init solver

README.md

@@ -44,4 +44,21 @@ this project uses submodules (maybe recursively), so either :
 5. find degree
 6. print degree
 7. solve
-8. print solution
+    -> discriminant          : Δ = b² - 4ac
+    -> Δ > 0  -> 2 solutions : x = ( -b / 2a ) +-  ( √|Δ| / 2a )
+    -> Δ == 0 ->             : x = ( -b / 2a )
+    -> Δ < 0  -> 2 solutions : x = ( -b / 2a ) +- i( √|Δ| / 2a )
+    -> solution : 
+      - delta_sign;              // + or -
+      - delta_absolute;          // |Δ|
+      - first_term_pgcd;         // pgcd(b, 2a)
+      - first_term_numerator;    // -b / pgcd
+      - first_term_denominator;  // 2a / pgcd
+      - first_term;              // double (-b / 2a)
+      - second_term_pgcd;        // pgcd(√|Δ|, 2a)
+      - second_term_numerator;   // √|Δ| / pgcd
+      - second_term_denominator; // 2a / pgcd
+      - second_term;             // double (√|Δ| / 2a)
+      - double solution1;        // first_term + second_term
+      - double solution2;        // first_term - second_term
+8. print solution