Dear David, On 21 Feb., 12:30, davidp <dav...@reed.edu> wrote: > sage: R = singular.ring(0,'(x,y,z)','dp') > sage: I = singular.ideal(['x^3-y^2*z','z^2-x*y']) > sage: I.hilb() > `sage90` > > Could someone please explain this?
Yes. First, let us see how Singular's hilb command works (compare http://www.singular.uni-kl.de/Manual/latest/sing_212.htm#SEC252 in Singular's online manual). Here, I consider a Singular session. If hilb is called without further argument, nothing is returned, only a few comments are printed: > ring r = 0,(x,y,z),dp; > ideal I = x3-y2z,z2-xy; > hilb(I); // ** I is no standard basis // 1 t^0 // -1 t^2 // -1 t^3 // 1 t^4 // 1 t^0 // 1 t^1 // -1 t^3 // dimension (proj.) = 1 // degree (proj.) = 1 What you probably want is data for either the first or the second hilbert series: > hilb(I,1); // ** I is no standard basis 1,0,-1,-1,1,0 > hilb(I,2); // ** I is no standard basis 1,1,0,-1,0 Now, return to Sage, and do as you did: sage: R = singular.ring(0,'(x,y,z)','dp') sage: I = singular.ideal(['x^3-y^2*z','z^2-x*y']) The ideal I is represented by an ideal in a Singular sub-process, and it gets a name that is automatically chosen: sage: I.name() 'sage3' sage: print singular.eval('sage3') sage3[1]=x^3-y^2*z sage3[2]=-x*y+z^2 When you say "I.hilb()", then internally the Singular command def sage4=hilb(sage3); is issued. But calling "hilb" without further arguments returns nothing. So, sage4 is defined, but has no value: sage: print singular.eval('typeof(sage4)') none It is very easy to call the "hilb" function with an additional argument: sage: I.hilb(1) 1, 0, -1, -1, 1, 0 sage: I.hilb(2) 1, 1, 0, -1, 0 So, this is the output of the corresponding Singular function. Best regards Simon --~--~---------~--~----~------------~-------~--~----~ 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 URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
