From 8c96ca43406df9a7a957268c8ccaf48655e14b98 Mon Sep 17 00:00:00 2001
From: Persson-dev <sim16.prib@gmail.com>
Date: Sat, 10 Feb 2024 12:18:34 +0100
Subject: [PATCH 01/29] remove useless dimension

---
 src/Matrix.cpp | 9 +++++----
 src/Matrix.h   | 1 -
 2 files changed, 5 insertions(+), 5 deletions(-)

diff --git a/src/Matrix.cpp b/src/Matrix.cpp
index 27341e2..535b7f9 100644
--- a/src/Matrix.cpp
+++ b/src/Matrix.cpp
@@ -9,14 +9,15 @@ Matrix::Matrix(const std::string& fileNameInput) {
 	Load(fileNameInput);
 }
 
-Matrix::Matrix(std::size_t lignes, std::size_t colonnes) : m_Lignes(lignes), m_Colonnes(colonnes), m_Dimension(lignes * colonnes) {
-	m_Data.resize(m_Dimension);
+Matrix::Matrix(std::size_t lignes, std::size_t colonnes) : m_Lignes(lignes), m_Colonnes(colonnes) {
+	m_Data.resize(m_Lignes * m_Colonnes);
 }
 Matrix::Matrix(std::size_t lignes, std::size_t colonnes, std::initializer_list<long double>&& initList) :
-	m_Lignes(lignes), m_Colonnes(colonnes), m_Dimension(lignes * colonnes) {
+	m_Lignes(lignes), m_Colonnes(colonnes) {
 	m_Data = initList;
-	m_Data.resize(m_Dimension);
+	m_Data.resize(m_Lignes * m_Colonnes);
 }
+
 Matrix::~Matrix() {}
 
 Matrix Matrix::operator*(const Matrix& other) const {
diff --git a/src/Matrix.h b/src/Matrix.h
index ad80018..fe397e8 100644
--- a/src/Matrix.h
+++ b/src/Matrix.h
@@ -7,7 +7,6 @@ class Matrix {
   private:
 	std::size_t m_Lignes;
 	std::size_t m_Colonnes;
-	std::size_t m_Dimension;
 	std::vector<long double> m_Data;
 
   public:

From 21a7268cbcab3894b42b1e0101c12dfc5865b60c Mon Sep 17 00:00:00 2001
From: Persson-dev <sim16.prib@gmail.com>
Date: Sat, 10 Feb 2024 14:31:54 +0100
Subject: [PATCH 02/29] add actions

---
 .gitea/workflows/ubuntu.yaml | 27 +++++++++++++++++++++++++++
 1 file changed, 27 insertions(+)
 create mode 100644 .gitea/workflows/ubuntu.yaml

diff --git a/.gitea/workflows/ubuntu.yaml b/.gitea/workflows/ubuntu.yaml
new file mode 100644
index 0000000..308f361
--- /dev/null
+++ b/.gitea/workflows/ubuntu.yaml
@@ -0,0 +1,27 @@
+name: Linux arm64
+run-name: Build And Test
+
+on: [push]
+
+jobs:
+  Build:
+    runs-on: ubuntu-latest
+    steps:     
+      - name: Check out repository code
+        uses: actions/checkout@v3
+
+      - name: Prepare XMake
+        uses: xmake-io/github-action-setup-xmake@v1
+        with:
+          xmake-version: branch@master
+          actions-cache-folder: '.xmake-cache'
+          actions-cache-key: 'ubuntu'
+
+      - name: XMake config
+        run: xmake f -p linux -y --root
+
+      - name: Build
+        run: xmake --root
+
+      - name: Test
+        run: xmake test --root

From 150e67e30bd9a2f36c88a72f9b8e9837bb4e3907 Mon Sep 17 00:00:00 2001
From: Persson-dev <sim16.prib@gmail.com>
Date: Sat, 10 Feb 2024 14:54:32 +0100
Subject: [PATCH 03/29] update readme

---
 README.md | 14 +++++++++++++-
 1 file changed, 13 insertions(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 1d1e02d..aa2b67b 100644
--- a/README.md
+++ b/README.md
@@ -2,4 +2,16 @@
 
