  $k\cdot p$ effective Hamiltonian is important for theoretical analysis in
condensed matter physics. Based on the 'kdotp-symmetry' package, we develop an
upgraded package named 'kdotp-generator'. This generator takes in arbitrary
magnetic symmetries with their representations and returns symmetry-allowed
$k\cdot p$ Hamiltonians. Using this package, we calculate $k\cdot p$
Hamiltonians for irreducible corepresentations in 1651 magnetic space groups up
to the third order, and their linear coupling to external fields including the
electromagnetic field and the strain tensor. We hope that the package will
facilitate related research in the future.
