6.47.13  Kernel of a linear function: Nullspace

The Nullspace command is the inert form of nullspace. Warning:
The Nullspace command is only useful in Maple mode. (See Section 3.5.2; you can get into Maple mode by hitting the state line red button then Prog style, then choosing Maple and Apply).

• Nullspace takes one argument:
  A, an integer matrix representing a linear function with respect to the standard basis.
• Nullspace(A) mod p returns a list of vectors that is a basis for the kernel of the linear transformation ℤ/pℤ[X].

Examples.

• Input:
  Nullspace([[1,1,2],[2,1,3],[3,1,4]])
  Output:

  nullspace

  ⎛ ⎜ ⎜ ⎝

  ⎡ ⎢ ⎢ ⎣

  1 1 2 2 1 3 3 1 4

  ⎤ ⎥ ⎥ ⎦

  ⎞ ⎟ ⎟ ⎠

• Input (in Maple mode):
  Nullspace([[1,2],[3,1]]) mod 5
  Output:

  ⎡ ⎣

  2,−1

  ⎤ ⎦

  In Xcas mode, the equivalent input is:
  Input (in Xcas mode):
  nullspace([[1,2],[3,1]] % 5)
  Output:

  ⎡ ⎣

  2%5 −1

  ⎤ ⎦