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 at > http://groups.google.com/group/sage-support > URL: http://www.sagemath.org > -- --- Iwao KIMURA Dept. Math., University of Toyama, Japan. -- 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
