How to change latex names of sympy vector? - sympy

Question

When creating a sympy vector, first I create the coordinate system, for example for cylindrical coordinates:
from sympy.vector import CoordSys3D
from IPython.display import display
R = CoordSys3D('', transformation='cylindrical', variable_names=("r", "theta", "z"),vector_names=('i', 'j', 'k'))
I want to change the latex names of variables and vectors. As I searched, the CoordSys3D has those inputs:
class sympy.vector.coordsysrect.CoordSys3D(name, transformation=None, parent=None, location=None, rotation_matrix=None, vector_names=None, variable_names=None)[source]
if I print R.theta with:
display(R.theta)
I get $theta$, but i would like to have $\theta$
However, inside its __init__, there are the latex_scalars and latex_vects
__init__(name, location=None, rotation_matrix=None, parent=None, vector_names=None, variable_names=None, latex_vects=None, pretty_vects=None, latex_scalars=None, pretty_scalars=None, transformation=None)
Can I give a value to it?

Answer 1

I was having the same problem, and I found an answer.
R = CoordSys3D('R', transformation='cylindrical', variable_names=("r", "theta", "z"),vector_names=('i', 'j', 'k'))
R.theta._latex_form = '\\theta'
R.j._latex_form = '\\vectorunit{\\theta}'
The ._latex_form attribute also works the same way when you define a sympy function:
E_phi = smp.Function('E_phi')()
E_phi._latex_form = 'E_{\\phi}'
However, there is no ._latex_form attribute for symbols. But I found another way to do it:
E_phi = Symbol('E_{\\phi}')
Remember to use double backslash when entering latex code in python.
Here is some example code I wrote. The output is formatted for MathJax. The output looks like this:
$$ \require{physics} $$
$$ \vb{E} = (E_{r})\vectorunit{r} + (7 e^{i \omega t})\vectorunit{\phi} + (E_{z})\vectorunit{z} $$
$$ \curl{\vb{E}} = (\frac{7 e^{i \omega t}}{r})\vectorunit{z} $$
$$ \vb{B} = (\begin{cases} \frac{7 i e^{i \omega t}}{r \omega} & \text{for}\: r \omega \neq 0 \\- \frac{7 t}{r} & \text{otherwise} \end{cases})\vectorunit{z} $$
import numpy as np
import sympy as smp
import matplotlib.pyplot as plt
from sympy import *
from sympy import symbols
from sympy.vector import divergence
from sympy.vector import curl
from sympy.vector import gradient
from sympy import diff
from sympy import exp
from sympy import integrate
from sympy import I, pi
from sympy.vector import CoordSys3D
N = CoordSys3D('N', transformation='cylindrical',
vector_names=("r", "phi", "z"),
variable_names=("R", "PHI", "Z"))
# Variables
R = N.R
PHI = N.PHI
Z = N.Z
R._latex_form = 'r'
PHI._latex_form = '\\phi'
Z._latex_form = 'z'
# Basis Unit Vectors
rhat = N.r
phihat = N.phi
zhat = N.z
rhat._latex_form = '\\vectorunit{r}'
phihat._latex_form = '\\vectorunit{\\phi}'
zhat._latex_form = '\\vectorunit{z}'
# The r, phi, and z components of the Electric Field
E_r = Symbol('E_{r}')
E_phi = Symbol('E_{\\phi}')
E_z = Symbol('E_{z}')
# Symbols
x, y, z, t = symbols('x y z t')
wavenumber = symbols('k')
E_0 = symbols('E_0') # Amplitude of E field
w = symbols('omega' , real=True, positive=True)
# Define E_phi(r,phi,z,t)
# Note: I = sqrt(-1)
# E_phi = (1/R) * smp.exp( I * ( w*t ))
E_phi = 7 * smp.exp( I * w * t)
# The Electric Field
E = (E_r * rhat) + (E_phi * phihat) + (E_z * zhat)
# Compute B by integrating the curl of E wrt time
# curl E = - dB/dt
# integrate( (curl E) , t ) = - B
jimmy = curl( E )
B = -integrate( jimmy, t )
# Display the answers as LATEX
# init_printing(use_unicode=True, wrap_line=False)
init_printing( use_latex='mathjax' )
print("$$ \\require{physics} $$")
print("$$ \\vb{E} = " + latex(E) + " $$")
print("$$ \\curl{\\vb{E}} = " + latex(jimmy) + " $$")
print("$$ \\vb{B} = " + latex(B.simplify()) + " $$")
# Alternative Way of defining the components of
# the Electric Field:
# The r, phi, and z components of the Electric Field
# E_r = smp.Function('E_r')()
# E_phi = smp.Function('E_phi')()
# E_z = smp.Function('E_z')()
# E_r._latex_form = 'E_{r}'
# E_phi._latex_form = 'E_{\\phi}'
# E_z._latex_form = 'E_{z}'
# Note that if we define these variables as symbols()
# Then we have to give the latex form this way:
# E_phi = symbol('E_{\\phi}')
# symbols have no attribute ._latex_form
# Whereas Functions do.