Generate LaTeX code for Markov chains

Simple application for generating latex code for ODE system (Kolmogorov equations). Supports only Markov chain with direct paths and no cycles.

Example

From this mermaid snippet:

graph LR;
    a-- \lambda -->b;
    a-- \lambda -->c;
    b-- 0.6 --> c;

we can get latex code:

\begin{cases}
\dfrac{dp_a}{dt} = -\lambda_{ab} p_{a}(t) - \lambda_{ac} p_{a}(t) \\[10pt]
\dfrac{dp_b}{dt} = \lambda_{ab}  p_{a}(t) \\[10pt]
\dfrac{dp_c}{dt} = \lambda_{ac}  p_{a}(t) 
\end{cases}

system of equations:

$$\begin{cases} \dfrac{dp_a}{dt} = -\lambda_{ab} p_{a}(t) - \lambda_{ac} p_{a}(t) \\[10pt] \dfrac{dp_b}{dt} = \lambda_{ab} p_{a}(t) \\[10pt] \dfrac{dp_c}{dt} = \lambda_{ac} p_{a}(t) \end{cases}$$

and figure:

Run

After cloning the repository:

cd mm_kolmogorov_ode
python3 -m venv .venv
source .venv/bin/activate
pip install -r requirements.txt
streamlit run app.py

In case of several installed streamlit versions use:

.venv/bin/python -m streamlit run app.py

Options

• From adjancecy matrix: build from mermaid code json, adjancecy matrix and the generate latex from matrix
• From mermaid code: build latex from mermaid code directly (skip json and matrix)

There are no any differences except order of positive and negative terms in final equations