Degree 2 enriched vector Galerkin on a hexahedron

\(\displaystyle \boldsymbol{\phi}_{0} = \left(\begin{array}{c}\displaystyle 8 x^{2} y^{2} z^{2} - 12 x^{2} y^{2} z + 4 x^{2} y^{2} - 12 x^{2} y z^{2} + 18 x^{2} y z - 6 x^{2} y + 4 x^{2} z^{2} - 6 x^{2} z + 2 x^{2} - 12 x y^{2} z^{2} + 18 x y^{2} z - 6 x y^{2} + 18 x y z^{2} - 27 x y z + 9 x y - 6 x z^{2} + 9 x z - 3 x + 4 y^{2} z^{2} - 6 y^{2} z + 2 y^{2} - 6 y z^{2} + 9 y z - 3 y + 2 z^{2} - 3 z + 1\\\displaystyle 0\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{1} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 8 x^{2} y^{2} z^{2} - 12 x^{2} y^{2} z + 4 x^{2} y^{2} - 12 x^{2} y z^{2} + 18 x^{2} y z - 6 x^{2} y + 4 x^{2} z^{2} - 6 x^{2} z + 2 x^{2} - 12 x y^{2} z^{2} + 18 x y^{2} z - 6 x y^{2} + 18 x y z^{2} - 27 x y z + 9 x y - 6 x z^{2} + 9 x z - 3 x + 4 y^{2} z^{2} - 6 y^{2} z + 2 y^{2} - 6 y z^{2} + 9 y z - 3 y + 2 z^{2} - 3 z + 1\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{2} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 0\\\displaystyle 8 x^{2} y^{2} z^{2} - 12 x^{2} y^{2} z + 4 x^{2} y^{2} - 12 x^{2} y z^{2} + 18 x^{2} y z - 6 x^{2} y + 4 x^{2} z^{2} - 6 x^{2} z + 2 x^{2} - 12 x y^{2} z^{2} + 18 x y^{2} z - 6 x y^{2} + 18 x y z^{2} - 27 x y z + 9 x y - 6 x z^{2} + 9 x z - 3 x + 4 y^{2} z^{2} - 6 y^{2} z + 2 y^{2} - 6 y z^{2} + 9 y z - 3 y + 2 z^{2} - 3 z + 1\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{3} = \left(\begin{array}{c}\displaystyle x \left(8 x y^{2} z^{2} - 12 x y^{2} z + 4 x y^{2} - 12 x y z^{2} + 18 x y z - 6 x y + 4 x z^{2} - 6 x z + 2 x - 4 y^{2} z^{2} + 6 y^{2} z - 2 y^{2} + 6 y z^{2} - 9 y z + 3 y - 2 z^{2} + 3 z - 1\right)\\\displaystyle 0\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{4} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle x \left(8 x y^{2} z^{2} - 12 x y^{2} z + 4 x y^{2} - 12 x y z^{2} + 18 x y z - 6 x y + 4 x z^{2} - 6 x z + 2 x - 4 y^{2} z^{2} + 6 y^{2} z - 2 y^{2} + 6 y z^{2} - 9 y z + 3 y - 2 z^{2} + 3 z - 1\right)\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{5} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 0\\\displaystyle x \left(8 x y^{2} z^{2} - 12 x y^{2} z + 4 x y^{2} - 12 x y z^{2} + 18 x y z - 6 x y + 4 x z^{2} - 6 x z + 2 x - 4 y^{2} z^{2} + 6 y^{2} z - 2 y^{2} + 6 y z^{2} - 9 y z + 3 y - 2 z^{2} + 3 z - 1\right)\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{6} = \left(\begin{array}{c}\displaystyle y \left(8 x^{2} y z^{2} - 12 x^{2} y z + 4 x^{2} y - 4 x^{2} z^{2} + 6 x^{2} z - 2 x^{2} - 12 x y z^{2} + 18 x y z - 6 x y + 6 x z^{2} - 9 x z + 3 x + 4 y z^{2} - 6 y z + 2 y - 2 z^{2} + 3 z - 1\right)\\\displaystyle 0\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{7} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle y \left(8 x^{2} y z^{2} - 12 x^{2} y z + 4 x^{2} y - 4 x^{2} z^{2} + 6 x^{2} z - 2 x^{2} - 12 x y z^{2} + 18 x y z - 6 x y + 6 x z^{2} - 9 x z + 3 x + 4 y z^{2} - 6 y z + 2 y - 2 z^{2} + 3 z - 1\right)\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{8} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 0\\\displaystyle y \left(8 x^{2} y z^{2} - 12 x^{2} y z + 4 x^{2} y - 4 x^{2} z^{2} + 6 x^{2} z - 2 x^{2} - 12 x y z^{2} + 18 x y z - 6 x y + 6 x z^{2} - 9 x z + 3 x + 4 y z^{2} - 6 y z + 2 y - 2 z^{2} + 3 z - 1\right)\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{9} = \left(\begin{array}{c}\displaystyle x y \left(8 x y z^{2} - 