Complete classification of perfect lattices in dimension 9
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A full classification of all 2.237.251.040 perfect lattices in dimension 9. Split up into 64 compressed netcdf files with the following dimensions and variables: dimensions: number_ctype = UNLIMITED ; sd = 45 ; hd = 2 ; variables: short form(number_ctype, sd) ; form:long_name = "Perfect form Q canonicalized coordinates (packed)" ; uint minQ(number_ctype) ; minQ:long_name = "|Min(Q)|/2" ; uint scale(number_ctype) ; scale:long_name = "First minimum of form after scaling to integral matrix." ; uint64 uid(number_ctype, hd) ; uid:long_name = "hash/uid used for node allocation and identification" ; uint64 p_uid(number_ctype, hd) ; p_uid:long_name = "Uid of parent form that first found this form" ; double autQ(number_ctype) ; autQ:long_name = "|Aut(Q)|" ; double neighbours(number_ctype) ; neighbours:long_name = "Number of neighbours" ; ubyte processed(number_ctype) ; processed:long_name = "Explored" ; } The "Number of neighbours" is the precise number of adjacent perfect forms when minQ <= 58 and the number of orbits under Aut(Q) when minQ > 58. One can access the data using netCDF utilities that can be found at NetCDF.Alternatively, one can use the python script at AccessPerfectDim9Py to download and query the data.



