An entry from the Catalogue of Lattices, which is a joint project of
Gabriele Nebe, RWTH Aachen University (nebe@math.rwth-aachen.de) and
Neil J. A. Sloane (njasloane@gmail.com)

Last modified Fri Jul 18 13:25:09 CEST 2014

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
DET
BASIS
GLUE_VECTORS
GRAM
PROPERTIES
NOTES
REFERENCES
LAST_LINE

• NAME
  P7.1
  

• DIMENSION
  7
  

• DET
  .200000000000E+01
  

• BASIS
  7 8
  -.100000000000E+01 .100000000000E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00
  .000000000000E+00 -.100000000000E+01 .100000000000E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 -.100000000000E+01
  .100000000000E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  -.100000000000E+01 .100000000000E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 -.100000000000E+01 .100000000000E+01
  .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 -.100000000000E+01
  .100000000000E+01 .000000000000E+00
  .500000000000E+00 .500000000000E+00 .500000000000E+00
  .500000000000E+00 -.500000000000E+00 -.500000000000E+00
  -.500000000000E+00 -.500000000000E+00
  

• GLUE_VECTORS
  2
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00
  .250000000000E+00 .250000000000E+00 .250000000000E+00
  .250000000000E+00 .250000000000E+00 .250000000000E+00
  -.750000000000E+00 -.750000000000E+00
  

• GRAM
  7 7
  2 -1 0 0 0 0 0
  -1 2 -1 0 0 0 0
  0 -1 2 -1 0 0 0
  0 0 -1 2 -1 0 -1
  0 0 0 -1 2 -1 0
  0 0 0 0 -1 2 0
  0 0 0 -1 0 0 2
  

• PROPERTIES
  INTEGRAL =1
  

• NOTES
  One of the perfect 7-dimensional lattices.
  This is E7.
  

• REFERENCES
  Conway & Sloane, Low-dimensional lattices III: perfect forms,
  Proc. Royal Soc. A 418 (1988), 43-80.
  Jaquet, Enumeration complete des classes de formes parfaites en dimension 7,
  Ann. Inst. Fourier 43 (1993), 21-55.
  

• LAST_LINE
  

  ---

  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe