Changeset a5918d in git


Ignore:
Timestamp:
Mar 3, 2021, 10:50:06 PM (3 years ago)
Author:
Hans Schoenemann <hannes@…>
Branches:
(u'fieker-DuVal', '117eb8c30fc9e991c4decca4832b1d19036c4c65')(u'spielwiese', 'd25190065115c859833252500a64cfb7b11e3a50')
Children:
334c8a7f6b196267781ae6344f1c21cbc3e28981
Parents:
2c159393db61218d41d7024bf7e6c7d296ab8652
Message:
doc: @math
Files:
2 edited

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  • Singular/LIB/hodge.lib

    r2c1593 ra5918d  
    88
    99OVERVIEW:
    10 A library for computing the Hodge ideals [MP19] of Q-divisors associated to any reduced hypersurface @math{f \\in R}.
     10A library for computing the Hodge ideals [MP19] of Q-divisors associated to any reduced hypersurface @math{f \in R}.
    1111@* 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].
    1212@* As a consequence, this library provides also an algorithm to compute the multiplier ideals and the jumping numbers of any hypersurface, see [BS05].
     
    2121
    2222PROCEDURES:
    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}.
    2727
    2828SEE ALSO: dmodapp_lib
     
    5050"USAGE:    Vfiltration(f, p [, eng]);     f a poly, p a non-negative integer, eng an optional integer.
    5151RETURN:    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}.
     52PURPOSE:   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}.
    5353NOTE:      activate the output ring with the @code{setring} command.
    5454@*In the output ring, the list @code{Vfilt} contains the @math{V}-filtration.
     
    252252"USAGE:    hodgeIdeals(f, p [, eng]);    f a reduced poly, p a non-negative integer, eng an optional integer.
    253253RETURN:    ring
    254 PURPOSE:   compute the Hodge ideals of @math{f^\\alpha} up to level @math{p}, for a reduced hypersurface @math{f}.
     254PURPOSE:   compute the Hodge ideals of @math{f^\alpha} up to level @math{p}, for a reduced hypersurface @math{f}.
    255255NOTE:      activate the output ring with the @code{setring} command.
    256256@*In the output ring, the list of ideals @code{hodge} contains the Hodge ideals of @math{f}.
     
    338338"USAGE:    multIdeals(f, [, eng]);    f a reduced poly, eng an optional integer.
    339339RETURN:    list
    340 PURPOSE:   compute the multiplier ideals of a hypersurface @math{f \\in R}.
     340PURPOSE:   compute the multiplier ideals of a hypersurface @math{f \in R}.
    341341NOTE:      The value of @code{eng} controls the algorithm used for Groebner basis computations.
    342342@* See the @code{engine} procedure from @ref{dmodapp_lib} for the available algorithms.
     
    377377"USAGE:    nextHodgeIdeal(f, I, p);  f a poly, I an ideal, p a non-negative integer
    378378RETURN:    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 that
     379PURPOSE:   given the @math{p}-th Hodge ideal @math{I} of @math{f^\alpha} compute the @math{p+1}-th Hodge ideal assuming that
    380380@*the Hodge filtration of the underlying mixed Hodge module is generated at level less than or equal to @math{p}.
    381381EXAMPLE:   example nextHodgeIdeal; shows an example
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