1. sympy
  2. examples
  3. notebooks
In [2]:
from sympy import symbols
from sympy.core.trace import Tr
from sympy.matrices.matrices import Matrix
from IPython.core.display import display_pretty
from sympy.printing.latex import *

%load_ext sympyprinting

Basic Examples

In [3]:
a, b, c, d = symbols('a b c d'); 
A, B = symbols('A B', commutative=False)
t = Tr(A*B)
In [4]:
t
Out[4]:
$$\mbox{Tr}\left(A B\right)$$
In [5]:
latex(t)
Out[5]:
\mbox{Tr}\left(A B\right)
In [14]:
display_pretty(t)

Tr(ρ((❘1,1⟩, 0.5),(❘1,-1⟩, 0.5)))

Using Matrices

In [15]:
t = Tr ( Matrix([ [2,3], [3,4] ]))
In [16]:
t
Out[16]:
$$6$$

Example using modules in physics.quantum

In [7]:
from sympy.physics.quantum.density import Density
from sympy.physics.quantum.spin import (
    Jx, Jy, Jz, Jplus, Jminus, J2,
    JxBra, JyBra, JzBra,
    JxKet, JyKet, JzKet,
)
In [8]:
d = Density([JzKet(1,1),0.5],[JzKet(1,-1),0.5]); d
Out[8]:
$$\rho\left(\begin{pmatrix}{\left|1,1\right\rangle }, & 0.5\end{pmatrix},\begin{pmatrix}{\left|1,-1\right\rangle }, & 0.5\end{pmatrix}\right)$$
In [9]:
t = Tr(d)
In [10]:
t
Out[10]:
$$\mbox{Tr}\left(\rho\left(\begin{pmatrix}{\left|1,1\right\rangle }, & 0.5\end{pmatrix},\begin{pmatrix}{\left|1,-1\right\rangle }, & 0.5\end{pmatrix}\right)\right)$$
In [11]:
latex(t)
Out[11]:
\mbox{Tr}\left(\rho\left(\begin{pmatrix}{\left|1,1\right\rangle }, & 0.5\end{p
matrix},\begin{pmatrix}{\left|1,-1\right\rangle }, & 0.5\end{pmatrix}\right)\r
ight)
In [12]:
t.doit()
Out[12]:
$$1.0$$