```python
from sympy import init_printing; init_printing();
from IPython.core.interactiveshell import InteractiveShell
InteractiveShell.ast_node_interactivity = "all"
```


```python
from silkpy.symbolic.geometry_map.coord_transform import CoordTransform
from silkpy.symbolic.geometry_map.coord_transform.predefined import Cylindrical2Cartesian, Cartesian2Cylindrical

Cylindrical2Cartesian().exprs
Cartesian2Cylindrical().exprs
Cylindrical2Cartesian().jacobian
Cartesian2Cylindrical().jacobian
```

    /home/wenyin/pyvenv/vsym/lib/python3.8/site-packages/IPython/lib/latextools.py:126: MatplotlibDeprecationWarning: 
    The to_png function was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use mathtext.math_to_image instead.
      mt.to_png(f, s, fontsize=12, dpi=dpi, color=color)
    /home/wenyin/pyvenv/vsym/lib/python3.8/site-packages/IPython/lib/latextools.py:126: MatplotlibDeprecationWarning: 
    The to_rgba function was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use mathtext.math_to_image instead.
      mt.to_png(f, s, fontsize=12, dpi=dpi, color=color)
    /home/wenyin/pyvenv/vsym/lib/python3.8/site-packages/IPython/lib/latextools.py:126: MatplotlibDeprecationWarning: 
    The to_mask function was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use mathtext.math_to_image instead.
      mt.to_png(f, s, fontsize=12, dpi=dpi, color=color)
    /home/wenyin/pyvenv/vsym/lib/python3.8/site-packages/IPython/lib/latextools.py:126: MatplotlibDeprecationWarning: 
    The MathtextBackendBitmap class was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use mathtext.math_to_image instead.
      mt.to_png(f, s, fontsize=12, dpi=dpi, color=color)





$\displaystyle \left[\begin{matrix}R \cos{\left(\phi \right)} & R \sin{\left(\phi \right)} & Z\end{matrix}\right]$






$\displaystyle \left[\begin{matrix}\sqrt{x^{2} + y^{2}} & z & \operatorname{atan_{2}}{\left(y,x \right)}\end{matrix}\right]$






$\displaystyle \left[\begin{matrix}\cos{\left(\phi \right)} & \sin{\left(\phi \right)} & 0\\0 & 0 & 1\\- R \sin{\left(\phi \right)} & R \cos{\left(\phi \right)} & 0\end{matrix}\right]$






$\displaystyle \left[\begin{matrix}\frac{x}{\sqrt{x^{2} + y^{2}}} & 0 & - \frac{y}{x^{2} + y^{2}}\\\frac{y}{\sqrt{x^{2} + y^{2}}} & 0 & \frac{x}{x^{2} + y^{2}}\\0 & 1 & 0\end{matrix}\right]$




```python
Cartesian2Cartesian = Cartesian2Cylindrical() | Cylindrical2Cartesian()
Cylindrical2Cylindrical = Cylindrical2Cartesian() | Cartesian2Cylindrical()
```


```python
Cartesian2Cartesian.exprs
Cartesian2Cartesian.syms
```


```python
Cylindrical2Cylindrical.exprs.simplify()
Cylindrical2Cylindrical.syms
```


```python

```

fabf1e7ab8e2985e3a9084ca964d5bcc252a711b
ipynb
Jupyter Notebook
nb/how_to_CoordTransform.ipynb
WenyinWei/silkpy
2e3773e15fbebc4914f5627d8361a24d35fb5935
MIT
2021-05-13T09:23:03.000Z
2021-05-13T09:23:03.000Z
nb/how_to_CoordTransform.ipynb
WenyinWei/silkpy
2e3773e15fbebc4914f5627d8361a24d35fb5935
MIT
nb/how_to_CoordTransform.ipynb
WenyinWei/silkpy
2e3773e15fbebc4914f5627d8361a24d35fb5935
MIT
2021-05-27T14:13:24.000Z
2021-05-27T14:13:24.000Z
Qwen/Qwen-72B
1. YES
2. YES