From cd6e2327e90cf71d80fda0c7ff88eb651cb72641 Mon Sep 17 00:00:00 2001
From: hugogogo <hugogogo@protonmail.com>
Date: Sun, 10 May 2026 18:27:34 +0200
Subject: [PATCH] solve all terms

---
 src/solver.c       | 55 +++++++++++++++++++++++++++++-----------------
 src/utils/errors.c |  4 ++--
 2 files changed, 37 insertions(+), 22 deletions(-)

diff --git a/src/solver.c b/src/solver.c
index 79ed1f0..dba7e5b 100644
--- a/src/solver.c
+++ b/src/solver.c
@@ -102,36 +102,51 @@ typedef struct
 static void solve_degree_2(s_solution_degree_2 *solution, double a, double b, double c)
 {
     double delta;
+    double delta_sqrt;
 
     solution->a = a;
     solution->b = b;
     solution->c = c;
 
     delta = b * b - 4 * a * c;
-    solution->delta_sign = ft_fsign(delta);
-    solution->delta_absolute = ft_fabs(delta);
-    solution->delta_sqrt = ft_sqrt(solution->delta_absolute);
+    solution->delta_sign = ft_fsign(delta);                   // DELTA_PLUS or DELTA_MINUS or DELTA_ZERO
+    solution->delta_absolute = ft_fabs(delta);                // |Δ| == |b² - 4ac|
+    solution->delta_sqrt = ft_sqrt(solution->delta_absolute); // √|Δ|
+    delta_sqrt = solution->delta_sqrt;
 
     // first term
-    solution->first_term_gcd = find_gcd(b, 2 * a);
-    solution->first_term_numerator = -b / solution->first_term_gcd;
-    solution->first_term_denominator = 2 * a / solution->first_term_gcd;
-    solution->first_term = -b / (2 * a);
+    solution->first_term_gcd = find_gcd(b, 2 * a);                       // gcd(b, 2a)
+    solution->first_term_numerator = -b / solution->first_term_gcd;      // -b / gcd
+    solution->first_term_denominator = 2 * a / solution->first_term_gcd; // 2a / gcd
+    solution->first_term = -b / (2 * a);                                 // double (-b / 2a)
 
     // second term
-    solution->second_term_gcd = find_gcd(solution->delta_sqrt, 2 * a);
-    // solution->second_term_numerator = ;
-    // solution->second_term_denominator = ;
-    // solution->second_term = ;
-    // solution->solution1 = solution->first_term;
-    // if (solution->delta_sign == DELTA_ZERO)
-    // {
-    //     solution->solution2 = ;
-    // }
-    // else
-    // {
-    //     solution->solution2 = 0.0;
-    // }
+    solution->second_term_gcd = find_gcd(delta_sqrt, 2 * a);                  // gcd(√|Δ|, 2a)
+    solution->second_term_numerator = delta_sqrt / solution->second_term_gcd; // √|Δ| / gcd
+    solution->second_term_denominator = 2 * a / solution->second_term_gcd;    // 2a / gcd
+    solution->second_term = delta_sqrt / 2 * a;                               // √|Δ| / 2a
+
+    // solution
+    /*
+    degree 2               : delta > 0        ( -b / 2a +-  √Δ / 2a   )
+                         delta == 0       ( -b / 2a               )
+                         delta < 0        ( -b / 2a +- i√|Δ| / 2a )
+    */
+    solution->solution1 = solution->first_term; // first_term + second_term
+    if (solution->delta_sign == DELTA_ZERO)
+    {
+        solution->solution1 = solution->first_term; // -b / 2a
+        solution->solution2 = NAN;                  // NAN (no solution)
+    }
+    else if (solution->delta_sign == DELTA_MINUS)
+    {
+        solution->solution1 = solution->first_term + solution->second_term; // -b / 2a + i√|Δ| / 2a
+        solution->solution2 = solution->first_term - solution->second_term; // -b / 2a - i√|Δ| / 2a
+    }
+    else if (solution->delta_sign == DELTA_PLUS)
+    {
+        // no real solution, but can output irreal solution with 'i'
+    }
 }
 
 void solve(const s_polynom *polynom, s_solution *solution)
diff --git a/src/utils/errors.c b/src/utils/errors.c
index 362bbdd..fe321e8 100644
--- a/src/utils/errors.c
+++ b/src/utils/errors.c
@@ -98,8 +98,8 @@ static void print_context_solution()
         dprintf(STDERR_FILENO, "second_term_denominator: %15i  (   2a / gcd            )\n", solution_2.second_term_denominator);
         dprintf(STDERR_FILENO, "second_term            : %15g  ( √|Δ| / 2a             )\n", solution_2.second_term);
 
-        dprintf(STDERR_FILENO, "solution1              : %15g  (                       )\n", solution_2.solution1);
-        dprintf(STDERR_FILENO, "solution2              : %15g  (                       )\n", solution_2.solution2);
+        dprintf(STDERR_FILENO, "solution1              : %15g  ( (-b / 2a) + (√Δ / 2a) )\n", solution_2.solution1);
+        dprintf(STDERR_FILENO, "solution2              : %15g  ( (-b / 2a) - (√Δ / 2a) )\n", solution_2.solution2);
     }
 
     ft_putchar_fd('\n', STDERR_FILENO);