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

# # Einstein Tensor calculations using Symbolic module

# In[1]:


import numpy as np
import pytest
import sympy
from sympy import cos, simplify, sin, sinh, tensorcontraction
from einsteinpy.symbolic import EinsteinTensor, MetricTensor, RicciScalar

sympy.init_printing()


# ### Defining the Anti-de Sitter spacetime Metric

# In[2]:


syms = sympy.symbols("t chi theta phi")
t, ch, th, ph = syms
m = sympy.diag(-1, cos(t) ** 2, cos(t) ** 2 * sinh(ch) ** 2, cos(t) ** 2 * sinh(ch) ** 2 * sin(th) ** 2).tolist()
metric = MetricTensor(m, syms)


# ### Calculating the Einstein Tensor (with both indices covariant)

# In[3]:


einst = EinsteinTensor.from_metric(metric)
einst.tensor()