symbolic_programming.py

# -*- coding: utf-8 -*-
"""Symbolic_Programming.ipynb

Automatically generated by Colaboratory.

Original file is located at
    https://colab.research.google.com/drive/1PDqLP9WtTffRMi1ZMAAU3WEa5Qr5zFgN
"""

# Program 1 :

import sympy
from sympy import *
print(N(sqrt(2),100))

# Program 2 :


from sympy import *
a = Rational(1,2)
b = Rational(1,3)
print(a+b)

# Program 3 :
import sympy as sym
x = sym.Symbol('x')
y = sym.Symbol('y')
sym.expand((x+y)**6)

# Program 4 :

import sympy
from sympy import *
x =Symbol('x')
simplify(sin(x)/cos(x))

# Program 5 :

import sympy
from sympy import *
x =Symbol('x')
solveset((sin(x)-x)/(x**3),x)

# Program 6 :
import sympy
from sympy import *

x = symbols('x')
expr1 = log(x)


# Use sympy.Derivative() method
expr1_diff = Derivative(expr, x)
	
print("Derivative of expression with respect to x : {}".format(expr1_diff))
print("Value of the derivative : {} ".format(expr1_diff.doit()))


x = symbols('x')
expr2 = 1/x


# Use sympy.Derivative() method
expr2_diff = Derivative(expr2, x)
	
print("Derivative of expression with respect to x : {}".format(expr2_diff))
print("Value of the derivative : {} ".format(expr2_diff.doit()))

x = symbols('x')
expr3 = sin (x)


# Use sympy.Derivative() method
expr3_diff = Derivative(expr3, x)
	
print("Derivative of expression with respect to x : {}".format(expr3_diff))
print("Value of the derivative : {} ".format(expr3_diff.doit()))

x = symbols('x')
expr4 = cos (x)


# Use sympy.Derivative() method
expr4_diff = Derivative(expr4, x)
	
print("Derivative of expression with respect to x : {}".format(expr4_diff))
print("Value of the derivative : {} ".format(expr4_diff.doit()))

# Program 7

import sympy
from sympy import *
x, y= symbols('x y')
expr1=Eq(x+y-2,0)
expr2=Eq(2*x+y,0)
solve((expr1,expr2), (x, y))

sol_dict = solve((expr1,expr2), (x, y))
print(f'x = {sol_dict[x]}')
print(f'y = {sol_dict[y]}')

# Program 8

import sympy
from sympy import *
a1= symbols('x')
x1 = integrate('x**2',a1)
print("Integration of x: "+ str(x1))

a2= symbols('x')
x2 = integrate('sin (x)',a2)
print("Integration of sin (x): "+ str(x2))

a3= symbols('x')
x3 = integrate('cos (x)',a3)
print("Integration of cos (x): "+ str(x3))

# Program 9

import sympy as sym
from sympy import *
x = sym.symbols('x')
f = sym.Function('f')(x)
equation = Eq(f.diff(x,x)+ 9*f,1)
print(sym.dsolve(equation,f))

# Program 10

import sympy as sym
x,y,z = sym.symbols('x y z')
M = sym.Matrix(((3,7,-12,0),(4,-2,-5,0)))
system = A, b = M[:, :-1], M[:, -1]
print(sym.linsolve(system,x,y,z))