#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Tue Jun 27 21:54:16 2023

@author: richardson
"""

# sympy
# symbolic python commands that are actually used a lot
# by sagemath


from sympy import *

#print(sqrt(700))
x , y, t = symbols(' x y t ')
init_printing()
#pprint(expand((x+3*y+1)**5))
#print(latex(expand((x+3*y+1)**5)))
#print(3**200)
#print(integrate(x**7*exp(-2*x),x))
#print(integrate(x**7*exp(-2*x),(x,0,oo)))

#print(Sum((y+1)/y**6,(y,1,oo)).doit())

#print(solve(x**6-4,x))
# I means sqrt(-1)

fff = Function('fff')

#print( dsolve(Eq(fff(t).diff(t)+3*fff(t).diff(t,t)+fff(t),sin(t)),fff(t)))
# Eq(A,B) means the equation A == B

M = Matrix([[1,2],[-3,2]])
# print(M)
# print(M.eigenvals())
# print(M.rref())
# P,D = M.diagonalize()
# print(D)
# print(P)
# print(simplify(P*D*P**(-1)))

print(expand(exp(2+3*I),complex=True))

print(pi)
print(pi.evalf(100))
# evalf() means numerically calculate

plot(sin(x),xlim=(0,4*pi))