#!/usr/bin/env python
# coding: utf-8

# # Watching Paint Dry
# 
# The composited _color_ of the **paint** must not change during drying. The
# optical blending function is used with this constraint to compensate for the new
# dry layer $C_{d}^{\prime}$, when some volume $\delta_{\alpha}$ is removed from
# the wet layer.
# 
# $$
# C_{d}^{\prime} = \frac{\alpha \times C_{w} + (1 - \delta) \times C_d - a^{\prime}C_w}{1 - \alpha^\prime}, \alpha^\prime = \alpha - \delta_\alpha
# $$
# 
# The dry layer of the canvas uses a relative height field to allow for unlimited
# volume of paint to be added, with a constraint only on the relative change in
# height between texels.

# In[1]:


from IPython.display import Markdown
Markdown(r"""# Non-Homogeneous Poisson Process Likelihood Function
$$
\frac{\left(Λ_{0,T}\left(t\right)\right)^k e^{\left(Λ_{0,T}\left(t\right)\right)}}{k!}
$$""")


# In[1]:


from IPython.display import Latex
display(Latex(r"\LaTeX"))


# In[3]:


from IPython.display import Latex
Latex(r"""\begin{eqnarray}
\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = & \frac{4\pi}{c}\vec{\mathbf{j}} \\
\nabla \cdot \vec{\mathbf{E}} & = & 4 \pi \rho \\
\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = & \vec{\mathbf{0}} \\
\nabla \cdot \vec{\mathbf{B}} & = & 0 
\end{eqnarray}""")


# https://github.com/nteract/nteract/issues/2434
# 
# $\hat{y}_{i}=\hat\beta_{0}+\hat\beta_{1}x_{i}$
# 
# $\sum\limits_{i=1}^nx_i$
# 
# 

# https://github.com/nteract/nteract/issues/2012
# 
# $$
# \begin{align}
# a &= 1 \\
# b &= 2
# \end{align}
# $$

# https://github.com/nteract/nteract/issues/1557
# 
# 
# | Age | Number of Cars owned | Owns House | Number of Children| Marital status (s/m/d/w) | Owns a dog | Bought a Boat|
# |-|-|-|-|-|-|-|
# |66|1|y|2|w|n|y|
# |52|2|y|3|m|n|y|
# |22|0|n|0|m|y|n|
# |25|1|n|1|s|n|n|
# |44|0|n|2|d|y|n|
# |39|1|y|2|m|y|n|
# |26|1|n|2|s|n|n|
# |40|3|y|1|m|y|n|
# |53|2|y|2|d|n|y|
# |64|2|y|3|d|n|n|
# |58|2|y|2|m|y|y|
# |33|1|n|1|s|n|n|
# 

# 
# ~~hey~~
# 
# ```python
# import this
# 
# print('hey')
# ```
# 
# 

# 1. Thing

# 1. This is a numbered list
# 2. And within it
#   * There's a bulleted list which should be indented
# 3. It's not, and totally should
# 4. Hopefully this gets fixed

#