BOOKS=3D/d1/axiom/books BYE=3Dbye CC=3Dgcc CCF=3D-O2 -fno-strength-reduce -= Wall -D_GNU_SOURCE -DLINUXplatform -I/usr/X11/include COMMAND=3D/usr/local/= axiom/mnt/slackware/bin/axiom DAASE=3D/d1/axiom/src/share DESTDIR=3D/usr/lo= cal/axiom DOCUMENT=3D/d1/axiom/mnt/slackware/bin/document GCLDIR=3D/d1/axio= m/lsp/gcl-2.6.8pre4 GCLOPTS=3D--enable-vssize=3D65536*2 --enable-locbfd --d= isable-dynsysbfd --disable-statsysbfd --enable-maxpage=3D512*1024 --disable= -xgcl --disable-tkconfig GCLVERSION=3Dgcl-2.6.8pre4 INC=3D/d1/axiom/src/inc= lude INT=3D/d1/axiom/int LDF=3D -L/usr/X11R6/lib -L/usr/lib -lXpm LIS= P=3Dlsp LSP=3D/d1/axiom/lsp MNT=3D/d1/axiom/mnt NOISE=3D-o /d1/axiom/obj/tm= p/trace O=3Do OBJ=3D/d1/axiom/obj PART=3Dcprogs PATCH=3Dpatch PLF=3DLINUXpl= atform RANLIB=3Dranlib RUNTYPE=3Dserial SPAD=3D/d1/axiom/mnt/slackware SPADBIN=3D/d1/axiom/mnt/slackware/bin SPD= =3D/d1/axiom SRC=3D/d1/axiom/src SRCDIRS=3Dinterpdir sharedir algebradir et= cdir clefdir docdir graphdir smandir hyperdir browserdir inputdir SUBPART= =3Deverything SYS=3Dslackware TANGLE=3D/d1/axiom/mnt/slackware/bin/lib/nota= ngle TAR=3Dtar TESTSET=3Dalltests TMP=3D/d1/axiom/obj/tmp TOUCH=3Dtouch UNC= OMPRESS=3Dgunzip VERSION=3DAxiom (January 2011) WEAVE=3D/d1/axiom/mnt/slack= ware/bin/lib/noweave XLIB=3D/usr/X11R6/lib ZIPS=3D/d1/axiom/zips int/inp= ut/ApplicationProgramInterface.regress:regression result FAILED 2 of 5 stan= zas file ApplicationProgramInterface int/input/DoubleFloat.regress:regre= ssion result FAILED 2 of 13 stanzas file DoubleFloat int/input/FileName.= regress:regression result FAILED 2 of 18 stanzas file FileName int/input= /GuessOptionFunctions0.regress:regression result FAILED 1 of 1 stanzas file= GuessOptionFunctions0 int/input/PlaneAlgebraicCurvePlot.regress:regress= ion result FAILED 2 of 5 stanzas file PlaneAlgebraicCurvePlot int/input/dfloat.regress:regressio= n result FAILED 3 of 10 stanzas file dfloat int/input/dftrig.regress:reg= ression result FAILED 233 of 672 stanzas file dftrig int/input/dop.regre= ss:regression result FAILED 8 of 127 stanzas file dop int/input/e1.regre= ss:regression result FAILED 4 of 7 stanzas file e1 int/input/ei.regress:= regression result FAILED 16 of 20 stanzas file ei int/input/elemnum.regr= ess:regression result FAILED 16 of 50 stanzas file elemnum int/input/en.= regress:regression result FAILED 5 of 7 stanzas file en int/input/fname.= regress:regression result FAILED 1 of 9 stanzas file fname int/input/fna= me1.regress:regression result FAILED 2 of 18 stanzas file fname1 int/inp= ut/gamma.regress:regression result FAILED 4 of 12 stanzas file gamma int= /input/grpthry.regress:regression result FAILED 8 of 68 stanzas file grpthr= y int/input/guess.regress:regression result FAILED 62 of 102 stanzas file guess int/input/ico.regress:regression result FAILED 11 of= 65 stanzas file ico int/input/newtonlisp.regress:regression result FAIL= ED 2 of 14 stanzas file newtonlisp int/input/numericgamma.regress:regres= sion result FAILED 7 of 36 stanzas file numericgamma int/input/r20bugs.r= egress:regression result FAILED 1 of 27 stanzas file r20bugs int/input/r= ichalgebraic000-099.regress:regression result FAILED 2 of 518 stanzas file = richalgebraic000-099 int/input/richalgebraic100-199.regress:regression r= esult FAILED 29 of 365 stanzas file richalgebraic100-199 int/input/richa= lgebraic100-199.regress:regression result FAILED early exit in file richalg= ebraic100-199? int/input/richalgebraic400-461.regress:regression result = FAILED 2 of 324 stanzas file richalgebraic400-461 int/input/richhyper100= 0-1098.regress:regression result FAILED 4 of 531 stanzas file richhyper1000= -1098 int/input/richlog300-391.regress:regression result FAILED 164 of 460 stanzas file richlog300-391 int/input/richtrig000-099.regres= s:regression result FAILED 31 of 520 stanzas file richtrig000-099 int/in= put/richtrig800-899.regress:regression result FAILED 165 of 526 stanzas fil= e richtrig800-899 toto125 |

