The Lattice mcc

An entry from the Catalogue of Lattices, which is a joint project of
Neil J. A. Sloane, AT&T Labs-Research (njas@research.att.com) and
Gabriele Nebe, University of Ulm (nebe@mathematik.uni-ulm.de)

Last modified Thu Sep 7 00:06:10 EDT 2000

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
DET
MINIMAL_NORM
DENSITY
GROUP_ORDER
TRIANGULAR_BASIS
GRAM
GRAM(MAPLE)
GRAM(PARI)
PROPERTIES
NOTES
REFERENCES
EIGENVALUES
THETA_SERIES
LAST_LINE

• NAME
  mcc
  
• DIMENSION
  3
  
• DET
  1
  
• MINIMAL_NORM
  1.20710678118654752440
  
• DENSITY
  .165778630469E+00
  
• GROUP_ORDER
  16
  
• TRIANGULAR_BASIS
  3 3
  .109868411347E+01 .000000000000E+00 .000000000000E+00
  -.455089860701E+00 .999999999939E+00 .000000000000E+00
  -.188504392394E+00 -.585786437865E+00 .910179720963E+00
  
• GRAM
  3 3
  .120710678119E+01 -.500000000153E+00 -.207106781242E+00
  -.500000000153E+00 .120710678119E+01 -.500000000153E+00
  -.207106781242E+00 -.500000000153E+00 .120710678119E+01
  
• GRAM(MAPLE)
  s2:=sqrt(2); linalg[ matrix](
  [ [ 1+s2,-1,-1],[ -1,1+s2,1-s2],[ -1,1-s2,1+s2]])/2;
  
• GRAM(PARI)
  s2=sqrt(2)
  [ 1+s2,-1,-1; -1,1+s2,1-s2; -1,1-s2,1+s2]/2
  
• PROPERTIES
  INTEGRAL =0
  
• NOTES
  The "mean-centered cuboidal" lattice, the densest iso-dual lattice
  in 3 dimensions.
  
• REFERENCES
  1. J. H. Conway and N. J. A. Sloane,
  On Lattices Equivalent to Their Duals,
  J. Number Theory, Vol. 48, 1994, pp. 373-382.
  
  2. M. Bernstein and N. J. A. Sloane
  Some Lattices Obtained from Riemann Surfaces
  in Recent Progress in Riemann Surfaces
  ed. J. Quine, Amer. Math. Soc. Providence, RI 1996 to appear
  
  
• EIGENVALUES
  .120710678119E+01 .999999999877E+00 .828427124452E+00
  
• THETA_SERIES
  0.000000D+00 1
  0.120711D+01 8
  0.141421D+01 4
  0.200000D+01 2
  0.282843D+01 4
  0.341421D+01 8
  0.403553D+01 16
  0.482843D+01 8
  0.520711D+01 8
  0.565685D+01 4
  0.686396D+01 8
  0.707107D+01 8
  0.765685D+01 8
  0.800000D+01 2
  0.803553D+01 16
  0.907107D+01 16
  0.941421D+01 8
  0.969239D+01 16
  
• LAST_LINE
  

INDEX FILE | ABBREVIATIONS

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