 
 # Cahier des charges
-![imagecdc](PeiP2_MAM-INFO_projet_02.jpg)
\ No newline at end of file
+![imagecdc](PeiP2_MAM-INFO_projet_02.jpg)
+
+# Build
+
+```
+xmake
+```
+
+# Run
+
+```
+xmake run
+```
\ No newline at end of file

From 4c217a4b20ab57c43e0cb0e57dc939ff861962f3 Mon Sep 17 00:00:00 2001
From: Persson-dev <sim16.prib@gmail.com>
Date: Sat, 10 Feb 2024 16:58:44 +0100
Subject: [PATCH 04/29] add basic test

---
 src/Matrix.cpp    | 14 ++++++++++++++
 src/Matrix.h      |  2 ++
 test/mainTest.cpp | 45 +++++++++++++++++++++++++++++++++++++++++++++
 xmake.lua         | 12 ++++++++++++
 4 files changed, 73 insertions(+)
 create mode 100644 test/mainTest.cpp

diff --git a/src/Matrix.cpp b/src/Matrix.cpp
index 535b7f9..22a62a9 100644
--- a/src/Matrix.cpp
+++ b/src/Matrix.cpp
@@ -134,6 +134,20 @@ bool Matrix::IsInversed() const {
 	return true;
 }
 
+bool Matrix::operator==(const Matrix& other) const {
+	if (m_Lignes != other.m_Lignes || m_Colonnes != other.m_Colonnes)
+		return false;
+
+	for (std::size_t i = 0; i < m_Lignes; i++) {
+		for (std::size_t j = 0; j < m_Colonnes; j++) {
+			if (!IsEqualZero(at(i, j) - other.at(i, j)))
+				return false;
+		}
+	}
+
+	return true;
+}
+
 void Matrix::GaussNonJordan(bool reduite) {
 	int r = -1;
 	for (std::size_t j = 0; j < m_Colonnes; j++) {
diff --git a/src/Matrix.h b/src/Matrix.h
index fe397e8..8ff0ec1 100644
--- a/src/Matrix.h
+++ b/src/Matrix.h
@@ -37,6 +37,8 @@ class Matrix {
 
 	bool IsInversed() const;
 
+	bool operator==(const Matrix& other) const;
+
 	long double& operator[](std::size_t indice);
 
 	long double& at(std::size_t ligne, std::size_t colonne);
diff --git a/test/mainTest.cpp b/test/mainTest.cpp
new file mode 100644
index 0000000..1748358
--- /dev/null
+++ b/test/mainTest.cpp
@@ -0,0 +1,45 @@
+#include "Matrix.h"
+#include <cassert>
+
+#ifdef NDEBUG
+#error "Il faut être en debug mode ! xmake f -m debug"
+#endif
+struct Test{
+    Matrix mat;
+    Matrix res;
+};
+
+static const std::vector<Test> TEST_MATRICES = {
+    // test 1
+    {{3, 3, {
+        1, 2, 3,
+        4, 5, 6,
+        7, 8, 9,
+    }}, {3, 3, {
+        1, 0, -1,
+        0, 1, 2,
+        0, 0, 0,
+    }}},
+    // test 2
+    {{3, 3, {
+        4, 5, 6,
+        1, 2, 3,
+        7, 8, 9,
+    }}, {3, 3, {
+        1, 0, -1,
+        0, 1, 2,
+        0, 0, 0,
+    }}}
+};
+
+void test() {
+	for (Test test : TEST_MATRICES) {
+        test.mat.GaussJordan(true);
+        assert(test.mat == test.res);
+    }
+}
+
+int main(int argc, char** argv) {
+	test();
+	return 0;
+}
diff --git a/xmake.lua b/xmake.lua
index 769129f..0cd4b3f 100644
--- a/xmake.lua
+++ b/xmake.lua
@@ -6,6 +6,18 @@ target("Pivot")
     set_rundir("$(projectdir)/matricies")
     set_languages("c++17")
 
+
+
+
+
+target("PivotTest")
+    set_kind("binary")
+    add_files("test/*.cpp", "src/Matrix.cpp")
+    add_includedirs("src")
+    set_default(false)
+    add_tests("compile_and_run")
+    set_rundir("$(projectdir)/matricies")
+
 --
 -- If you want to known more usage about xmake, please see https://xmake.io
 --

