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

# # Distance-regular graph parameter checking in Sage
# 
# [![DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.1418410.svg)](https://doi.org/10.5281/zenodo.1418410)
# 
# A Sage package for checking the feasibility of distance-regular graph parameter sets.
# A more detailed description, along with some results, is available in a [manuscript](https://arxiv.org/abs/1803.10797) currently available on arXiv.

# ## Contents
# 
# ### `drg`
# 
# The `drg` folder contains the package source. After you make sure that Sage sees this folder, you can import it as a Python module.

# In[1]:


import drg
p = drg.DRGParameters([80, 63, 12], [1, 12, 60])
p.check_feasible()


# You can also give an intersection array with parameters.

# In[2]:


r = var("r")
fam = drg.DRGParameters([2*r^2*(2*r + 1), (2*r - 1)*(2*r^2 + r + 1), 2*r^2], [1, 2*r^2 , r*(4*r^2 - 1)])
fam.check_feasible()


# In[3]:


fam1 = fam.subs(r == 1)
fam1


# In[4]:


fam2 = fam.subs(r == 2)
fam2


# In[5]:


fam2.check_feasible()


# ### `jupyter`
# 
# A collection of sample Jupyter notebooks giving some nonexistence results.
# 
# * [Demo.ipynb](jupyter/Demo.ipynb) - demonstration of the `sage-drg` package
# * [DRG-135-128-16-1-16-120.ipynb](jupyter/DRG-135-128-16-1-16-120.ipynb) - proof of nonexistence of a distance-regular graph with intersection array $\{135, 128, 16; 1, 16, 120\}$ with $1360$ vertices
# * [DRG-234-165-12-1-30-198.ipynb](jupyter/DRG-234-165-12-1-30-198.ipynb) - proof of nonexistence of a distance-regular graph with intersection array $\{234, 165, 12; 1, 30, 198\}$ with $1600$ vertices
# * [DRG-55-54-50-35-10-bipartite.ipynb](jupyter/DRG-55-54-50-35-10-bipartite.ipynb) - proof of nonexistence of a bipartite distance-regular graph with intersection array $\{55, 54, 50, 35, 10; 1, 5, 20, 45, 55\}$ with $3500$ vertices
# * [DRG-d3-2param.ipynb](jupyter/DRG-d3-2param.ipynb) - proof of nonexistence of a family of distance-regular graphs with intersection arrays $\{(2r+1)(4r+1)(4t-1), 8r(4rt-r+2t), (r+t)(4r+1); 1, (r+t)(4r+1), 4r(2r+1)(4t-1)\}$ ($r, t \ge 1$)
# * [QPoly-d4-tight4design.ipynb](jupyter/QPoly-d4-tight4design.ipynb) - proof of nonexistence of a $Q$-polynomial association scheme with Krein array $\{r^2-4, r^2-9, 10, 1; 1, 2, r^2-9, r^2-4\}$ ($r \ne 9$)

# ## Citing
# 
# If you use `sage-drg` in your research, please cite both the manuscript and the repository:
# 
# * J. Vidali. Using symbolic computation to prove nonexistence of distance-regular graphs, 2018. [`arXiv:1803.10797`](http://arxiv.org/abs/1803.10797).
# 
# * J. Vidali. `jaanos/sage-drg`: `sage-drg` v0.8, 2018. [`https://github.com/jaanos/sage-drg/`](https://github.com/jaanos/sage-drg/), [`doi:10.5281/zenodo.1418410`](http://dx.doi.org/10.5281/zenodo.1418410).
# 
# ```latex
# @other {v18a,
#     AUTHOR = {Vidali, Jano\v{s}},
#      TITLE = {Using symbolic computation to prove nonexistence of distance-regular graphs},
#       NOTE = {\href{http://arxiv.org/abs/1803.10797}{\texttt{arXiv:1803.10797}}},
#       YEAR = {2018},
# }
# 
# @software{v18b,
#    AUTHOR = {Vidali, Jano\v{s}},
#     TITLE = {{\tt jaanos/sage-drg}: {\tt sage-drg} v0.8},
#      NOTE = {\url{https://github.com/jaanos/sage-drg/},
#              \href{http://dx.doi.org/10.5281/zenodo.1418410}{\texttt{10.5281/zenodo.1418410}}},
#      YEAR = {2018},
# }
# ```
# 
# Additionally, `sage-drg` has been used in the following research:
# 
# * A. Gavrilyuk, S. Suda and J. Vidali. On tight 4-designs in Hamming association schemes, 2018. [`arXiv:1809.07553`](http://arxiv.org/abs/1809.07553).
# 
# If you would like your research to be listed here, feel free to open an issue or pull request.