Changeset f4490f5 in git for Singular/LIB/dmodvar.lib
 Timestamp:
 Sep 30, 2010, 10:05:15 PM (13 years ago)
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 (u'spielwiese', 'd0474371d8c5d8068ab70bfb42719c97936b18a6')
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 9f5ebf25535e7f3b32e56ffc7635be3bcf1c05bf
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 0a2f7deb9cde7da147b192a31ec765e4f3923a09
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Singular/LIB/dmodvar.lib
r0a2f7d rf4490f5 9 9 Jorge MartinMorales, jorge@unizar.es 10 10 11 THEORY: Let K be a field of characteristic 0. Given a polynomial ring R = K[x_1,...,x_n] and 11 OVERVIEW: 12 Theory: Let K be a field of characteristic 0. Given a polynomial ring R = K[x_1,...,x_n] and 12 13 @* a set of polynomial f_1,..., f_r in R, define F = f_1 * ... * f_r and F^s:=f_1^s_1*...*f_r^s_r 13 14 @* for symbolic discrete (that is shiftable) variables s_1,..., s_r. 14 @* The module R[1/F]*F^s has a structure of a D<S>module, where D<S> := D(R) tensored with S over K, where 15 @* The module R[1/F]*F^s has a structure of a D<S>module, where 16 D<S> := D(R) tensored with S over K, where 15 17 @*  D(R) is an nth Weyl algebra K<x_1,...,x_n,d_1,...,d_n  d_j x_j = x_j d_j +1> 16 18 @*  S is the universal enveloping algebra of gl_r, generated by s_{ij}, where s_{ii}=s_i. … … 23 25 @* sum(k=1 to k=r) P_k*f_k*F^s = bs*F^s holds in R[1/F]*F^s. 24 26 25 R EFERENCES:27 References: 26 28 (BMS06) Budur, Mustata, Saito: BernsteinSato polynomials of arbitrary varieties (2006). 27 29 (ALM09) Andres, Levandovskyy, MartinMorales : Principal Intersection and BernsteinSato Polynomial of an Affine Variety (2009). … … 487 489 } 488 490 489 proc makeIF (ideal F, list #)491 static proc makeIF (ideal F, list #) 490 492 "USAGE: makeIF(F [,ORD]); F an ideal, ORD an optional string 491 493 RETURN: ring
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