= =0A=0A=0A=0A=0A --0-991340133-1296742399=:88858-- From MAILER-DAEMON Sat Feb 05 09:45:25 2011 Received: from mailman by lists.gnu.org with archive (Exim 4.43) id 1PljO9-0002R1-55 for mharc-axiom-developer@gnu.org; Sat, 05 Feb 2011 09:45:25 -0500 Received: from [140.186.70.92] (port=53129 helo=eggs.gnu.org) by lists.gnu.org with esmtp (Exim 4.43) id 1PkNPt-00048r-HM for axiom-developer@nongnu.org; Tue, 01 Feb 2011 16:05:39 -0500 Received: from Debian-exim by eggs.gnu.org with spam-scanned (Exim 4.71) (envelope-from

I haven't been paying close
attention but I think the following might work:

define the gcd() implicitly: i.e. minimize over [m,n integer,G>0]( m(a/b)+n(c/d))=G

This seems to make sense in Euclidean domains.

This leads to

G=gcd(da,bc)/bd

let's see how this works

gcd(1/4,1/6) would yield 2/24=1/12

gcd(3/12,9/54) would yield gcd(3*54,12*9)=gcd(3*9*6,3*4*9)=3*9*2

3*9*2/(3*4*9*6)=1/12

So it seems consistent.

Sorry if this is off-topic or I have overlooked something obvious. Of course the actual reasonableness and verification needs proof.

I think I have developed a formalism that makes sense over Principal Ideal Rings, extended to include inverses. Bur the ideas are not mathematically well defined.

Ray

On 02/11/2011 03:55 AM, daly wrote:

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From MAILER-DAEMON Fri Feb 18 02:06:41 2011
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(envelope-from define the gcd() implicitly: i.e. minimize over [m,n integer,G>0]( m(a/b)+n(c/d))=G

This seems to make sense in Euclidean domains.

This leads to

G=gcd(da,bc)/bd

let's see how this works

gcd(1/4,1/6) would yield 2/24=1/12

gcd(3/12,9/54) would yield gcd(3*54,12*9)=gcd(3*9*6,3*4*9)=3*9*2

3*9*2/(3*4*9*6)=1/12

So it seems consistent.

Sorry if this is off-topic or I have overlooked something obvious. Of course the actual reasonableness and verification needs proof.

I think I have developed a formalism that makes sense over Principal Ideal Rings, extended to include inverses. Bur the ideas are not mathematically well defined.

Ray

On 02/11/2011 03:55 AM, daly wrote:

On Fri, 2011-02-11 at 01:49 -0800, Simon King wrote:

Hi,That's why I was asking for an algorithm for gcd and lcm

On 11 Feb., 09:56, Simon King<simon.k...@uni-jena.de> wrote:

Well, I had the impression that a couple of people are in favour ofIt just occurs to me that I am incredibly stupid.

the following:

gcd(a/b,c/d) := gcd(a,c)/lcm(b,d)

lcm(a/b,c/d) := lcm(a,c)/gcd(b,d)

The definition above wouldn't work at all, it isn't even well-defined.

Just replace gcd(1/4,1/6) by gcd(3/12,9/54). You obtain gcd(1,1)/

lcm(4,6) = 1/12, but gcd(3,9)/lcm(12,54) = 1/36.

Does anyone have a better idea? Would it be a correct definition if

one insisted on reduced fractions?

Cheers,

Simon

in the subdomain. I'm not sure what answer is expected.

The unit (1) is correct but not by your definition, and

apparently not helpful for the original poster.

Tim Daly

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