From a7a2986336b8759b6f17c388f0b3d46bf05bc5c4 Mon Sep 17 00:00:00 2001
From: Persson-dev <sim16.prib@gmail.com>
Date: Sat, 10 Feb 2024 16:59:33 +0100
Subject: [PATCH 05/29] ignore .vscode folder

---
 .gitignore | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/.gitignore b/.gitignore
index 1521057..f928f14 100644
--- a/.gitignore
+++ b/.gitignore
@@ -5,4 +5,5 @@ build/
 # MacOS Cache
 .DS_Store
 
-
+# VsCode
+.vscode

From 820308b6c76d1832c4165247ceaa75ebecec7a3b Mon Sep 17 00:00:00 2001
From: Persson-dev <sim16.prib@gmail.com>
Date: Sat, 10 Feb 2024 17:37:00 +0100
Subject: [PATCH 06/29] fix action

---
 .gitea/workflows/ubuntu.yaml | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/.gitea/workflows/ubuntu.yaml b/.gitea/workflows/ubuntu.yaml
index 308f361..e4d31e4 100644
--- a/.gitea/workflows/ubuntu.yaml
+++ b/.gitea/workflows/ubuntu.yaml
@@ -24,4 +24,6 @@ jobs:
         run: xmake --root
 
       - name: Test
-        run: xmake test --root
+        run: |
+          xmake f -m debug --root
+          xmake test --root

From 23de24e9a17af9ee9c109826de371fa771595dc1 Mon Sep 17 00:00:00 2001
From: Persson-dev <sim16.prib@gmail.com>
Date: Tue, 13 Feb 2024 11:38:52 +0100
Subject: [PATCH 07/29] add stuff

---
 src/Matrix.cpp    | 32 ++++++++++++++++++++++++++------
 src/Matrix.h      | 14 ++++++++++++--
 src/Vect.cpp      | 20 ++++++++++++++++++++
 src/Vect.h        | 22 ++++++++++++++++++++++
 test/mainTest.cpp |  1 +
 5 files changed, 81 insertions(+), 8 deletions(-)
 create mode 100644 src/Vect.cpp
 create mode 100644 src/Vect.h

diff --git a/src/Matrix.cpp b/src/Matrix.cpp
index 22a62a9..bae35f9 100644
--- a/src/Matrix.cpp
+++ b/src/Matrix.cpp
@@ -1,4 +1,5 @@
 #include <algorithm>
+#include <cassert>
 #include <cmath>
 #include <fstream>
 #include <iostream>
@@ -39,10 +40,6 @@ Matrix Matrix::operator*(const Matrix& other) const {
 	return result;
 }
 
-static bool IsEqualZero(long double var) {
-	return std::abs(var) < std::pow(10, -5);
-}
-
 void Matrix::Print() const {
 	for (size_t i = 0; i < m_Lignes; ++i) {
 		std::cout << "[ ";
@@ -101,12 +98,14 @@ void Matrix::Load(const std::string& filename) {
 	}
 }
 
-void Matrix::Transpose() {
+Matrix Matrix::Transpose() const {
+	Matrix result{m_Colonnes, m_Lignes};
 	for (std::size_t i = 0; i < m_Lignes; i++) {
 		for (std::size_t j = i; j < m_Colonnes; j++) {
-			std::swap(at(i, j), at(j, i));
+			result.at(j, i) = at(i, j);
 		}
 	}
+	return result;
 }
 
 void Matrix::Identity() {
@@ -224,4 +223,25 @@ long double& Matrix::at(std::size_t ligne, std::size_t colonne) {
 