12 x y z + 4 x y - 4 x z^{2} + 6 x z - 2 x - 4 y z^{2} + 6 y z - 2 y + 2 z^{2} - 3 z + 1\right)\\\displaystyle 0\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{10} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle x y \left(8 x y z^{2} - 12 x y z + 4 x y - 4 x z^{2} + 6 x z - 2 x - 4 y z^{2} + 6 y z - 2 y + 2 z^{2} - 3 z + 1\right)\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{11} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 0\\\displaystyle x y \left(8 x y z^{2} - 12 x y z + 4 x y - 4 x z^{2} + 6 x z - 2 x - 4 y z^{2} + 6 y z - 2 y + 2 z^{2} - 3 z + 1\right)\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{12} = \left(\begin{array}{c}\displaystyle z \left(8 x^{2} y^{2} z - 4 x^{2} y^{2} - 12 x^{2} y z + 6 x^{2} y + 4 x^{2} z - 2 x^{2} - 12 x y^{2} z + 6 x y^{2} + 18 x y z - 9 x y - 6 x z + 3 x + 4 y^{2} z - 2 y^{2} - 6 y z + 3 y + 2 z - 1\right)\\\displaystyle 0\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{13} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle z \left(8 x^{2} y^{2} z - 4 x^{2} y^{2} - 12 x^{2} y z + 6 x^{2} y + 4 x^{2} z - 2 x^{2} - 12 x y^{2} z + 6 x y^{2} + 18 x y z - 9 x y - 6 x z + 3 x + 4 y^{2} z - 2 y^{2} - 6 y z + 3 y + 2 z - 1\right)\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{14} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 0\\\displaystyle z \left(8 x^{2} y^{2} z - 4 x^{2} y^{2} - 12 x^{2} y z + 6 x^{2} y + 4 x^{2} z - 2 x^{2} - 12 x y^{2} z + 6 x y^{2} + 18 x y z - 9 x y - 6 x z + 3 x + 4 y^{2} z - 2 y^{2} - 6 y z + 3 y + 2 z - 1\right)\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{15} = \left(\begin{array}{c}\displaystyle x z \left(8 x y^{2} z - 4 x y^{2} - 12 x y z + 6 x y + 4 x z - 2 x - 4 y^{2} z + 2 y^{2} + 6 y z - 3 y - 2 z + 1\right)\\\displaystyle 0\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{16} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle x z \left(8 x y^{2} z - 4 x y^{2} - 12 x y z + 6 x y + 4 x z - 2 x - 4 y^{2} z + 2 y^{2} + 6 y z - 3 y - 2 z + 1\right)\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{17} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 0\\\displaystyle x z \left(8 x y^{2} z - 4 x y^{2} - 12 x y z + 6 x y + 4 x z - 2 x - 4 y^{2} z + 2 y^{2} + 6 y z - 3 y - 2 z + 1\right)\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{18} = \left(\begin{array}{c}\displaystyle y z \left(8 x^{2} y z - 4 x^{2} y - 4 x^{2} z + 2 x^{2} - 12 x y z + 6 x y + 6 x z - 3 x + 4 y z - 2 y - 2 z + 1\right)\\\displaystyle 0\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{19} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle y z \left(8 x^{2} y z - 4 x^{2} y - 4 x^{2} z + 2 x^{2} - 12 x y z + 6 x y + 6 x z - 3 x + 4 y z - 2 y - 2 z + 1\right)\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{20} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 0\\\displaystyle y z \left(8 x^{2} y z - 4 x^{2} y - 4 x^{2} z + 2 x^{2} - 12 x y z + 6 x y + 6 x z - 3 x + 4 y z - 2 y - 2 z + 1\right)\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{21} = \left(\begin{array}{c}\displaystyle x y z \left(8 x y z - 4 x y - 4 x z + 2 x - 4 y z + 2 y + 2 z - 1\right)\\\displaystyle 0\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{22} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle x y z \left(8 x y z - 4 x y - 4 x z + 2 x - 4 y z + 2 y + 2 z - 