MathExpressionCompiler

How does it work?

  Before I tell you how compilers read and solve mathematical expressions, there are things that you must know.

• Yours math expressions are called infix expressions.
  • mx+b
• Compilers can only read postfix expressions.
  • mx*b+

  So, compilers do not read mathematical expressions like we do. They first change an infix to a postfix expression and then, evaluate it. Some compilers do this two steps at the same time. To return the expression answer, Queue and Stack are used during the process.
  The English Algorithm can be seen here.

How to use MathExpressionsCompiler functions

Import

from MathExpressionCompiler import to_postfix, evaluate

NOTE: My Queue and Stack AbstractDataTypes are needed at the same MathExpressionCompiler path

Infix to Postfix expression

infix_01 = 'a - b'
print(f'>> {to_postfix(infix_01)}')
# >> a b -

infix_02 = 'a - b * c'
print(f'>> {to_postfix(infix_02)}')
# a b c * -

infix_03 = '( a - b ) * c'
print(f'>> {to_postfix(infix_03)}')
# >> a b - c *

infix_04 = 'a + b * c ** d - e'
print(f'>> {to_postfix(infix_04)}')
# >> a b c d ** * + e -

infix_05 = 'a * ( b + c ) * ( d - g ) * h'
print(f'>> {to_postfix(infix_05)}')
# >> a b c + * d g - * h *

infix_06 = 'a * b - c * d ** e / f + g * h'
print(f'>> {to_postfix(infix_06)}')
# >> a b * c d e ** * f / - g h * +

Evaluate the postfix expression

print(f'>> {evaluate("8 7 2 * -")}')
# >> -6

Evaluate the postfix expression with variables

variables = {'a': 8, 'b': 7, 'c': 2}
print(f'>> {evaluate("a b c * -", variables)}')
# >> -6

Real/Usefull Exemple

Bhaskara Formula

expr_1 = '( 0 - b + ( ( b ** 2 - 4 * a * c ) ) ** sqrt ) / 2 * a'
expr_2 = '( 0 - b - ( ( b ** 2 - 4 * a * c ) ) ** sqrt ) / 2 * a'

print(f">> {to_postfix(expr_1)}")
# >> 0 b - b 2 ** 4 a * c * - sqrt ** + 2 / a *

print(f">> {to_postfix(expr_2)}")
# >> 0 b - b 2 ** 4 a * c * - sqrt ** - 2 / a *

variables = {'a': 1, 'b': -5, 'c': 6, 'sqrt': 0.5}
print(f">> {evaluate('0 b - b 2 ** 4 a * c * - sqrt ** + 2 / a *', variables)}")
# >> 3.0
print(f">> {evaluate('0 b - b 2 ** 4 a * c * - sqrt ** - 2 / a *', variables)}")
# >> 2.0

Tips

This algorithm doesn't support square root. But try:

sqrt(8) == pow(8, 0.5) == 8 ** 0.5

This algorithm doesn't support negative numbers in to_postfix() method. But try::

-8 == 0 - 8