Changeset b324567 in git


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Timestamp:
Jun 21, 2023, 4:03:31 PM (11 months ago)
Author:
Hans Schoenemann <hannes@…>
Branches:
(u'fieker-DuVal', '117eb8c30fc9e991c4decca4832b1d19036c4c65')(u'spielwiese', '38dfc5131670d387a89455159ed1e071997eec94')
Children:
3e5fb164b8ee4bc009257c64c0b7ad6b395d60d5
Parents:
b197ee994445c4a01b68b4fefc30a7fb79f36bc1
Message:
doc: sagbiNormal.lib
File:
1 edited

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  • Singular/LIB/sagbiNormaliz.lib

    rb197ee9 rb324567  
    99
    1010OVERVIEW:
    11 @texinfo
    1211
    1312The library sagbiNormaliz.lib provides functions for the computations of Sagbi bases. It
     
    2726directory. The user can overwrite it by setting another name.
    2827
    29 @end texinfo
    30 
    3128KEYWORDS: Sagbi basis, initial algebra
    3229
    3330PROCEDURES:
    34  SagbiGeneral(ideal Q [, int sagbiMaxRounds, int sorting, int verb]) computes the Sagbi basis of the subalgebra of
     31sagbiGeneral(ideal Q [, int sagbiMaxRounds, int sorting, int verb]) computes the Sagbi basis of the subalgebra of
    3532                              the current polynomial ring that is generated by the elements of Q. The computation is stopped after at most sagbiMaxRounds rounds if trhe parameter is set. If sorting is set, the  compouted elements are degrevlex sorted before a round of the algorithm.
    3633                              The optional parameter verb sets the terminal output. Fefault is 1 = on..
    3734
    38 sagbiByDegree(ideal Q, int Sagbi_degree_bound, , [,int sorting, int verb])
    39                               computes the Sagbi basis degree by degree until thwe degree bound is reached or the Sagbi basis has been computed compltely.
    40 
    41  SagbiHilbControlled(ideal Q, intvec HS_num_algebra, intvec HS_denom_algebra, int Sagbi_degree_bound[, int finalCheck, int sorting, int verb])
    42                               computes the Sagbi basis up to the degree bound. The Hilbert series of the subalgebra
     35sagbiByDegree(ideal Q, int Sagbi_degree_bound,[,int sorting, int verb]) computes the Sagbi basis degree by degree until thwe degree bound is reached or the Sagbi basis has been computed compltely.
     36
     37sagbiHilbControlled(ideal Q, intvec HS_num_algebra, intvec HS_denom_algebra, int Sagbi_degree_bound[, int finalCheck, int sorting, int verb]) computes the Sagbi basis up to the degree bound. The Hilbert series of the subalgebra
    4338                              generated by the elements of Q is given by its numerator and denominator as a rational
    4439                              function. HS_denom_algebra lists the exponents g_i in the factors 1 -t^g_i of the denominator.
     
    852847          The component has a second integer component. Its possible values are: 0, if the full Sagbi basis has
    853848          not been reached, 1 if this is unknown, and 2 if the full Sagbi basis has been computed.
    854 
    855 EXAMPLE:  SagbiHilbControlled; shows an example
     849EXAMPLE:  sagbiHilbControlled; shows an example
    856850"
    857851{
     
    907901
    908902proc sagbiByDegree(ideal Q, int Sagbi_degree_bound, list #)
    909 "USAGE:   SagbiGeneral(ideal Q, int sagbiDegreeBound [,int sorting, int verb]);
     903"USAGE:   sagbiByDegree(ideal Q, int sagbiDegreeBound [,int sorting, int verb]);
    910904RETURN:   RETURN:   An ideal whose generators form the Sagbi basis of the algebra generated
    911905          by the polynomials inin degrwees <= Sagbi_degree_bound.
     
    917911          not been reached, 1 if this is unknown, and 2 if the full Sagbi basis has been computed.
    918912
    919 EXAMPLE:  example agbiByDegree; shows an example
     913EXAMPLE:  example sagbiByDegree; shows an example
    920914"
    921915{
     
    973967
    974968proc sagbiGeneral(ideal Q, list #)
    975 "USAGE:   SagbiGeneral(ideal Q [, int sagbiMaxRounds, int sorting, int verb]));
     969"USAGE:   sagbiGeneral(ideal Q [, int sagbiMaxRounds, int sorting, int verb]));
    976970RETURN:   An ideal whose generators form the Sagbi basis of the algebra generated
    977971          by the polynomials in Q as far as computwed in at most sagbiMaxRounds.
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