Wu–Xu

\(\mathcal{P}_k=\operatorname{span}\left\{\prod_{i=1}^dx_i^{p_i}\middle|\sum_{i=1}^dp_i\leqslant k\right\}\)

\(\mathcal{Z}^{(53)}_k=\left\{x(1-x)p\middle|p\in\mathcal{P}_{k-1}\setminus\{1\}\right\}\)

\(\mathcal{Z}^{(54)}_k=\left\{xy(1-x-y)p\middle|p\in\mathcal{P}_{k-1}\setminus\{1\}\right\}\)

\(\mathcal{Z}^{(55)}_k=\left\{xyz(1-x-y-z)p\middle|p\in\mathcal{P}_{k-1}\setminus\{1\}\right\}\)

Before trying this example, you must install Symfem:

pip3 install symfem

This element can then be created with the following lines of Python:

import symfem

# Create Wu-Xu order 2 on a interval
element = symfem.create_element("interval", "Wu-Xu", 2)

# Create Wu-Xu order 3 on a triangle
element = symfem.create_element("triangle", "Wu-Xu", 3)

# Create Wu-Xu order 4 on a tetrahedron
element = symfem.create_element("tetrahedron", "Wu-Xu", 4)