On Wednesday, May 15, 2019 at 10:08:05 PM UTC+9, Santanu wrote: > > > > On Wed, 15 May 2019 at 17:03, Kwankyu <ekwa...@gmail.com <javascript:>> > wrote: > >> Hi Chandra, >> >> What is Place (x^2 + x + 1, x*y + 1)? Is it ideal generated by >>> >>> (x^2 + x + 1, x*y + 1). >>> >>> >> No. Place (x^2 + x + 1, x*y + 1) is the unique place of the function field >> >> at which both functions x^2 + x +1, x*y + 1 vanish. >> >> Thank you for your response. We know that a place is the unique maximal > ideal of a local (valuation) ring obtained from the valuation map, which is > well known to be a principle ideal. So, there will be a single generator > for a place. But here it is represented by two polynomials. We didn't get > what it means. >
A place generally cannot be represented by a single polynomial. The generator of the principal ideal does not specify the local ring itself. Can we find the corresponding valuation ring, valuation map > ant the generator for the place? > Use p.valuation_ring() for the valuation ring, which is only a facade for the ring. Use p.local_uniformizer() for the generator. Look at this example: sage: p1,p2 = L(x^2+x+1).zeros() sage: p1.local_uniformizer() x^2 + x + 1 sage: p2.local_uniformizer() x^2 + x + 1 -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at https://groups.google.com/group/sage-support. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/dae3358f-0854-41d3-8c3b-f14048c57049%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.
