Changeset b324567 in git
- Timestamp:
- Jun 21, 2023, 4:03:31 PM (11 months ago)
- Branches:
- (u'fieker-DuVal', '117eb8c30fc9e991c4decca4832b1d19036c4c65')(u'spielwiese', '38dfc5131670d387a89455159ed1e071997eec94')
- Children:
- 3e5fb164b8ee4bc009257c64c0b7ad6b395d60d5
- Parents:
- b197ee994445c4a01b68b4fefc30a7fb79f36bc1
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-
- 1 edited
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Singular/LIB/sagbiNormaliz.lib
rb197ee9 rb324567 9 9 10 10 OVERVIEW: 11 @texinfo12 11 13 12 The library sagbiNormaliz.lib provides functions for the computations of Sagbi bases. It … … 27 26 directory. The user can overwrite it by setting another name. 28 27 29 @end texinfo30 31 28 KEYWORDS: Sagbi basis, initial algebra 32 29 33 30 PROCEDURES: 34 SagbiGeneral(ideal Q [, int sagbiMaxRounds, int sorting, int verb]) computes the Sagbi basis of the subalgebra of31 sagbiGeneral(ideal Q [, int sagbiMaxRounds, int sorting, int verb]) computes the Sagbi basis of the subalgebra of 35 32 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. 36 33 The optional parameter verb sets the terminal output. Fefault is 1 = on.. 37 34 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 35 sagbiByDegree(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 37 sagbiHilbControlled(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 43 38 generated by the elements of Q is given by its numerator and denominator as a rational 44 39 function. HS_denom_algebra lists the exponents g_i in the factors 1 -t^g_i of the denominator. … … 852 847 The component has a second integer component. Its possible values are: 0, if the full Sagbi basis has 853 848 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 849 EXAMPLE: sagbiHilbControlled; shows an example 856 850 " 857 851 { … … 907 901 908 902 proc 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]); 910 904 RETURN: RETURN: An ideal whose generators form the Sagbi basis of the algebra generated 911 905 by the polynomials inin degrwees <= Sagbi_degree_bound. … … 917 911 not been reached, 1 if this is unknown, and 2 if the full Sagbi basis has been computed. 918 912 919 EXAMPLE: example agbiByDegree; shows an example913 EXAMPLE: example sagbiByDegree; shows an example 920 914 " 921 915 { … … 973 967 974 968 proc 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])); 976 970 RETURN: An ideal whose generators form the Sagbi basis of the algebra generated 977 971 by the polynomials in Q as far as computwed in at most sagbiMaxRounds.
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