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

# This example is kindly contributed by [FreddyBaudine](https://github.com/FreddyBaudine) for reproducing [pygae/galgebra#15](https://github.com/pygae/galgebra/issues/15) with modifications by [utensil](https://github.com/utensil).

# In[1]:


import sys
from galgebra.printer import  Format, xpdf, Fmt
Format()
from sympy import symbols, Rational, latex
from galgebra.ga import Ga


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# st4: Spacetime Algebra I
st4coords = (t,x,y,z) = symbols('t x y z', real=True) 
st4 = Ga('e_t e_x e_y e_z', g=[1,-1,-1,-1], coords=st4coords)
(e_t,e_x,e_y,e_z) = st4.mv()
(e__t,e__x,e__y,e__z) = st4.mvr(norm = False) 


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Format(Fmode = True, Dmode = True)


# In[4]:


(grad,rgrad) = st4.grads()


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s = st4.mv('s','scalar',f = True)
a = st4.mv('a','vector',f = True)
b = st4.mv('b','vector',f = True)
B = st4.mv('B','bivector',f = True)
C = st4.mv('C',3)
I = st4.mv('I','pseudo')
S = st4.mv('S','spinor',f = True)
M = st4.mv('M','mv',f = True)

M1inv = M.grade(1).inv()
M3inv = M.grade(3).inv()


# In[6]:


a.Fmt(1,r'\mathbf{a}')


# In[7]:


(a*a).Fmt(2,r'\mathbf{a} \mathbf{a}')


# In[8]:


a.inv().Fmt(3,r'\mathbf{a}^{-1}')


# In[9]:


(M.grade(1) * M.grade(1)).\
 Fmt(1,r'\langle \mathbf{M} \rangle _1 \langle \mathbf{M} \rangle _1')


# In[10]:


M1inv.Fmt(3,r'\langle \mathbf{M} \rangle _1 ^{-1}')


# In[11]:


M.grade(3).Fmt(2,r'\langle \mathbf{M} \rangle _3')


# In[12]:


(M.grade(3) * M.grade(3)).\
 Fmt(1,r'\langle \mathbf{M} \rangle _3 \langle \mathbf{M} \rangle _3')


# In[13]:


M3inv.Fmt(3,r'\langle \mathbf{M} \rangle _3^{-1}')


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