42_EXT_05_computorv1/README.md

42_EXT_05_computorv1

ressources

• project intra : https://projects.intra.42.fr/projects/42cursus-computorv1
• project luke : https://github.com/LuckyLaszlo/computorv1

install

this project uses submodules (maybe recursively), so either :

• git clone --recurse-submodules <repo-url>
• or, after cloning : git submodule update --init --recursive

steps

1. lexer -> tokens types :
   • TOKEN_VARIABLE // x, y, etc.
   • TOKEN_NUMBER_INT // int
   • TOKEN_NUMBER_DOUBLE // double
   • TOKEN_POWER // ^ or **
   • TOKEN_SIGN_PLUS // +
   • TOKEN_SIGN_MINUS // -
   • TOKEN_FACTOR_MULT // *
   • TOKEN_FACTOR_DIV // / or :
   • TOKEN_EQUAL // =
   • END // null
2. parser -> terms :
   • POSITION // left or righ from =
   • SIGN // + or -
   • COEFFICIENT // double
   • EXPONENT // double
3. reduce -> polynom :
   • sign
   • coefficient
   • exponent
4. print reduced form -> print reduced form -> if degree 1 :
   • if c = 0 -> print "any real is a solution"
   • if c != 0 -> print "no solution" -> if degree 2 :
   • print degree -> if degree 3 :
   • print degree
5. solve -> degree 1 : -> ax + b = 0 <=> ax = -b <=> x = -b / a -> solution : - a; // double - b; // double - solution_gcd; // gcd(b, a) - solution_numerator; // -b / gcd - solution_denominator; // a / gcd - solution; // double (-b / a) -> degree 2 : -> discriminant : Δ = b² - 4ac -> Δ > 0 -> 2 solutions : x = ( -b / 2a ) +- ( √|Δ| / 2a ) -> Δ == 0 -> 1 solution : x = ( -b / 2a ) -> Δ < 0 -> 2 solutions : x = ( -b / 2a ) +- i( √|Δ| / 2a ) -> solution : - a; // double - b; // double - c; // double - delta_sign; // + or - - delta_absolute; // |Δ| - first_term_gcd; // gcd(b, 2a) - first_term_numerator; // -b / gcd - first_term_denominator; // 2a / gcd - first_term; // double (-b / 2a) - second_term_gcd; // gcd(√|Δ|, 2a) - second_term_numerator; // √|Δ| / gcd - second_term_denominator; // 2a / gcd - second_term; // double (√|Δ| / 2a) - double solution1; // first_term + second_term - double solution2; // first_term - second_term
6. print solution