Hi Santanu, On 19 Mai, 19:51, Santanu Sarkar <[email protected]> wrote: > Dear Simon, > Thanks for your effort. Just two algebraic question. > 1. What is the dimension of an ideal in a polynomial ring?
It's the Krull dimension. It can be found in any textbook on commutative algebra, or of course in Wikipedia. Originally, the Krull dimension is defined for rings, namely as the supremum of the lengths of strictly ascending chains of prime ideals. But if you have an ideal I in a polynomial ring R = k[x1,...,xn], then you can also define the dimension for I, namely as the Krull dimension of the quotient ring R/I. In Sage, you would call the method I.dimension(), which relies on the fact that one can determine the dimension if one knows a Gröbner basis of I. It is indeed related with the dimension of the variety of I. The variety of I is a subset of k^n, namely the set of common zeroes of the elements of I. Since the dimension of a variety is defined > Please refer some books or study materials. With a strong computer algebra flavour: A Singular introduction to commutative algebra > With regards, > Santanu > > On 19 May 2011 13:12, Simon King <[email protected]> wrote: > > > On 19 Mai, 09:08, Simon King <[email protected]> wrote: > >> /mnt/local/king/SAGE/sage-4.7.rc2/local/lib/python2.6/site-packages/ > >> sage/rings/ring.so in sage.rings.ring.Ring.is_finite (sage/rings/ > >> ring.c:5955)() > > >> NotImplementedError: > > >> I think that is a bug, and I will open a trac ticket for it. > > > It is trac ticket #11350, ready for review. > > > -- > > To post to this group, send email to [email protected] > > To unsubscribe from this group, send email to > > [email protected] > > 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 [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