 long double Matrix::at(std::size_t ligne, std::size_t colonne) const {
 	return m_Data[ligne * m_Lignes + colonne];
+}
+
+std::size_t Matrix::GetRawCount() const {
+	return m_Lignes;
+}
+
+std::size_t Matrix::GetColumnCount() const {
+	return m_Colonnes;
+}
+
+Matrix Matrix::SubMatrix(std::size_t origine_ligne, std::size_t origine_colonne, std::size_t ligne, std::size_t colonne) const {
+	assert(m_Lignes >= ligne && m_Colonnes >= colonne);
+	Matrix result{ligne, colonne};
+
+	for (std::size_t i = 0; i < ligne; i++) {
+		for (std::size_t j = 0; j < colonne; j++) {
+			result.at(i, j) = at(i + origine_ligne, j + origine_colonne);
+		}
+	}
+
+	return result;
 }
\ No newline at end of file
diff --git a/src/Matrix.h b/src/Matrix.h
index 8ff0ec1..dcd8198 100644
--- a/src/Matrix.h
+++ b/src/Matrix.h
@@ -1,5 +1,7 @@
 #pragma once
 
+#include <cmath>
+#include <cstddef>
 #include <string>
 #include <vector>
 
@@ -15,6 +17,9 @@ class Matrix {
 	Matrix(std::size_t lignes, std::size_t colonnes, std::initializer_list<long double>&& initList);
 	~Matrix();
 
+	std::size_t GetRawCount() const;
+	std::size_t GetColumnCount() const;
+
 	Matrix operator*(const Matrix& other) const;
 
 	void GaussNonJordan(bool reduite);
@@ -31,12 +36,14 @@ class Matrix {
 
 	void Load(const std::string& filename);
 
-	void Transpose();
+	Matrix Transpose() const;
 
 	void Identity();
 
 	bool IsInversed() const;
 
+	Matrix SubMatrix(std::size_t origine_ligne, std::size_t origine_colonne, std::size_t ligne, std::size_t colonne) const;
+
 	bool operator==(const Matrix& other) const;
 
 	long double& operator[](std::size_t indice);
@@ -46,4 +53,7 @@ class Matrix {
 	long double at(std::size_t ligne, std::size_t colonne) const;
 };
 
-static bool IsEqualZero(long double var);
\ No newline at end of file
+template <typename T>
+bool IsEqualZero(T var) {
+	return std::abs(var) < std::pow(10, -5);
+}
\ No newline at end of file
diff --git a/src/Vect.cpp b/src/Vect.cpp
new file mode 100644
index 0000000..f4be1ea
--- /dev/null
+++ b/src/Vect.cpp
@@ -0,0 +1,20 @@
+#include "Vect.h"
+
+Vect::Vect(const Matrix& mat) {
+	for (std::size_t i = 0; i < mat.GetColumnCount(); i++) {
+		std::size_t j;
+		for (j = 0; j < mat.GetRawCount(); j++) {
+			if(!IsEqualZero(mat.at(i, j)))
+				break;
+		}
+		if (j == mat.GetRawCount()) {
+			m_Data = mat.SubMatrix(0, 0, mat.GetRawCount(), j);
+		}
+	}
+	m_Data = mat;
+}
+
+// TODO
+void Vect::Print() const {
+
+}
\ No newline at end of file
diff --git a/src/Vect.h b/src/Vect.h
new file mode 100644
index 0000000..2cad493
--- /dev/null
+++ b/src/Vect.h
@@ -0,0 +1,22 @@
+#pragma once
+
+#include "Matrix.h"
+
+// espace vectoriel
+class Vect {
+  private:
+	Matrix m_Data{0, 0};
+
+  public:
+	/**
+	 * \brief Construit une base d'un espace vectoriel à partir des colonnes d'une matrice.
+	 * Ne prend pas en compte les colonnes de 0
+	 * \param mat Une matrice échelonnée.
+	 */
+	Vect(const Matrix& mat);
+
+	/**
+	* \brief Affiche la base de l'espace vectoriel dans la console
+	*/
+	void Print() const;
+};
\ No newline at end of file
diff --git a/test/mainTest.cpp b/test/mainTest.cpp
index 1748358..43efd2a 100644
--- a/test/mainTest.cpp
+++ b/test/mainTest.cpp
@@ -4,6 +4,7 @@
 #ifdef NDEBUG
 #error "Il faut être en debug mode ! xmake f -m debug"
 #endif
+
 struct Test{
     Matrix mat;
     Matrix res;

From 715bc843b2b9fe57a83dd591f2cf516f721a242e Mon Sep 17 00:00:00 2001
From: Persson-dev <sim16.prib@gmail.com>
Date: Wed, 14 Feb 2024 20:22:14 +0100
Subject: [PATCH 08/29] O_o

---
 src/Matrix.cpp | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/Matrix.cpp b/src/Matrix.cpp
index bae35f9..5c11454 100644
--- a/src/Matrix.cpp
+++ b/src/Matrix.cpp
@@ -218,11 +218,11 @@ long double& Matrix::operator[](std::size_t indice) {
 }
 
 long double& Matrix::at(std::size_t ligne, std::size_t colonne) {
-	return m_Data[ligne * m_Lignes + colonne];
+	return m_Data[ligne * m_Colonnes + colonne];
 }
 
 long double Matrix::at(std::size_t ligne, std::size_t colonne) const {
-	return m_Data[ligne * m_Lignes + colonne];
+	return m_Data[ligne * m_Colonnes + colonne];
 }
 
 std::size_t Matrix::GetRawCount() const {

From b90195cac1b9b8c7c5a1ce9b7d4316311b6c062a Mon Sep 17 00:00:00 2001
From: Persson-dev <sim16.prib@gmail.com>
Date: Wed, 14 Feb 2024 20:29:02 +0100
Subject: [PATCH 09/29] change transpose signature

---
 src/Matrix.cpp | 6 +++---
 src/Matrix.h   | 2 +-
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/src/Matrix.cpp b/src/Matrix.cpp
index 5c11454..0a7908c 100644
--- a/src/Matrix.cpp
+++ b/src/Matrix.cpp
@@ -98,14 +98,14 @@ void Matrix::Load(const std::string& filename) {
 	}
 }
 
-Matrix Matrix::Transpose() const {
+void Matrix::Transpose() {
 	Matrix result{m_Colonnes, m_Lignes};
 	for (std::size_t i = 0; i < m_Lignes; i++) {
-		for (std::size_t j = i; j < m_Colonnes; j++) {
+		for (std::size_t j = 0; j < m_Colonnes; j++) {
 			result.at(j, i) = at(i, j);
 		}
 	}
-	return result;
+	*this = result;
 }
 
 void Matrix::Identity() {
diff --git a/src/Matrix.h b/src/Matrix.h
index dcd8198..3bb3f39 100644
--- a/src/Matrix.h
+++ b/src/Matrix.h
@@ -36,7 +36,7 @@ class Matrix {
 
 	void Load(const std::string& filename);
 
-	Matrix Transpose() const;
+	void Transpose();
 
 	void Identity();
 

From d91d35a3af060f5eba28fa2d60f5c7894b115c55 Mon Sep 17 00:00:00 2001
From: Persson-dev <sim16.prib@gmail.com>
Date: Wed, 14 Feb 2024 20:29:25 +0100
Subject: [PATCH 10/29] implement Vect

---
 src/Vect.cpp | 28 ++++++++++++++++++++--------
 src/Vect.h   |  9 ++++++---
 2 files changed, 26 insertions(+), 11 deletions(-)

diff --git a/src/Vect.cpp b/src/Vect.cpp
index f4be1ea..d49695c 100644
--- a/src/Vect.cpp
+++ b/src/Vect.cpp
@@ -1,20 +1,32 @@
 #include "Vect.h"
+#include <iostream>
 
-Vect::Vect(const Matrix& mat) {
-	for (std::size_t i = 0; i < mat.GetColumnCount(); i++) {
-		std::size_t j;
-		for (j = 0; j < mat.GetRawCount(); j++) {
-			if(!IsEqualZero(mat.at(i, j)))
+Vect::Vect(const Matrix& mat) : m_Data(mat) {
+	Simplify();
+}
+
+void Vect::Simplify() {
+	Matrix mat = m_Data;
+	for (std::size_t j = 0; j < mat.GetColumnCount(); j++) {
+		std::size_t i;
+		for (i = 0; i < mat.GetRawCount(); i++) {
+			if (!IsEqualZero(mat.at(i, j)))
 				break;
 		}
-		if (j == mat.GetRawCount()) {
+		if (i == mat.GetRawCount()) {
 			m_Data = mat.SubMatrix(0, 0, mat.GetRawCount(), j);
+			return;
 		}
 	}
 	m_Data = mat;
 }
 
-// TODO
 void Vect::Print() const {
-
+	std::cout << "Espace vectoriel de dimension " << m_Data.GetColumnCount() << " de base :\n\n";
+	for (std::size_t i = 0; i < m_Data.GetRawCount(); i++) {
+		for (std::size_t j = 0; j < m_Data.GetColumnCount(); j++) {
+			printf("[ %.3f ]\t", static_cast<float>(m_Data.at(i, j)));
+		}
+		std::cout << "\n";
+	}
 }
\ No newline at end of file
diff --git a/src/Vect.h b/src/Vect.h
index 2cad493..0a5782d 100644
--- a/src/Vect.h
+++ b/src/Vect.h
@@ -5,7 +5,7 @@
 // espace vectoriel
 class Vect {
   private:
-	Matrix m_Data{0, 0};
+	Matrix m_Data;
 
   public:
 	/**
@@ -16,7 +16,10 @@ class Vect {
 	Vect(const Matrix& mat);
 
 	/**
-	* \brief Affiche la base de l'espace vectoriel dans la console
-	*/
+	 * \brief Affiche la base de l'espace vectoriel dans la console
+	 */
 	void Print() const;
+
+  private:
+	void Simplify();
 };
\ No newline at end of file

From a016163b86960df1611c8273bd95692fe8e71258 Mon Sep 17 00:00:00 2001
From: Persson-dev <sim16.prib@gmail.com>
Date: Wed, 14 Feb 2024 20:30:16 +0100
Subject: [PATCH 11/29] more example

---
 src/main.cpp | 18 +++++++++++++++++-
 1 file changed, 17 insertions(+), 1 deletion(-)

diff --git a/src/main.cpp b/src/main.cpp
index 1e71236..8d66b28 100644
--- a/src/main.cpp
+++ b/src/main.cpp
@@ -1,4 +1,4 @@
-#include "Matrix.h"
+#include "Vect.h"
 #include <iostream>
 
 void test() {
@@ -15,6 +15,22 @@ void test() {
 	std::cout << "<<\nTransposée:\n";
 	mat.Print();
 	// mat.Save("matrice4x4echelonne.mat");
+
+	Matrix mat2 {"matrice4x4.mat"};
+	mat2.Print();
+	
+	mat2.Transpose();
+	std::cout << "Transposée : \n";
+	mat2.Print();
+	
+	mat2.GaussJordan(true);
+	mat2.Transpose();
+
+	std::cout << "Echelonnée en colonne :\n";
+	mat2.Print();
+
+	Vect sol {mat2};
+	sol.Print();
 }
 
 void prompt() {

From cf64e4d33ce1e94d56c68cde76056fbd83b4de57 Mon Sep 17 00:00:00 2001
From: Persson-dev <sim16.prib@gmail.com>
Date: Wed, 14 Feb 2024 21:30:41 +0100
Subject: [PATCH 12/29] improve identity

---
 src/Matrix.cpp | 13 ++++++++-----
 src/Matrix.h   |  2 ++
 2 files changed, 10 insertions(+), 5 deletions(-)

diff --git a/src/Matrix.cpp b/src/Matrix.cpp
index 0a7908c..8b3a7c9 100644
--- a/src/Matrix.cpp
+++ b/src/Matrix.cpp
@@ -109,17 +109,20 @@ void Matrix::Transpose() {
 }
 
 void Matrix::Identity() {
+	assert(m_Lignes == m_Colonnes);
 	for (std::size_t i = 0; i < m_Lignes; i++) {
 		for (std::size_t j = i; j < m_Colonnes; j++) {
-			if (i != j) {
-				at(i, j) = 0;
-			} else {
-				at(i, j) = 1;
-			}
+			at(i, j) = i == j;
 		}
 	}
 }
 
+Matrix Matrix::Identity(std::size_t taille) {
+	Matrix id{taille, taille};
+	id.Identity();
+	return id;
+}
+
 bool Matrix::IsInversed() const {
 	for (std::size_t i = 0; i < m_Lignes; ++i) {
 		std::size_t j;
diff --git a/src/Matrix.h b/src/Matrix.h
index 3bb3f39..5122715 100644
--- a/src/Matrix.h
+++ b/src/Matrix.h
@@ -40,6 +40,8 @@ class Matrix {
 
 	void Identity();
 
