kernel(Matrix) -- kernel of a matrix

Synopsis

• Function: kernel

• Usage:

  kernel f

• Inputs:
  • f, a matrix, a map of modules M --> N
• Optional inputs:
  • SubringLimit => ..., default value infinity,
• Outputs:
  • a module, the kernel of f, a submodule of M

Description

i1 : R = ZZ/32003[vars(0..10)]

o1 = R

o1 : PolynomialRing

i2 : M = genericSkewMatrix(R,a,5)

o2 = | 0  a  b  c  d |
     | -a 0  e  f  g |
     | -b -e 0  h  i |
     | -c -f -h 0  j |
     | -d -g -i -j 0 |

             5      5
o2 : Matrix R  <-- R

i3 : ker M

o3 = image {1} | gh-fi+ej  |
           {1} | -dh+ci-bj |
           {1} | df-cg+aj  |
           {1} | -de+bg-ai |
           {1} | ce-bf+ah  |

                             5
o3 : R-module, submodule of R

See also

• syz -- the syzygy matrix
• genericSkewMatrix -- make a generic skew symmetric matrix of variables