From c0475c4997dcd3f601cf00073563e99d943c6d35 Mon Sep 17 00:00:00 2001
From: Alejandro Mcewen <alejandromcewen@Alejandros-MacBook-Pro.local>
Date: Thu, 11 Sep 2025 16:24:58 -0500
Subject: [PATCH 1/2] Agregando comentario de gauss jordan

---
 code/math/gaussjordan_modular.cpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/code/math/gaussjordan_modular.cpp b/code/math/gaussjordan_modular.cpp
index 0c8602b..67105a1 100644
--- a/code/math/gaussjordan_modular.cpp
+++ b/code/math/gaussjordan_modular.cpp
@@ -1,6 +1,6 @@
 const int eps = 0, mod = 1e9+7;
 
-int gauss(vector<vi> &a, vi &ans) {
+int gauss(vector<vi> &a, vi &ans) { // a matrix n, m + 1 donde la ultima columna es b
   int n = sz(a), m = sz(a[0]) - 1;
   vi where(m, -1);
   for(int col=0, row=0; col<m && row<n; ++col) {

From fc16fcbb3fb3f8f43fef8fbac7ddf37bba1e4cca Mon Sep 17 00:00:00 2001
From: Alejandro Mcewen <alejandromcewen@Alejandros-MacBook-Pro.local>
Date: Thu, 11 Sep 2025 16:38:46 -0500
Subject: [PATCH 2/2] Done with changes

---
 code/math/gaussjordan.cpp         |  9 +++++----
 code/math/gaussjordan_modular.cpp | 10 +++++-----
 2 files changed, 10 insertions(+), 9 deletions(-)

diff --git a/code/math/gaussjordan.cpp b/code/math/gaussjordan.cpp
index 48ad56f..a74819f 100644
--- a/code/math/gaussjordan.cpp
+++ b/code/math/gaussjordan.cpp
@@ -1,4 +1,5 @@
-int gauss(vector<vector<double>> &a, vector<double> &ans) {
+// a := matriz n x (m+1)  , la ultima columna es b, en el sistema Ax = b 
+int gauss(vector<vector<double>> &a, vector<double> &x) {
   int n = sz(a), m = sz(a[0]) - 1;
   vi where(m, -1);
   for(int col=0, row=0; col<m && row<n; ++col) {
@@ -19,13 +20,13 @@ int gauss(vector<vector<double>> &a, vector<double> &ans) {
     ++row;
   }
 
-  ans.assign(m, 0);
+  x.assign(m, 0);
   forn(i,m){
-    if(where[i] != -1) ans[i] = a[where[i]][m] / a[where[i]][i];
+    if(where[i] != -1) x[i] = a[where[i]][m] / a[where[i]][i];
   }
   forn(i,n){
     double sum = 0;
-    forn(j,m) sum += ans[j] * a[i][j];
+    forn(j,m) sum += x[j] * a[i][j];
     if(abs(sum - a[i][m]) > eps) return 0;
   }
 
diff --git a/code/math/gaussjordan_modular.cpp b/code/math/gaussjordan_modular.cpp
index 67105a1..8832b13 100644
--- a/code/math/gaussjordan_modular.cpp
+++ b/code/math/gaussjordan_modular.cpp
@@ -1,6 +1,6 @@
 const int eps = 0, mod = 1e9+7;
-
-int gauss(vector<vi> &a, vi &ans) { // a matrix n, m + 1 donde la ultima columna es b
+// a := matriz n x (m+1)  , la ultima columna es b, en el sistema Ax = b 
+int gauss(vector<vi> &a, vi &x) { 
   int n = sz(a), m = sz(a[0]) - 1;
   vi where(m, -1);
   for(int col=0, row=0; col<m && row<n; ++col) {
@@ -21,13 +21,13 @@ int gauss(vector<vi> &a, vi &ans) { // a matrix n, m + 1 donde la ultima columna
     ++row;
   }
 
-  ans.assign(m, 0);
+  x.assign(m, 0);
   forn(i,m){
-    if(where[i] != -1) ans[i] = 1LL*a[where[i]][m] * inv(a[where[i]][i])%mod;
+    if(where[i] != -1) x[i] = 1LL*a[where[i]][m] * inv(a[where[i]][i])%mod;
   }
   forn(i,n){
     ll sum = 0;
-    forn(j,m) sum = (sum + 1LL*ans[j] * a[i][j])%mod;
+    forn(j,m) sum = (sum + 1LL*x[j] * a[i][j])%mod;
     if(abs(sum - a[i][m]) > eps) return 0;
   }