

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



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a, b, c, d = symbols('a b c d'); 
A, B = symbols('A B', commutative=False)
t = Tr(A*B)



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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



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t = Tr ( Matrix([ [2,3], [3,4] ]))



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t









    Out[16]:





$$6$$

Example using modules in physics.quantum



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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]:





$$\rho\left(\begin{pmatrix}{\left|1,1\right\rangle }, & 0.5\end{pmatrix},\begin{pmatrix}{\left|1,-1\right\rangle }, & 0.5\end{pmatrix}\right)$$



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t = Tr(d)



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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)



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t.doit()









    Out[12]:





$$1.0$$



In [12]: