2009/9/3 John H Palmieri <jhpalmier...@gmail.com>: > > On Sep 3, 12:36 am, William Stein <wst...@gmail.com> wrote: >> >> Sage has the Gaussian integers, and I'm sure the basic arithmetic and >> functionality is as good or better than Mathematica already. >> >> sage: R.<I> = ZZ[sqrt(-1)]; R >> Order in Number Field in I with defining polynomial x^2 + 1 > > Okay, this looks like a bug to me: > > ---------------------------------------------------------------------- > | Sage Version 4.1.1, Release Date: 2009-08-14 | > | Type notebook() for the GUI, and license() for information. | > ---------------------------------------------------------------------- > sage: I > I > sage: R.<I> = ZZ[sqrt(-1)] > sage: I > 1 > sage: I^2 > 1 > > Why is I equal to 1 all of a sudden? Same problem here:
Here is the reason, which caught me out also. ZZ[sqrt(-1)] is an order, and has two gens, namely its ZZ-module generators: sage: R = ZZ[sqrt(-1)] sage: R.gens() [1, I] sage: R.<one,I> = ZZ[sqrt(-1)] sage: one 1 sage: I I sage: I^2 -1 So, R needs two names, you only gave it one. I guess WAS is about to say the same thing but I'll post anyway... John > > sage: reset() > sage: R.<a> = ZZ[sqrt(-5)] > sage: a > 1 > sage: R.1 > a > sage: R.1 == a > False > sage: (R.1)^2 > -5 > sage: R.inject_variables() > Defining a > sage: a > 1 > > > Ouch. > -- > John > > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
