Changeset a5918d in git
 Timestamp:
 Mar 3, 2021, 10:50:06 PM (3 years ago)
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 (u'fiekerDuVal', '117eb8c30fc9e991c4decca4832b1d19036c4c65')(u'spielwiese', 'd25190065115c859833252500a64cfb7b11e3a50')
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 334c8a7f6b196267781ae6344f1c21cbc3e28981
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 2c159393db61218d41d7024bf7e6c7d296ab8652
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 2 edited
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Singular/LIB/hodge.lib
r2c1593 ra5918d 8 8 9 9 OVERVIEW: 10 A library for computing the Hodge ideals [MP19] of Qdivisors associated to any reduced hypersurface @math{f \ \in R}.10 A library for computing the Hodge ideals [MP19] of Qdivisors associated to any reduced hypersurface @math{f \in R}. 11 11 @* The implemented algorithm [Bla21] is based on the characterization of the Hodge ideals in terms of the @math{V}filtration of Malgrange and Kashiwara on @math{R_f f^s}, see [MP20]. 12 12 @* As a consequence, this library provides also an algorithm to compute the multiplier ideals and the jumping numbers of any hypersurface, see [BS05]. … … 21 21 22 22 PROCEDURES: 23 Vfiltration(f, p [, eng]); compute @math{R}generators for the @math{V}filtration on @math{R_f f^s} truncated up to degree @math{p} in @math{\ \partial_t}.24 hodgeIdeals(f, p [, eng]); compute the Hodge ideals of @math{f^\ \alpha} up to level @math{p}, for a reduced hypersurface @math{f \\in R}.25 multIdeals(f, p [, eng]); compute the multiplier ideals of a hypersurface @math{f \ \in R}.26 nextHodgeIdeal(f, I, p); given the @math{p}th Hodge ideal @math{I} of @math{f^\ \alpha} compute the @math{p+1}th Hodge ideal assuming that the Hodge filtration of the underlying mixed Hodge module is generated at level less than or equal to @math{p}.23 Vfiltration(f, p [, eng]); compute @math{R}generators for the @math{V}filtration on @math{R_f f^s} truncated up to degree @math{p} in @math{\partial_t}. 24 hodgeIdeals(f, p [, eng]); compute the Hodge ideals of @math{f^\alpha} up to level @math{p}, for a reduced hypersurface @math{f \in R}. 25 multIdeals(f, p [, eng]); compute the multiplier ideals of a hypersurface @math{f \in R}. 26 nextHodgeIdeal(f, I, p); given the @math{p}th Hodge ideal @math{I} of @math{f^\alpha} compute the @math{p+1}th Hodge ideal assuming that the Hodge filtration of the underlying mixed Hodge module is generated at level less than or equal to @math{p}. 27 27 28 28 SEE ALSO: dmodapp_lib … … 50 50 "USAGE: Vfiltration(f, p [, eng]); f a poly, p a nonnegative integer, eng an optional integer. 51 51 RETURN: ring 52 PURPOSE: compute @math{R}generators for the @math{V}filtration on @math{R_f f^s} truncated up to degree @math{p} in @math{\ \partial_t}.52 PURPOSE: compute @math{R}generators for the @math{V}filtration on @math{R_f f^s} truncated up to degree @math{p} in @math{\partial_t}. 53 53 NOTE: activate the output ring with the @code{setring} command. 54 54 @*In the output ring, the list @code{Vfilt} contains the @math{V}filtration. … … 252 252 "USAGE: hodgeIdeals(f, p [, eng]); f a reduced poly, p a nonnegative integer, eng an optional integer. 253 253 RETURN: ring 254 PURPOSE: compute the Hodge ideals of @math{f^\ \alpha} up to level @math{p}, for a reduced hypersurface @math{f}.254 PURPOSE: compute the Hodge ideals of @math{f^\alpha} up to level @math{p}, for a reduced hypersurface @math{f}. 255 255 NOTE: activate the output ring with the @code{setring} command. 256 256 @*In the output ring, the list of ideals @code{hodge} contains the Hodge ideals of @math{f}. … … 338 338 "USAGE: multIdeals(f, [, eng]); f a reduced poly, eng an optional integer. 339 339 RETURN: list 340 PURPOSE: compute the multiplier ideals of a hypersurface @math{f \ \in R}.340 PURPOSE: compute the multiplier ideals of a hypersurface @math{f \in R}. 341 341 NOTE: The value of @code{eng} controls the algorithm used for Groebner basis computations. 342 342 @* See the @code{engine} procedure from @ref{dmodapp_lib} for the available algorithms. … … 377 377 "USAGE: nextHodgeIdeal(f, I, p); f a poly, I an ideal, p a nonnegative integer 378 378 RETURN: ideal 379 PURPOSE: given the @math{p}th Hodge ideal @math{I} of @math{f^\ \alpha} compute the @math{p+1}th Hodge ideal assuming that379 PURPOSE: given the @math{p}th Hodge ideal @math{I} of @math{f^\alpha} compute the @math{p+1}th Hodge ideal assuming that 380 380 @*the Hodge filtration of the underlying mixed Hodge module is generated at level less than or equal to @math{p}. 381 381 EXAMPLE: example nextHodgeIdeal; shows an example
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