We discussed this briefly on #sage-devel a couple weeks ago, though the discussion died out and nobody got around to submitting a trac ticket about it (probably because it's not really clear which way to go on this...). Here's the log, which might answer some questions: http://sage.pastebin.com/EBq7Zud5 See also http://trac.sagemath.org/sage_trac/ticket/3214 which is mentioned at the end of the IRC log.
-Keshav On Dec 29, 6:09 am, Johannes <dajo.m...@web.de> wrote: > Ok, from this point of view see the point. But I dont know if it's > documented this way somewhere. > > greatz > Am 28.12.2010 23:00, schrieb Iwao Kimura: > > > Hi Johannes, > > > I'm not sure but if we think gcd(2, 0) is the generator of the ideal > > generated by 2 and 0 in the rationals, we see gcd(2,0) is 1 because > > the ideal is not zero (and QQ is a field :) > > > Best regards. > > > On Wed, Dec 29, 2010 at 6:33 AM, Johannes <dajo.m...@web.de> wrote: > >> I got it solved. It's a type error: > >> the matrix sing is a matrix over QQ. > >> If its a matrix over ZZ it works fine. > > >> but why is gcd(2,0) = 1 for 2,0 as Rationals? > >> in my eyes its not well defined or should be the maximum of those values. > > >> greatz > > >> Am 28.12.2010 22:08, schrieb Johannes: > >>> Hi list, > >>> I've a very confusing problem with some simple algorithm: > > >>> following setting: a matrix sing: > >>> sage: sing > >>> [ 3 0 1] > >>> [-2 -1 -2] > >>> [ 0 1 0] > >>> sage: l = sings.column(2);l > >>> (1, -2, 0) > >>> #my algorithem, code see below: > >>> sage: extgcd(l) > >>> #some printoutput for debugging: > >>> l: (1, -2, 0) > >>> tlist: (-2, 0) > >>> #this should not be, d = gcd(tlist) > >>> d: 1 > >>> l: [1, 1] > >>> [u, v]: [0, 1] > >>> l: (-2, 0) > >>> [u, v]: [1, 0] > >>> res: [0, 1, 0] > >>> #the result: > >>> [0, 1, 0] > >>> #now the same but i construct the vector on my own: > >>> sage: l = vector([1,-2,0]);l > >>> (1, -2, 0) > >>> sage: extgcd(l) > >>> l: (1, -2, 0) > >>> tlist: (-2, 0) > >>> #here it works fine > >>> d: 2 > >>> l: [1, 2] > >>> [u, v]: [1, 0] > >>> l: (-2, 0) > >>> [u, v]: [1, 0] > >>> res: [1, 0, 0] > >>> #getting the expected result: > >>> [1, 0, 0] > > >>> the code of my algorithm: > > >>> def extgcd(l): > >>> print "l: " + str(l) > >>> assert len(l) > 1 > > >>> if len(l) == 2: > >>> #calculated ext euclidean for two values > >>> a = l[0] > >>> b = l[1] > > >>> u=t=1 > >>> v=s=0 > >>> while b>0: > >>> q=a//b > >>> a, b = b, a-q*b > >>> u, s = s, u-q*s > >>> v, t = t, v-q*t > >>> print "[u, v]: " + str([u, v]) > >>> return [u, v] > >>> else: > > >>> #this is the part where it does not work! > >>> tlist = l[1:] > >>> print "tlist: " + str(tlist) > >>> d = gcd(tlist) > >>> print "d: " + str(gcd(tlist)) > > >>> #calculate part decomp > >>> u, v = extgcd([l[0],d]) > >>> #calculate rest > >>> ttlist = extgcd(tlist) > >>> res = [u] > >>> #combine results > >>> res.extend([v * item for item in ttlist]) > >>> print "res: " + str(res) > >>> return res > > >>> I hope somebody can help me. > >>> greatz Johannes > > >> -- > >> To post to this group, send email to sage-support@googlegroups.com > >> To unsubscribe from this group, send email to > >> sage-support+unsubscr...@googlegroups.com > >> For more options, visit this group > >> athttp://groups.google.com/group/sage-support > >> URL:http://www.sagemath.org > > -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
