Changeset 7c7ca9 in git
- Timestamp:
- Jan 9, 2001, 5:16:14 PM (23 years ago)
- Branches:
- (u'spielwiese', '5b153614cbc72bfa198d75b1e9e33dab2645d9fe')
- Children:
- 6ab8550563f4cfbca9c234cb8589bc1220901b4f
- Parents:
- 958e16a5bb9d642b48e254c0cc79880bbf3b9b7f
- File:
-
- 1 edited
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Singular/LIB/gaussman.lib
r958e16 r7c7ca9 1 1 /////////////////////////////////////////////////////////////////////////////// 2 version="$Id: gaussman.lib,v 1.2 1 2001-01-07 15:21:09 greuelExp $";2 version="$Id: gaussman.lib,v 1.22 2001-01-09 16:16:14 mschulze Exp $"; 3 3 category="Singularities"; 4 4 … … 148 148 @format 149 149 if mode=0: 150 150 matrix M: exp(-2*pi*i*M) is a monodromy matrix of f 151 151 if mode=1: 152 152 ideal e: exp(-2*pi*i*e) is the spectrum of the monodromy of f 153 153 @end format 154 154 SEE ALSO: monodromy.lib, jordan.lib … … 371 371 372 372 proc vfiltration(poly f,list #) 373 "USAGE: vfiltration(f[,mode]); poly f, int mode[ default=1]374 ASSUME: local ordering, fisolated singularity at 0375 RETURN: list l:376 @format 373 "USAGE: vfiltration(f[,mode]); poly f, int mode[=1] 374 ASSUME: basering has local ordering, f has isolated singularity at 0 375 RETURN: 376 @format 377 377 list l: 378 378 if mode=0 or mode=1: 379 l[1]: ideal,spectral numbers in increasing order380 l[2]: intvec381 l[2][i]: int,multiplicity of spectral number l[1][i]382 if mode=1 383 l [3]: list384 l[3][i]: module, vector space basis of l[1][i]-th graded385 partof the V-filtration on H''/H' in terms of l[4]386 l[4]: ideal,monomial vector space basis of H''/H'387 l[5]: ideal, standard basis ofJacobian ideal388 389 NOTE: H' and H'' denote Brieskorn lattices379 ideal l[1]: spectral numbers in increasing order 380 intvec l[2]: 381 int l[2][i]: multiplicity of spectral number l[1][i] 382 if mode=1: 383 list l[3]: 384 module l[3][i]: vector space basis of l[1][i]-th graded part 385 of the V-filtration on H''/H' in terms of l[4] 386 ideal l[4]: monomial vector space basis of H''/H' 387 ideal l[5]: standard basis of the Jacobian ideal 388 @end format 389 NOTE: H' and H'' denote the Brieskorn lattices 390 390 SEE ALSO: spectrum.lib 391 391 KEYWORDS: singularities; Gauss-Manin connection; spectrum; … … 749 749 750 750 proc vfiltjacalg(list l) 751 "USAGE: vfiltjacalg(vfiltration(f)); 752 ASSUME: local ordering, fisolated singularity at 0753 RETURN: 754 @format 751 "USAGE: vfiltjacalg(vfiltration(f)); poly f 752 ASSUME: basering has local ordering, f has isolated singularity at 0 753 RETURN: 754 @format 755 755 list l: 756 l[1]: ideal, spectral numbers of the V-filtration on the757 Jacobian algebra in increasing order758 l[2]: intvec759 l[2][i]: int,multiplicity of spectral number l[1][i]760 l [3]: list761 l[3][i]: module, vector space basis ofl[1][i]-th graded part762 of the V-filtration on the Jacobian algebra in terms763 of l[4]764 l[4]: ideal,monomial vector space basis of the Jacobian algebra765 l[5]: ideal, standard basis ofJacobian ideal756 ideal l[1]: spectral numbers of the V-filtration 757 on the Jacobian algebra in increasing order 758 intvec l[2]: 759 int l[2][i]: multiplicity of spectral number l[1][i] 760 list l[3]: 761 module l[3][i]: vector space basis of the l[1][i]-th graded part 762 of the V-filtration on the Jacobian algebra 763 in terms of l[4] 764 ideal l[4]: monomial vector space basis of the Jacobian algebra 765 ideal l[5]: standard basis of the Jacobian ideal 766 766 @end format 767 767 EXAMPLE: example vfiltjacalg; shows an example
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