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

# # Ricci Tensor and Scalar Curvature calculations using Symbolic module

# In[1]:


import sympy
from einsteinpy.symbolic import RicciTensor, RicciScalar
from einsteinpy.symbolic.predefined import AntiDeSitter

sympy.init_printing()


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

# In[2]:


metric = AntiDeSitter()
metric.tensor()


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

# In[3]:


Ric = RicciTensor.from_metric(metric)
Ric.tensor()


# ### Calculating the Ricci Scalar(Scalar Curvature) from the Ricci Tensor

# In[4]:


R = RicciScalar.from_riccitensor(Ric)
R.simplify()
R.expr


# The curavture is -12 which is in-line with the theoretical results