1\right)\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{23} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 0\\\displaystyle x y z \left(8 x y z - 4 x y - 4 x z + 2 x - 4 y z + 2 y + 2 z - 1\right)\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{24} = \left(\begin{array}{c}\displaystyle 4 x \left(- 4 x y^{2} z^{2} + 6 x y^{2} z - 2 x y^{2} + 6 x y z^{2} - 9 x y z + 3 x y - 2 x z^{2} + 3 x z - x + 4 y^{2} z^{2} - 6 y^{2} z + 2 y^{2} - 6 y z^{2} + 9 y z - 3 y + 2 z^{2} - 3 z + 1\right)\\\displaystyle 0\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{25} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 4 x \left(- 4 x y^{2} z^{2} + 6 x y^{2} z - 2 x y^{2} + 6 x y z^{2} - 9 x y z + 3 x y - 2 x z^{2} + 3 x z - x + 4 y^{2} z^{2} - 6 y^{2} z + 2 y^{2} - 6 y z^{2} + 9 y z - 3 y + 2 z^{2} - 3 z + 1\right)\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{26} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 0\\\displaystyle 4 x \left(- 4 x y^{2} z^{2} + 6 x y^{2} z - 2 x y^{2} + 6 x y z^{2} - 9 x y z + 3 x y - 2 x z^{2} + 3 x z - x + 4 y^{2} z^{2} - 6 y^{2} z + 2 y^{2} - 6 y z^{2} + 9 y z - 3 y + 2 z^{2} - 3 z + 1\right)\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{27} = \left(\begin{array}{c}\displaystyle 4 y \left(- 4 x^{2} y z^{2} + 6 x^{2} y z - 2 x^{2} y + 4 x^{2} z^{2} - 6 x^{2} z + 2 x^{2} + 6 x y z^{2} - 9 x y z + 3 x y - 6 x z^{2} + 9 x z - 3 x - 2 y z^{2} + 3 y z - y + 2 z^{2} - 3 z + 1\right)\\\displaystyle 0\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{28} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 4 y \left(- 4 x^{2} y z^{2} + 6 x^{2} y z - 2 x^{2} y + 4 x^{2} z^{2} - 6 x^{2} z + 2 x^{2} + 6 x y z^{2} - 9 x y z + 3 x y - 6 x z^{2} + 9 x z - 3 x - 2 y z^{2} + 3 y z - y + 2 z^{2} - 3 z + 1\right)\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{29} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 0\\\displaystyle 4 y \left(- 4 x^{2} y z^{2} + 6 x^{2} y z - 2 x^{2} y + 4 x^{2} z^{2} - 6 x^{2} z + 2 x^{2} + 6 x y z^{2} - 9 x y z + 3 x y - 6 x z^{2} + 9 x z - 3 x - 2 y z^{2} + 3 y z - y + 2 z^{2} - 3 z + 1\right)\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{30} = \left(\begin{array}{c}\displaystyle 4 z \left(- 4 x^{2} y^{2} z + 4 x^{2} y^{2} + 6 x^{2} y z - 6 x^{2} y - 2 x^{2} z + 2 x^{2} + 6 x y^{2} z - 6 x y^{2} - 9 x y z + 9 x y + 3 x z - 3 x - 2 y^{2} z + 2 y^{2} + 3 y z - 3 y - z + 1\right)\\\displaystyle 0\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{31} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 4 z \left(- 4 x^{2} y^{2} z + 4 x^{2} y^{2} + 6 x^{2} y z - 6 x^{2} y - 2 x^{2} z + 2 x^{2} + 6 x y^{2} z - 6 x y^{2} - 9 x y z + 9 x y + 3 x z - 3 x - 2 y^{2} z + 2 y^{2} + 3 y z - 3 y - z + 1\right)\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{32} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 0\\\displaystyle 4 z \left(- 4 x^{2} y^{2} z + 4 x^{2} y^{2} + 6 x^{2} y z - 6 x^{2} y - 2 x^{2} z + 2 x^{2} + 6 x y^{2} z - 6 x y^{2} - 9 x y z + 9 x y + 3 x z - 3 x - 2 y^{2} z + 2 y^{2} + 3 y z - 3 y - z + 1\right)\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{33} = \left(\begin{array}{c}\displaystyle 4 x y \left(- 4 x y z^{2} + 6 x y z - 2 x y + 4 x z^{2} - 6 x z + 2 x + 2 y z^{2} - 3 y z + y - 2 z^{2} + 3 z - 1\right)\\\displaystyle 0\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{34} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 4 x y \left(- 4 x y z^{2} + 