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

# # [Goulib](../notebook.ipynb).expr
# 
# math expressions
# (see [polynomials](polynomials.ipynb) for more)

# In[1]:


from Goulib.notebook import *
from Goulib.expr import *
from Goulib.table import Table
from math import pi,sin
from Goulib.math2 import sqrt


# Expr can be created from:
# * numbers
# * text (python-like formula)
# 
# Expr has LaTeX representation in notebooks

# In[2]:


Expr(3**5) # is evaluated before Expr is created


# In[3]:


e=Expr(3)**Expr(5) # combine Expr essions
h('as LaTeX (default) :',e)
print('as math formula :',e)
print('as python code :',repr(e))
print('evaluated :',e())


# In[4]:


e=Expr('5**3+(-3^2)') # ^ and ** are both considered as power operator for clarity+compatibility
h('as LaTeX (default) :',e)
print('as math formula :',e)
print('as python code :',repr(e))
print('evaluated :',e())


# ## Functions

# In[5]:


e=Expr('x^2')
h('an Expr may contain variables :',e)
h('and be evaluated as a function : for x=2, ',e,'=',e(x=2))


# all functions defined in math module can be used:

# In[6]:


functions=default_context.functions # functions known by default to Expr
t=Table()
for n in functions:
    f=functions[n][0] # get the function itself
    try:
        e=Expr(f)
        t.append([n,repr(e),str(e),e])
    except Exception as e:
        t.append([n,e])
t


# In[7]:


e=Expr(sqrt) #(Expr(pi))+Expr(1/5)
h('as LaTeX (default) :',e)
print('as math formula :',e)
print('as python code :',repr(e))
print('evaluated :',e())


# In[8]:


e1=Expr('3*x+2') #a very simple expression defined from text
e1


# In[9]:


e1=Expr(lambda x:3*x+2) #the same expression defined from a lambda function
e1


# In[10]:


def f(x):
    return 3*x+2
Expr(f) #the same expression defined from a regular (simple...) function


# In[11]:


e3=Expr(sqrt)(e1) #Expr can be composed
e3


# In[12]:


print(e3(x=1)) # Expr can be evaluated as a function
print(e3((pi-4)/6)) #the x variable is implicit


# In[13]:


e1([-2,1,0,1,2]) # Expr can be evaluated at different x values at once


# In[14]:


e3.plot()  # Expr can be also plotted. Note the X axis is automatically restricted to the definition domain


# In[15]:


Expr('1/x').plot(x=range(-100,100))


# ## multivariable

# In[16]:


e=Expr('(-b+sqrt(b^2-4*a*c))/(2*a)') #laTex is rendered with some simple simplifications
e


# In[17]:


e(a=1) # substitution doesn't work yet ...


# ## complex

# In[18]:


e=Expr("e**(i*pi)")
e


# In[19]:


e() # should be -1 one day...