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PencilsOfQuadrics :: symMatrix

symMatrix -- part of a CliffordModule

Synopsis

Description

Computes the matrix given by the pencil of quadrics defining the Clifford algebra.

i1 : kk = ZZ/101

o1 = kk

o1 : QuotientRing
i2 : g = 1

o2 = 1
i3 : (S, qq,  R,  u, M1, M2, Mu1, Mu2)=randomNicePencil(kk,g);
i4 : M = cliffordModule(M1,M2, R)

o4 = CliffordModule{...6...}

o4 : CliffordModule
i5 : M.evenOperators

o5 = {{-1} | 0  0  0 -1 0  0   0  0  |, {-1} | 0  0  0 0 0  -1 0  0  |, {-1}
      {-1} | 0  0  1 0  0  0   0  0  |  {-1} | 0  0  0 0 1  0  0  0  |  {-1}
      {-1} | 0  -1 0 0  0  0   0  0  |  {-1} | 0  0  0 0 0  0  0  0  |  {-1}
      {-1} | 0  0  0 0  0  0   0  5t |  {-1} | 0  -1 0 0 0  0  0  -s |  {-1}
      {-2} | -1 0  0 0  0  0   0  0  |  {-2} | 0  0  0 0 0  0  0  0  |  {-2}
      {-2} | 0  0  0 0  0  0   5t 0  |  {-2} | -1 0  0 0 0  0  -s 0  |  {-2}
      {-2} | 0  0  0 0  0  -5t 0  0  |  {-2} | 0  0  0 0 0  s  0  0  |  {-2}
      {-2} | 0  0  0 0  5t 0   0  0  |  {-2} | 0  0  0 0 -s 0  0  0  |  {-2}
     ------------------------------------------------------------------------
     | 0  0     0    0      0    0     -1   0     |, {-1} | 0  0    0   0   
     | 0  0     0    0      0    0     0    s+30t |  {-1} | 0  0    0   0   
     | 0  0     0    0      1    0     0    -18t  |  {-1} | 0  0    0   0   
     | 0  0     -1   0      0    0     0    -12t  |  {-1} | 0  0    0   -1  
     | 0  0     0    0      0    s+30t -18t 0     |  {-2} | 0  0    0   0   
     | 0  0     0    -s-30t 0    0     -12t 0     |  {-2} | 0  0    48t 6t  
     | -1 0     0    18t    0    12t   0    0     |  {-2} | 0  -48t 0   -10t
     | 0  s+30t -18t 0      -12t 0     0    0     |  {-2} | -1 -6t  10t 0   
     ------------------------------------------------------------------------
     0    0    0   -48t |}
     0    0    -1  -6t  |
     0    1    0   10t  |
     0    0    0   12t  |
     -48t -6t  10t 0    |
     0    0    12t 0    |
     0    -12t 0   0    |
     12t  0    0   0    |

o5 : List
i6 : symMatrix(M.evenOperators,M.oddOperators)

o6 = | -5t  -50s 6t     -6t  |
     | -50s 0    -9t    5t   |
     | 6t   -9t  -s-30t 3t   |
     | -6t  5t   3t     -48t |

             4       4
o6 : Matrix R  <--- R

See also

For the programmer

The object symMatrix is a function closure.