6 x y z - 2 x y + 4 x z^{2} - 6 x z + 2 x + 2 y z^{2} - 3 y z + y - 2 z^{2} + 3 z - 1\right)\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{35} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 0\\\displaystyle 4 x y \left(- 4 x y z^{2} + 6 x y z - 2 x y + 4 x z^{2} - 6 x z + 2 x + 2 y z^{2} - 3 y z + y - 2 z^{2} + 3 z - 1\right)\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{36} = \left(\begin{array}{c}\displaystyle 4 x z \left(- 4 x y^{2} z + 4 x y^{2} + 6 x y z - 6 x y - 2 x z + 2 x + 2 y^{2} z - 2 y^{2} - 3 y z + 3 y + z - 1\right)\\\displaystyle 0\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{37} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 4 x z \left(- 4 x y^{2} z + 4 x y^{2} + 6 x y z - 6 x y - 2 x z + 2 x + 2 y^{2} z - 2 y^{2} - 3 y z + 3 y + z - 1\right)\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{38} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 0\\\displaystyle 4 x z \left(- 4 x y^{2} z + 4 x y^{2} + 6 x y z - 6 x y - 2 x z + 2 x + 2 y^{2} z - 2 y^{2} - 3 y z + 3 y + z - 1\right)\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{39} = \left(\begin{array}{c}\displaystyle 4 x y \left(- 4 x y z^{2} + 6 x y z - 2 x y + 2 x z^{2} - 3 x z + x + 4 y z^{2} - 6 y z + 2 y - 2 z^{2} + 3 z - 1\right)\\\displaystyle 0\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{40} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 4 x y \left(- 4 x y z^{2} + 6 x y z - 2 x y + 2 x z^{2} - 3 x z + x + 4 y z^{2} - 6 y z + 2 y - 2 z^{2} + 3 z - 1\right)\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{41} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 0\\\displaystyle 4 x y \left(- 4 x y z^{2} + 6 x y z - 2 x y + 2 x z^{2} - 3 x z + x + 4 y z^{2} - 6 y z + 2 y - 2 z^{2} + 3 z - 1\right)\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{42} = \left(\begin{array}{c}\displaystyle 4 y z \left(- 4 x^{2} y z + 4 x^{2} y + 2 x^{2} z - 2 x^{2} + 6 x y z - 6 x y - 3 x z + 3 x - 2 y z + 2 y + z - 1\right)\\\displaystyle 0\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{43} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 4 y z \left(- 4 x^{2} y z + 4 x^{2} y + 2 x^{2} z - 2 x^{2} + 6 x y z - 6 x y - 3 x z + 3 x - 2 y z + 2 y + z - 1\right)\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{44} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 0\\\displaystyle 4 y z \left(- 4 x^{2} y z + 4 x^{2} y + 2 x^{2} z - 2 x^{2} + 6 x y z - 6 x y - 3 x z + 3 x - 2 y z + 2 y + z - 1\right)\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{45} = \left(\begin{array}{c}\displaystyle 4 x y z \left(- 4 x y z + 4 x y + 2 x z - 2 x + 2 y z - 2 y - z + 1\right)\\\displaystyle 0\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{46} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 4 x y z \left(- 4 x y z + 4 x y + 2 x z - 2 x + 2 y z - 2 y - z + 1\right)\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{47} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 0\\\displaystyle 4 x y z \left(- 4 x y z + 4 x y + 2 x z - 2 x + 2 y z - 2 y - z + 1\right)\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{48} = \left(\begin{array}{c}\displaystyle 4 x z \left(- 4 x y^{2} z + 2 x y^{2} + 6 x y z - 3 x y - 2 x z + x + 4 y^{2} z - 2 y^{2} - 6 y z + 3 y + 2 z - 1\right)\\\displaystyle 0\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{49} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 