Update README.md

README.md

@@ -19,22 +19,11 @@ pip install adapol
 
 
 # Examples
-In the `examples` directory, we provide two examples [`discrete.ipynb`](https://github.com/Hertz4/adapol/blob/main/example/discrete.ipynb) and [`semicircle.ipynb`](https://github.com/Hertz4/adapol/blob/main/example/semicircle.ipynb), showcasing how to use `adapol` for both discrete spectrum and continuous spectrum. We also demonstrate how to use our code through the triqs interface.
+In the `examples` directory, we provide two examples [`discrete.ipynb`](https://github.com/Hertz4/adapol/blob/main/example/discrete.ipynb) and [`semicircle.ipynb`](https://github.com/Hertz4/adapol/blob/main/example/semicircle.ipynb), showcasing how to use `adapol` for both discrete spectrum and continuous spectrum.
+
+In these notebooks, we also demonstrate how to use our code through the triqs interface.
 
-Below is a quick introduction through the following toy example:
-### Setup
-```python
-import numpy as np
-beta = 20
-Z = np.linspace(-25.,25.,26)*np.pi/beta  #Matsubara frequencies
-Delta = 1.0/(1j*Z-0.5) + 2.0/(1j*Z+0.2) + 0.5/(1j*Z+0.7) # Matsubara functions on these frequencies
-```
 
-### Hybridization Fitting
-The hybridization fitting is handled by the `hybfit` function.
-```python
-from adapol import hybfit
-```
 There are two choices for doing hybridization fitting. One can either fit with desired accuracy tolerance `tol`:
 ```python
 bath_energy, bath_hyb, final_error, func = hybfit(Delta, Z, tol=tol)
@@ -43,24 +32,15 @@ Or fit with specified number of interpolation points `Np`:
 ```python
 bath_energy, bath_hyb, final_error, func = hybfit(Delta, Z, Np = Np)
 ```
-Here `bath_energy` $E$ and `bath_hyb` $V$ are desired quantities of hybridization orbitals. They satisfy
-
-```math
-\Delta(\mathrm i \omega_k)_{mn} \approx \sum_l \frac{V_{lm} V_{ln}^*}{\mathrm i\omega_k - E_l}.
-```
+Here `bath_energy` $E$ and `bath_hyb` $V$ are desired quantities of hybridization orbitals. 
 
 In more sophisticated applications, one might need to specify other flags, such as `maxiter`, `cleanflag` and `disp`. See the documentation for details.
 
-One can look at the final error of the hybridization fitting:
 
-```python
-print(final_error)
-```
 ### Triqs interface
 
 For triqs users, if the Green's function data `delta_triqs` is stored as a `triqs.gf.Gf` object or `triqs.gf.BlockGf` object, then the hybridization fitting could be done using the `hybfit_triqs` function:
 ```python
-from adapol import hybfit_triqs
 bathhyb, bathenergy, delta_fit, final_error = hybfit_triqs(delta_triqs, tol=tol, debug=True)
 ```
 ### Analytic continuation