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 Font size: Tiny Small Normal Large Huge Font colour [quote="gstic"]Hello everybody I found the solution. Singular command [b]codim(I, J) [/b] return the vectorspace dimension of I/J , I and J ideals. Here We consider the ring S=K[x,y] as ideal, generated by 1. If J is the ideal J = Jacob (f), the Milnor global number is the codimension of the ideal generated by the jacobian and f^2 (for 3 variables f^3) So, codim((1), std(I)) where I=J, f*f; Example for f= (y^2*(y+1)-x^3)^2-x^3*y^3, Milnor global number it is indeed 20. gstic[/quote]
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Topic review - Milnor global number
Author Message
 gstic
 Post subject: Re: Milnor global number
 Hello everybodyI found the solution.Singular command codim(I, J) return the vectorspace dimension of I/J , I and J ideals.Here We consider the ring S=K[x,y] as ideal, generated by 1.If J is the ideal J = Jacob (f), the Milnor global number is the codimension of the ideal generated by the jacobian and f^2 (for 3 variables f^3)So, codim((1), std(I)) where I=J, f*f;Example for f= (y^2*(y+1)-x^3)^2-x^3*y^3, Milnor global number it is indeed 20.gstic Hello everybodyI found the solution.Singular command [b]codim(I, J) [/b] return the vectorspace dimension of I/J , I and J ideals.Here We consider the ring S=K[x,y] as ideal, generated by 1.If J is the ideal J = Jacob (f), the Milnor global number is the codimension of the ideal generated by the jacobian and f^2 (for 3 variables f^3)So, codim((1), std(I)) where I=J, f*f;Example for f= (y^2*(y+1)-x^3)^2-x^3*y^3, Milnor global number it is indeed 20.gstic
 Posted: Thu Aug 25, 2016 2:12 pm
 hannes
 Post subject: Re: Milnor global number
 see http://www.singular.uni-kl.de/Manual/4-0-3/sing_418.htm(vector space dimension of a polynomial ring modulo an ideal)see http://www.singular.uni-kl.de/Manual/4- ... g_1567.htm(Milnor number)Code:> ring r=0,(x,y> ring r=0,(x,y),dp;> poly f= (y^2*(y+1)-x^3)^2-x^3*y^3;// first possibility:> ideal i=jacob(f);> ideal j=std(i);> vdim(j);25// or, second possibility:> LIB "sing.lib";> milnor(f);25// and the vector space basis:> kbase(j);.... see http://www.singular.uni-kl.de/Manual/4-0-3/sing_418.htm(vector space dimension of a polynomial ring modulo an ideal)see http://www.singular.uni-kl.de/Manual/4-0-3/sing_1567.htm(Milnor number)[code]> ring r=0,(x,y> ring r=0,(x,y),dp;> poly f= (y^2*(y+1)-x^3)^2-x^3*y^3;// first possibility:> ideal i=jacob(f);> ideal j=std(i);> vdim(j);25// or, second possibility:> LIB "sing.lib";> milnor(f);25// and the vector space basis:> kbase(j);....[/code]
 Posted: Thu Aug 25, 2016 10:23 am
 gstic
 Post subject: Milnor global number
 Hello,I want to calculate Milnor global number for a polynomial f in 2 variables in polynomial ring S=K[x,y].If J is the ideal J = Jacob (f), the Milnor global is the size of S/J as a vector space.How do I calculate the size of S/J as a vector space over K?Example for f= (y^2*(y+1)-x^3)^2-x^3*y^3, Milnor_global need to get = 20.Thanks in advance Hello,I want to calculate Milnor global number for a polynomial f in 2 variables in polynomial ring S=K[x,y].If J is the ideal J = Jacob (f), the Milnor global is the size of S/J as a vector space.How do I calculate the size of S/J as a vector space over K?Example for f= (y^2*(y+1)-x^3)^2-x^3*y^3, Milnor_global need to get = 20.Thanks in advance
 Posted: Wed Aug 24, 2016 8:42 pm

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