4 x z \left(- 4 x y^{2} z + 2 x y^{2} + 6 x y z - 3 x y - 2 x z + x + 4 y^{2} z - 2 y^{2} - 6 y z + 3 y + 2 z - 1\right)\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{50} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 0\\\displaystyle 4 x z \left(- 4 x y^{2} z + 2 x y^{2} + 6 x y z - 3 x y - 2 x z + x + 4 y^{2} z - 2 y^{2} - 6 y z + 3 y + 2 z - 1\right)\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{51} = \left(\begin{array}{c}\displaystyle 4 y z \left(- 4 x^{2} y z + 2 x^{2} y + 4 x^{2} z - 2 x^{2} + 6 x y z - 3 x y - 6 x z + 3 x - 2 y z + y + 2 z - 1\right)\\\displaystyle 0\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{52} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 4 y z \left(- 4 x^{2} y z + 2 x^{2} y + 4 x^{2} z - 2 x^{2} + 6 x y z - 3 x y - 6 x z + 3 x - 2 y z + y + 2 z - 1\right)\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{53} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 0\\\displaystyle 4 y z \left(- 4 x^{2} y z + 2 x^{2} y + 4 x^{2} z - 2 x^{2} + 6 x y z - 3 x y - 6 x z + 3 x - 2 y z + y + 2 z - 1\right)\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{54} = \left(\begin{array}{c}\displaystyle 4 x y z \left(- 4 x y z + 2 x y + 4 x z - 2 x + 2 y z - y - 2 z + 1\right)\\\displaystyle 0\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{55} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 4 x y z \left(- 4 x y z + 2 x y + 4 x z - 2 x + 2 y z - y - 2 z + 1\right)\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{56} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 0\\\displaystyle 4 x y z \left(- 4 x y z + 2 x y + 4 x z - 2 x + 2 y z - y - 2 z + 1\right)\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{57} = \left(\begin{array}{c}\displaystyle 4 x y z \left(- 4 x y z + 2 x y + 2 x z - x + 4 y z - 2 y - 2 z + 1\right)\\\displaystyle 0\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{58} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 4 x y z \left(- 4 x y z + 2 x y + 2 x z - x + 4 y z - 2 y - 2 z + 1\right)\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{59} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 0\\\displaystyle 4 x y z \left(- 4 x y z + 2 x y + 2 x z - x + 4 y z - 2 y - 2 z + 1\right)\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{60} = \left(\begin{array}{c}\displaystyle 16 x y \left(2 x y z^{2} - 3 x y z + x y - 2 x z^{2} + 3 x z - x - 2 y z^{2} + 3 y z - y + 2 z^{2} - 3 z + 1\right)\\\displaystyle 0\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{61} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 16 x y \left(2 x y z^{2} - 3 x y z + x y - 2 x z^{2} + 3 x z - x - 2 y z^{2} + 3 y z - y + 2 z^{2} - 3 z + 1\right)\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{62} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 0\\\displaystyle 16 x y \left(2 x y z^{2} - 3 x y z + x y - 2 x z^{2} + 3 x z - x - 2 y z^{2} + 3 y z - y + 2 z^{2} - 3 z + 1\right)\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{63} = \left(\begin{array}{c}\displaystyle 16 x z \left(2 x y^{2} z - 2 x y^{2} - 3 x y z + 3 x y + x z - x - 2 y^{2} z + 2 y^{2} + 3 y z - 3 y - z + 1\right)\\\displaystyle 0\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{64} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 16 x z \left(2 x y^{2} z - 2 x y^{2} - 3 x y z + 3 x y + x z - x - 2 y^{2} z + 2 y^{2} + 3 y z - 3 y - z + 1\right)\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{65} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 0\\\displaystyle 16 x z \left(2 x y^{2} z - 2 x y^{2} - 3 x y z + 3 x y + x z - x - 2 y^{2} z + 2 y^{2} + 3 y z - 3 y - z + 1\right)\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{66} = \left(\begin{array}{c}\displaystyle 16 y z \left(2 x^{2} y z - 2 x^{2} y - 2 x^{2} z + 2 x^{2} - 3 x y z + 3 x y + 3 x z - 3 x + y z - y - z + 1\right)\\\displaystyle 0\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{67} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 16 y z \left(2 x^{2} y z - 2 x^{2} y - 2 x^{2} z + 2 x^{2} - 3 x y z + 3 x y + 3 x z - 3 x + y z - y - z + 1\right)\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{68} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 0\\\displaystyle 16 y z \left(2 x^{2} y z - 2 x^{2} y - 2 x^{2} z + 2 x^{2} - 3 x y z + 3 x y + 3 x z - 3 x + y z - y - z + 1\right)\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{69} = \left(\begin{array}{c}\displaystyle 16 x y z \left(2 x y z - 2 x y - 2 x z + 2 x - y z + y + z - 1\right)\\\displaystyle 0\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{70} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 16 x y z \left(2 x y z - 2 x y - 2 x z + 2 x - y z + y + z - 1\right)\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{71} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 0\\\displaystyle 16 x y z \left(2 x y z - 2 x y - 2 x z + 2 x - y z + y + z - 1\right)\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{72} = \left(\begin{array}{c}\displaystyle 16 x y z \left(2 x y z - 2 x y - x z + x - 2 y z + 2 y + z - 1\right)\\\displaystyle 0\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{73} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 16 x y z \left(2 x y z - 2 x y - x z + x - 2 y z + 2 y + z - 1\right)\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{74} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 0\\\displaystyle 16 x y z \left(2 x y z - 2 x y - x z + x - 2 y z + 2 y + z - 1\right)\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{75} = \left(\begin{array}{c}\displaystyle 16 x y z \left(2 x y z - x y - 2 x z + x - 2 y z + y + 2 z - 1\right)\\\displaystyle 0\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{76} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 16 x y z \left(2 x y z - x y - 2 x z + x - 2 y z + y + 2 z - 1\right)\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{77} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 0\\\displaystyle 16 x y z \left(2 x y z - x y - 2 x z + x - 2 y z + y + 2 z - 1\right)\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{78} = \left(\begin{array}{c}\displaystyle 64 x y z \left(- x y z + x y + x z - x + y z - y - z + 1\right)\\\displaystyle 0\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{79} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 64 x y z \left(- x y z + x y + x z - x + y z - y - z + 1\right)\\\displaystyle 0\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{80} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 0\\\displaystyle 64 x y z \left(- x y z + x y + x z - x + y z - y - z + 1\right)\end{array}\right)\)

\(\displaystyle \boldsymbol{\phi}_{81} = \left(\begin{array}{c}\displaystyle x - \frac{1}{2}\\\displaystyle y - \frac{1}{2}\\\displaystyle z - \frac{1}{2}\end{array}\right)\)