Types-of-codes.md

@@ -2,27 +2,39 @@
 # Static and time-dependent codes
 There are two main branches of codes:
 * Static codes `st-wslda-?d` for solving self-consistently static DFT equations.
-* Time-dependent codes `td-wslda-?d` for solving time dependent DFT equations. The `td-wslda-?d` codes require starting point for the time evolution (i.e $`\psi(\vec{r},t=0)`$) which is typically generated by the static codes.  
+* Time-dependent codes `td-wslda-?d` for solving time-dependent DFT equations. The `td-wslda-?d` codes require a starting point for the time evolution (i.e. $`\psi(\vec{r},t=0)`$), which is typically generated by the static codes.  
 
-In codes names `?` stand for dimensionality, as described below.
+In code names, `?` stands for dimensionality, as described below.
 
 # Codes dimensionality (xx: st or td)
 ## 3D codes: `xx-wslda-3d`
-The 3D codes do not impose any restriction for form of the wave-functions. The wave-functions are assumed to be:  
-![\psi=\varphi(x,y,z)](https://render.githubusercontent.com/render/math?math=%5Cpsi%3D%5Cvarphi(x%2Cy%2Cz))
+The 3D codes do not impose any restriction on the form of the wave functions. The wave functions are assumed to be:  
+```math
+\psi=\varphi(x,y,z)
+```
 
 ## 2D codes: `xx-wslda-2d`
-In 2D codes the wave-functions are assumed to be:  
-![\psi=\varphi(x,y)\frac{1}{\sqrt{L_z}}e^{ik_z z}](https://render.githubusercontent.com/render/math?math=%5Cpsi%3D%5Cvarphi(x%2Cy)%5Cfrac%7B1%7D%7B%5Csqrt%7BL_z%7D%7De%5E%7Bik_z%20z%7D%0A)  
+In 2D codes, the wave functions are assumed to be:  
+```math
+\psi=\varphi(x,y)\frac{1}{\sqrt{L_z}}e^{ik_z z}
+```  
 where  
-![k_z = 0, \pm 1 \frac{2\pi}{L_z}, \pm 2 \frac{2\pi}{L_z}, \ldots , +(N_z-1) \frac{2\pi}{L_z}](https://render.githubusercontent.com/render/math?math=k_z%20%3D%200%2C%20%5Cpm%201%20%5Cfrac%7B2%5Cpi%7D%7BL_z%7D%2C%20%5Cpm%202%20%5Cfrac%7B2%5Cpi%7D%7BL_z%7D%2C%20%5Cldots%20%2C%20%2B(N_z-1)%20%5Cfrac%7B2%5Cpi%7D%7BL_z%7D%0A)  
-For `NZ=1` the code solves 2D problem (there is only one mode in z-directions, which reduces to 1). Note however, that 2D problem requires different prescription for coupling constant regularization than the one implemented in W-SLDA toolkit. 
+```math
+k_z = 0, \pm 1 \frac{2\pi}{L_z}, \pm 2 \frac{2\pi}{L_z}, \ldots , +(N_z-1) \frac{2\pi}{L_z}
+``` 
+For `NZ=1`, the code solves a 2D problem (there is only one mode in z-directions, which reduces to 1). Note, however, that the 2D problem requires a different prescription for coupling constant regularization than the one implemented in the W-SLDA toolkit. 
 
 
 ## 1D codes: `xx-wslda-1d`
-In 1D codes the wave-functions are assumed to be:  
-![\psi=\varphi(x)\frac{1}{\sqrt{L_y}}e^{ik_y y}\frac{1}{\sqrt{L_z}}e^{ik_z z}](https://render.githubusercontent.com/render/math?math=%5Cpsi%3D%5Cvarphi(x)%5Cfrac%7B1%7D%7B%5Csqrt%7BL_y%7D%7De%5E%7Bik_y%20y%7D%5Cfrac%7B1%7D%7B%5Csqrt%7BL_z%7D%7De%5E%7Bik_z%20z%7D%0A)  
+In 1D codes, the wave functions are assumed to be:  
+```math
+\psi=\varphi(x)\frac{1}{\sqrt{L_y}}e^{ik_y y}\frac{1}{\sqrt{L_z}}e^{ik_z z}
+```  
 where  
-![k_y = 0, \pm 1 \frac{2\pi}{L_y}, \pm 2 \frac{2\pi}{L_y}, \ldots , +(N_y-1) \frac{2\pi}{L_y}](https://render.githubusercontent.com/render/math?math=k_y%20%3D%200%2C%20%5Cpm%201%20%5Cfrac%7B2%5Cpi%7D%7BL_y%7D%2C%20%5Cpm%202%20%5Cfrac%7B2%5Cpi%7D%7BL_y%7D%2C%20%5Cldots%20%2C%20%2B(N_y-1)%20%5Cfrac%7B2%5Cpi%7D%7BL_y%7D%0A)  
-![k_z = 0, \pm 1 \frac{2\pi}{L_z}, \pm 2 \frac{2\pi}{L_z}, \ldots , +(N_z-1) \frac{2\pi}{L_z}](https://render.githubusercontent.com/render/math?math=k_z%20%3D%200%2C%20%5Cpm%201%20%5Cfrac%7B2%5Cpi%7D%7BL_z%7D%2C%20%5Cpm%202%20%5Cfrac%7B2%5Cpi%7D%7BL_z%7D%2C%20%5Cldots%20%2C%20%2B(N_z-1)%20%5Cfrac%7B2%5Cpi%7D%7BL_z%7D%0A)  
-For `NY=1` and `NZ=1` the code solves 1D problem . Note however, that 1D problem requires different prescription for coupling constant regularization than the one implemented in W-SLDA toolkit. 
\ No newline at end of file
+```math
+k_y = 0, \pm 1 \frac{2\pi}{L_y}, \pm 2 \frac{2\pi}{L_y}, \ldots , +(N_y-1) \frac{2\pi}{L_y}
+```
+```math 
+k_z = 0, \pm 1 \frac{2\pi}{L_z}, \pm 2 \frac{2\pi}{L_z}, \ldots , +(N_z-1) \frac{2\pi}{L_z}
+```
+For `NY=1` and `NZ=1`, the code solves a 1D problem. Note, however, that the 1D problem requires a different prescription for coupling constant regularization than the one implemented in the W-SLDA toolkit. 
\ No newline at end of file