```
import sympy
sympy.init_printing(use_latex='mathjax')
```


```
t0,t1,t2,t3,t4,t5 = sympy.symbols("t_0,t_1,t_2,t_3,t_4,t_5")
M = sympy.Matrix([[1, t0, t3], [0, t1, t4], [0, t2, t5]])
M
```




$$\left[\begin{matrix}1 & t_{0} & t_{3}\\0 & t_{1} & t_{4}\\0 & t_{2} & t_{5}\end{matrix}\right]$$




```
MI = M.inv()
MI
```




$$\left[\begin{matrix}1 & - \frac{t_{0}}{t_{1}} + \frac{t_{2} \left(- \frac{t_{0} t_{4}}{t_{1}} + t_{3}\right)}{t_{1} \left(t_{5} - \frac{t_{2} t_{4}}{t_{1}}\right)} & - \frac{- \frac{t_{0} t_{4}}{t_{1}} + t_{3}}{t_{5} - \frac{t_{2} t_{4}}{t_{1}}}\\0 & \frac{1}{t_{1}} + \frac{t_{2} t_{4}}{t_{1}^{2} \left(t_{5} - \frac{t_{2} t_{4}}{t_{1}}\right)} & - \frac{t_{4}}{t_{1} \left(t_{5} - \frac{t_{2} t_{4}}{t_{1}}\right)}\\0 & - \frac{t_{2}}{t_{1} \left(t_{5} - \frac{t_{2} t_{4}}{t_{1}}\right)} & \frac{1}{t_{5} - \frac{t_{2} t_{4}}{t_{1}}}\end{matrix}\right]$$




```
sympy.printing.print_tree(MI)
```


```
print repr(MI)
```

    Matrix([
    [1, -t_0/t_1 + t_2*(-t_0*t_4/t_1 + t_3)/(t_1*(t_5 - t_2*t_4/t_1)), -(-t_0*t_4/t_1 + t_3)/(t_5 - t_2*t_4/t_1)],
    [0,                  1/t_1 + t_2*t_4/(t_1**2*(t_5 - t_2*t_4/t_1)),            -t_4/(t_1*(t_5 - t_2*t_4/t_1))],
    [0,                                -t_2/(t_1*(t_5 - t_2*t_4/t_1)),                     1/(t_5 - t_2*t_4/t_1)]])



```
p,l,x, y = sympy.symbols("p,l,x,y")
e = sympy.Matrix([[1, x, y]]) * MI
print sympy.Eq(p, e.tolist()[0][1])
```

    p == -t_0/t_1 + x*(1/t_1 + t_2*t_4/(t_1**2*(t_5 - t_2*t_4/t_1))) - t_2*y/(t_1*(t_5 - t_2*t_4/t_1)) + t_2*(-t_0*t_4/t_1 + t_3)/(t_1*(t_5 - t_2*t_4/t_1))



```
print sympy.Eq(l, e.tolist()[0][2])
```

    l == y/(t_5 - t_2*t_4/t_1) - (-t_0*t_4/t_1 + t_3)/(t_5 - t_2*t_4/t_1) - t_4*x/(t_1*(t_5 - t_2*t_4/t_1))



```

```

4b5955a5276107a92bd7a6b9c026d5101e2a4434
ipynb
Jupyter Notebook
ProjectionInverse.ipynb
SkyTruth/pelagos-data
9ebf58e490058e38409d3f1f552ac4ca76bf2167
MIT
2016-10-04T17:09:39.000Z
2016-10-04T17:09:39.000Z
ProjectionInverse.ipynb
SkyTruth/pelagos-data
9ebf58e490058e38409d3f1f552ac4ca76bf2167
MIT
2016-02-11T20:51:40.000Z
2016-02-12T17:46:47.000Z
ProjectionInverse.ipynb
SkyTruth/pelagos-data
9ebf58e490058e38409d3f1f552ac4ca76bf2167
MIT
Qwen/Qwen-72B
1. YES
2. YES