Macaulay2 » Documentation
Packages » PencilsOfQuadrics :: symMatrix
next | previous | forward | backward | up | index | toc

# symMatrix -- part of a CliffordModule

- Usage:
    `s = symMatrix(eOdd,eEv)`
- Inputs:
  - eOdd, a list,
  - eEv, a list, operators on a Clifford Module
- Outputs:
  - s, a matrix, over k[s,t], the base of the Clifford algebra

## Description

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

    i1 : kk = ZZ/101

    o1 = kk

    o1 : QuotientRing

    i2 : setRandomSeed 0
     -- setting random seed to 0

    o2 = 0

    i3 : g = 1

    o3 = 1

    i4 : (S, qq,  R,  u, M1, M2, Mu1, Mu2)=randomNicePencil(kk,g);

    i5 : M = cliffordModule(M1,M2, R)

    o5 = CliffordModule{...6...}

    o5 : CliffordModule

    i6 : M.evenOperators

    o6 = {{-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    |

    o6 : List

    i7 : symMatrix(M.evenOperators,M.oddOperators)

    o7 = | -5t  -50s 6t     -6t  |
         | -50s 0    -9t    5t   |
         | 6t   -9t  -s-30t 3t   |
         | -6t  5t   3t     -48t |

                 4      4
    o7 : Matrix R  <-- R

## See also

- evenOperators -- part of a CliffordModule
- oddOperators -- part of a CliffordModule
- oddCenter -- part of a CliffordModule
- oddCenter -- part of a CliffordModule
- hyperellipticBranchEquation -- part of a CliffordModule

## For the programmer

The object symMatrix is a function closure.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/PencilsOfQuadrics.m2:2286:0.