External-potentials.md

 # Form of the functional
-W-SLDA codes minimize functional of generic form:  
-![E=\int \mathcal{E}_{\textrm{edf}}(n,\nu,\ldots)\,d^3r-\sum_{\sigma}\int\left(\mu_{\sigma}-V_{\sigma}^{\textrm{(ext)}}(r)\right)n_{\sigma}(r)\,d^3r-\int\left(\Delta^{\textrm{(ext)}}(r)\nu^*(r)+\textrm{h.c.}\right)d^3r-\sum_{\sigma}\int \vec{v}_{\sigma}^{\textrm{(ext)}}(r)\cdot\vec{j}_{\sigma}(r)\,d^3r](https://render.githubusercontent.com/render/math?math=E%3D%5Cint%20%5Cmathcal%7BE%7D_%7B%5Ctextrm%7Bedf%7D%7D(n%2C%5Cnu%2C%5Cldots)%5C%2Cd%5E3r-%5Csum_%7B%5Csigma%7D%5Cint%5Cleft(%5Cmu_%7B%5Csigma%7D-V_%7B%5Csigma%7D%5E%7B%5Ctextrm%7B(ext)%7D%7D(r)%5Cright)n_%7B%5Csigma%7D(r)%5C%2Cd%5E3r-%5Cint%5Cleft(%5CDelta%5E%7B%5Ctextrm%7B(ext)%7D%7D(r)%5Cnu%5E*(r)%2B%5Ctextrm%7Bh.c.%7D%5Cright)d%5E3r-%5Csum_%7B%5Csigma%7D%5Cint%20%5Cvec%7Bv%7D_%7B%5Csigma%7D%5E%7B%5Ctextrm%7B(ext)%7D%7D(r)%5Ccdot%5Cvec%7Bj%7D_%7B%5Csigma%7D(r)%5C%2Cd%5E3r)   
+W-SLDA codes minimize functional of the generic form:  
+```math
+E=\int \mathcal{E}_{\textrm{edf}}(n,\nu,\ldots)\,d^3r-\sum_{\sigma}\int\left(\mu_{\sigma}-V_{\sigma}^{\textrm{(ext)}}(r)\right)n_{\sigma}(r)\,d^3r\\-\frac{1}{2}\int\left(\Delta^{\textrm{(ext)}}(r)\nu^*(r)+\textrm{h.c.}\right)d^3r-\sum_{\sigma}\int \vec{v}_{\sigma}^{\textrm{(ext)}}(r)\cdot\vec{j}_{\sigma}(r)\,d^3r
+``` 
 where:  
-* ![\mathcal{E}_{\textrm{edf}}(n,\nu,\ldots)](https://render.githubusercontent.com/render/math?math=%5Cmathcal%7BE%7D_%7B%5Ctextrm%7Bedf%7D%7D(n%2C%5Cnu%2C%5Cldots)) is energy density functional which defines the physical system,
-* ![V_{\sigma}^{\textrm{(ext)}}(r)](https://render.githubusercontent.com/render/math?math=V_%7B%5Csigma%7D%5E%7B%5Ctextrm%7B(ext)%7D%7D(r)) is spin dependent external potential, and ![\mu_{\sigma}](https://render.githubusercontent.com/render/math?math=%5Cmu_%7B%5Csigma%7D) are chemical potentials (Lagrange multipliers) for constraining particle number.
-* ![\Delta^{\textrm{(ext)}}(r)](https://render.githubusercontent.com/render/math?math=%5CDelta%5E%7B%5Ctextrm%7B(ext)%7D%7D(r)) is external pairing potential,
-* ![\vec{v}_{\sigma}^{\textrm{(ext)}}(r)](https://render.githubusercontent.com/render/math?math=%5Cvec%7Bv%7D_%7B%5Csigma%7D%5E%7B%5Ctextrm%7B(ext)%7D%7D(r)) is external velocity field. 
+* $`\mathcal{E}_{\textrm{edf}}(n,\nu,\ldots)`$ is energy density functional which defines the physical system,
+* $`V_{\sigma}^{\textrm{(ext)}}(r)`$ is spin dependent external potential, and $`\mu_{\sigma}`$ are chemical potentials (Lagrange multipliers) for constraining particle number.
+* $`\Delta^{\textrm{(ext)}}(r)`$ is external pairing potential,
+* $`\vec{v}_{\sigma}^{\textrm{(ext)}}(r)`$ is external velocity field. 
 
 W-SLDA toolkit provides flexible framework that allows for custom definition of all these terms. User must provide body of following functions contained in file: *problem-definition.h*. Each function can be parametrized by [User defined parameters](User defined parameters).
 
-# Definition of the external potential ![V_{\sigma}^{\textrm{(ext)}}(r)](https://render.githubusercontent.com/render/math?math=V_%7B%5Csigma%7D%5E%7B%5Ctextrm%7B(ext)%7D%7D(r))
+# Definition of the external potential $`V_{\sigma}^{\textrm{(ext)}}(r)`$
 ```c
 /** 
  * EXTERNAL POTENTIAL V_ext
@@ -34,7 +36,7 @@ double v_ext(int ix, int iy, int iz, int it, int spin, double *params, size_t ex
 }
 ```
 
-# Definition of the external pairing potential ![\Delta^{\textrm{(ext)}}(r)](https://render.githubusercontent.com/render/math?math=%5CDelta%5E%7B%5Ctextrm%7B(ext)%7D%7D(r))
+# Definition of the external pairing potential $`\Delta^{\textrm{(ext)}}(r)`$
 ```c
 /** 
  * EXTERNAL PAIRING POTENTIAL Delta_ext
@@ -62,7 +64,7 @@ double complex delta_ext(int ix, int iy, int iz, int it, double complex delta, d
 * `st-wslda`: return type must be C99 [double complex](https://en.cppreference.com/w/c/numeric/complex)
 * `td-wslda`: return type must be compatible with [CUDA Complex](https://thrust.github.io/doc/group__complex__numbers.html)
 
-# Definition of the external velocity field ![\vec{v}_{\sigma}^{\textrm{(ext)}}(r)](https://render.githubusercontent.com/render/math?math=%5Cvec%7Bv%7D_%7B%5Csigma%7D%5E%7B%5Ctextrm%7B(ext)%7D%7D(r))
+# Definition of the external velocity field $`\vec{v}_{\sigma}^{\textrm{(ext)}}(r)`$
 ```c
 /** 
  * EXTERNAL VELOCITY FIELD vec[v]_ext