Dear Timm, dear GAP Forum, > On 27 Mar 2017, at 09:52, Timm von Puttkamer <tv...@gmx.net> wrote: > > Dear all, > > I have defined some numeric invariant for a group whose value I would like to > save for each finite group in the SmallGroups library so that I do not have > to compute it over and over again. Is there a preferred way to do this in > GAP? My first idea was to set up some database, e.g. SQLite, but it seems GAP > does not offer any SQL database interface directly. Of course I could use > text files, but I want to be able to quickly select groups with specific > values of the invariant and I wish not to reinvent basic database > functionality. > > Kind regards, > Timm
What about the following example, which uses lists to store data, and relies on the fact that i-th entry of the list for groups of order n is the value of the parameter for SmallGroup(n,i) ? Consider the function that returns an average order of the element of a group (this function is taken from the GAP Software Carpentry lesson at http://alex-konovalov.github.io/gap-lesson/): gap> AvgOrd:=function(G) return Sum(List(G,Order))/Size(G); end; function( G ) ... end Now we will compute lists of its values for groups, for example, of orders 8 and 105: gap> d8:=List(AllSmallGroups(8),AvgOrd); [ 43/8, 23/8, 19/8, 27/8, 15/8 ] gap> d105:=List(AllSmallGroups(105),AvgOrd); [ 17, 301/5 ] Then we will store them in a global record, where the names of component correspond to the order of the group: gap> AVG_ORD_DB:=rec( (8):= d8, (105):= d105); rec( 105 := [ 17, 301/5 ], 8 := [ 43/8, 23/8, 19/8, 27/8, 15/8 ] ) Finally, the function `AvgOrdById` will retrieve the value of the parameter from this record, based on the IdGroup(G): gap> AvgOrdById:=function(G) return AVG_ORD_DB.(IdGroup(G)[1])[IdGroup(G)[2]]; end; function( G ) ... end Now you can use it as follows: gap> AllSmallGroups(8, g -> AvgOrdById(g)>3 ); [ <pc group of size 8 with 3 generators>, <pc group of size 8 with 3 generators> ] gap> AllSmallGroups(105, g -> IsInt( AvgOrdById(g) ) ); [ <pc group of size 105 with 3 generators> ] Of course, in this case AvgOrd computes the result quite fast and perhaps it's not worth efforts to create such "database" but I presume that in your case the calculation could be much more expensive, so it may be worth efforts. Further extensions could be: - triggering an error in `AvgOrdById` in case the data for a given order are not available - automation of adding further data to AVG_ORD_DB - splitting AVG_ORD_DB record into multiple files and reading (or unbinding) its components on demand - storing values of parameters retrieved from the database as attributes in groups (so next time one does not even need to perform the lookup for the same object again), etc. I hope that this approach would not only nicely fit into selecting groups with AllSmallGroups, but will also protect from accidental mix-up of using another parameter or a list of parameters for a different order. It will also work for any group for which IdGroup works, although it may be slower - however, groups from the Small Groups Library would already have their IdGroup stored in them, so in this case there will be no overhead. Hope this helps Alexander _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
