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gstic
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Post subject: Milnor global number Posted: Wed Aug 24, 2016 8:42 pm |
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Joined: Fri Jun 24, 2011 10:10 am Posts: 12
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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
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hannes
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Post subject: Re: Milnor global number Posted: Thu Aug 25, 2016 10:23 am |
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Joined: Wed May 25, 2005 4:16 pm Posts: 275
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gstic
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Post subject: Re: Milnor global number Posted: Thu Aug 25, 2016 2:12 pm |
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Joined: Fri Jun 24, 2011 10:10 am Posts: 12
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Hello everybody
I 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
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