Changeset b8973d in git
- Timestamp:
- Apr 14, 2009, 11:55:34 AM (14 years ago)
- Branches:
- (u'jengelh-datetime', 'ceac47cbc86fe4a15902392bdbb9bd2ae0ea02c6')(u'spielwiese', 'f875bbaccd0831e36aaed09ff6adeb3eb45aeb94')
- Children:
- 346b725eab88cd8b630daf32c263f1068708f2c0
- Parents:
- c13ff567ed904c82c5b40b8d18a42a7c5275627a
- Files:
-
- 2 edited
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Singular/LIB/standard.lib
rc13ff56 rb8973d 5 5 //### Todo: im lokalen Fall die Hilbert-Samuel Funktion verwenden 6 6 ////////////////////////////////////////////////////////////////////////////// 7 version="$Id: standard.lib,v 1.10 7 2009-02-12 13:31:40 SingularExp $";7 version="$Id: standard.lib,v 1.108 2009-04-14 09:54:52 seelisch Exp $"; 8 8 category="Miscellaneous"; 9 9 info=" … … 157 157 PURPOSE: Compute a Groebner basis of the ideal/module in the basering by 158 158 using the Hilbert driven Groebner basis algorithm. 159 If an argument of type string @code{\"std\"} resp. @code{\"slimgb\"}159 If an argument of type string, stating @code{\"std\"} resp. @code{\"slimgb\"}, 160 160 is given, the standard basis computation uses @code{std} or 161 161 @code{slimgb}, otherwise a heuristically chosen method (default)@* … … 170 170 w does not coincide with the variable weights of the basering, the 171 171 result may not be a groebner basis in the original ring. 172 NOTE: ' homogeneous' means weighted homogeneous with respect to the weights172 NOTE: 'Homogeneous' means weighted homogeneous with respect to the weights 173 173 w[i] of the variables var(i) of the basering. Parameters are not 174 174 converted to variables. … … 807 807 @code{groebner (} module_expression @code{)} @* 808 808 @code{groebner (} ideal_expression@code{,} int_expression @code{)} @* 809 @code{groebner (} module_expression@code{,} int_expression @code{)} 809 @code{groebner (} module_expression@code{,} int_expression @code{)} @* 810 810 @code{groebner (} ideal_expression@code{,} list of string_expressions 811 811 @code{)} @* 812 812 @code{groebner (} ideal_expression@code{,} list of string_expressions 813 813 and int_expression @code{)} @* 814 @code{groebner (} ideal_expression@code{,} int_expression @code{)} @*814 @code{groebner (} ideal_expression@code{,} int_expression @code{)} 815 815 TYPE: type of the first argument 816 816 PURPOSE: computes a standard basis of the first argument @code{I} 817 (ideal or module) ,by a heuristically chosen method (default)817 (ideal or module) by a heuristically chosen method (default) 818 818 or by a method specified by further arguments of type string. 819 819 Possible methods are: @* 820 820 - the direct methods @code{\"std\"} or @code{\"slimgb\"} without 821 conversion @*821 conversion, @* 822 822 - conversion methods @code{\"hilb\"} or @code{\"fglm\"} where 823 823 a Groebner basis is first computed with an \"easy\" ordering … … 826 826 The actual computation of the Groebner basis can be 827 827 specified by @code{\"std\"} or by @code{\"slimgb\"} 828 (not implemented for all orderings)@*828 (not for all orderings implemented). @* 829 829 A further string @code{\"par2var\"} converts parameters to an extra 830 830 block of variables before a Groebner basis computation (and 831 831 afterwards back). 832 @code{option(prot)} tells about the chosen method.833 NOTE: If a furtherargument, say @code{wait}, of type int is given,834 then the computation proceedsat most @code{wait} seconds.832 @code{option(prot)} informs about the chosen method. 833 NOTE: If an additional argument, say @code{wait}, of type int is given, 834 then the computation runs for at most @code{wait} seconds. 835 835 That is, if no result could be computed in @code{wait} seconds, 836 836 then the computation is interrupted, 0 is returned, a warning 837 837 message is displayed, and the global variable 838 838 @code{Standard::groebner_error} is defined. 839 This feature uses MP and is hence only available on UNIX platforms.839 This feature uses MP and hence it is available on UNIX platforms, only. 840 840 HINT: Since there exists no uniform best method for computing standard 841 841 bases, and since the difference in performance of a method on … … 1319 1319 computes a (possibly minimal) free resolution of an ideal or module using 1320 1320 a heuristically chosen method. 1321 @* The second (int) argument (say ,@code{k}) specifies the length of1321 @* The second (int) argument (say @code{k}) specifies the length of 1322 1322 the resolution. If it is not positive then @code{k} is assumed to be the 1323 1323 number of variables of the basering. … … 1340 1340 @end table 1341 1341 @item @strong{Note:} 1342 Accessing single elements of a resolution may require thatsome partial1343 computations haveto be finished and may therefore take some time.1342 Accessing single elements of a resolution may require some partial 1343 computations to be finished and may therefore take some time. 1344 1344 @end table 1345 1345 @c ref … … 1747 1747 The control string @code{fmt} is simply text to be copied, 1748 1748 except that the string may contain conversion specifications.@* 1749 Do@code{help print;} for a listing of valid conversion1749 Type @code{help print;} for a listing of valid conversion 1750 1750 specifications. As an addition to the conversions of @code{print}, 1751 1751 the @code{%n} and @code{%2} conversion specification does not … … 1753 1753 character. 1754 1754 NOTE: If one of the additional arguments is a list, then it should be 1755 enclosed once more into a@code{list()} command, since passing a list1755 wrapped in an additional @code{list()} command, since passing a list 1756 1756 as an argument flattens the list by one level. 1757 1757 SEE ALSO: fprintf, printf, print, string … … 1836 1836 The control string @code{fmt} is simply text to be copied, except 1837 1837 that the string may contain conversion specifications. @* 1838 Do@code{help print;} for a listing of valid conversion1838 Type @code{help print;} for a listing of valid conversion 1839 1839 specifications. As an addition to the conversions of @code{print}, 1840 1840 the @code{%n} and @code{%2} conversion specification does not … … 1878 1878 The control string @code{fmt} is simply text to be copied, except 1879 1879 that the string may contain conversion specifications.@* 1880 Do@code{help print;} for a listing of valid conversion1880 Type @code{help print;} for a listing of valid conversion 1881 1881 specifications. As an addition to the conversions of @code{print}, 1882 1882 the @code{%n} and @code{%2} conversion specification does not … … 1950 1950 @code{wim[1]} weights for all variables (positive), 1951 1951 @code{wim[2]} weights for the module generators. 1952 NOTE: This is a generali sation forthe command @code{kbase} with the same1952 NOTE: This is a generalization of the command @code{kbase} with the same 1953 1953 first two arguments. 1954 1954 SEE ALSO: kbase
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