+	static Matrix Identity(std::size_t taille);
+
 	bool IsInversed() const;
 
 	Matrix SubMatrix(std::size_t origine_ligne, std::size_t origine_colonne, std::size_t ligne, std::size_t colonne) const;

From 8ef738db5520a3228c6c32c8a91f12a5a22b0990 Mon Sep 17 00:00:00 2001
From: Persson-dev <sim16.prib@gmail.com>
Date: Wed, 14 Feb 2024 21:31:05 +0100
Subject: [PATCH 13/29] matrice augmenter

---
 src/Matrix.cpp | 19 +++++++++++++++++++
 src/Matrix.h   |  2 ++
 2 files changed, 21 insertions(+)

diff --git a/src/Matrix.cpp b/src/Matrix.cpp
index 8b3a7c9..a30e09b 100644
--- a/src/Matrix.cpp
+++ b/src/Matrix.cpp
@@ -136,6 +136,25 @@ bool Matrix::IsInversed() const {
 	return true;
 }
 
+void Matrix::Augmenter(const Matrix& droite) {
+	assert(droite.m_Lignes == m_Lignes);
+	Matrix temp{m_Lignes, m_Colonnes + droite.m_Colonnes};
+
+	for (std::size_t i = 0; i < m_Lignes; i++) {
+		for (std::size_t j = 0; j < m_Colonnes; j++) {
+			temp.at(i, j) = at(i, j);
+		}
+	}
+
+	for (std::size_t i = 0; i < m_Lignes; i++) {
+		for (std::size_t j = 0; j < droite.m_Colonnes; j++) {
+			temp.at(i, j + m_Colonnes) = droite.at(i, j);
+		}
+	}
+
+	*this = temp;
+}
+
 bool Matrix::operator==(const Matrix& other) const {
 	if (m_Lignes != other.m_Lignes || m_Colonnes != other.m_Colonnes)
 		return false;
diff --git a/src/Matrix.h b/src/Matrix.h
index 5122715..a858f89 100644
--- a/src/Matrix.h
+++ b/src/Matrix.h
@@ -44,6 +44,8 @@ class Matrix {
 
 	bool IsInversed() const;
 
+	void Augmenter(const Matrix& droite);
+
 	Matrix SubMatrix(std::size_t origine_ligne, std::size_t origine_colonne, std::size_t ligne, std::size_t colonne) const;
 
 	bool operator==(const Matrix& other) const;

From e1f501237da9b4b21282266b24573a0b1a2fe4d0 Mon Sep 17 00:00:00 2001
From: Persson-dev <sim16.prib@gmail.com>
Date: Wed, 14 Feb 2024 21:31:23 +0100
Subject: [PATCH 14/29] vect dimension

---
 src/Vect.cpp | 6 +++++-
 src/Vect.h   | 2 ++
 2 files changed, 7 insertions(+), 1 deletion(-)

diff --git a/src/Vect.cpp b/src/Vect.cpp
index d49695c..1dad13f 100644
--- a/src/Vect.cpp
+++ b/src/Vect.cpp
@@ -22,11 +22,15 @@ void Vect::Simplify() {
 }
 
 void Vect::Print() const {
-	std::cout << "Espace vectoriel de dimension " << m_Data.GetColumnCount() << " de base :\n\n";
+	std::cout << "Espace vectoriel de dimension " << GetDimension() << " de base :\n\n";
 	for (std::size_t i = 0; i < m_Data.GetRawCount(); i++) {
 		for (std::size_t j = 0; j < m_Data.GetColumnCount(); j++) {
 			printf("[ %.3f ]\t", static_cast<float>(m_Data.at(i, j)));
 		}
 		std::cout << "\n";
 	}
+}
+
+std::size_t Vect::GetDimension() const {
+	return m_Data.GetColumnCount();
 }
\ No newline at end of file
diff --git a/src/Vect.h b/src/Vect.h
index 0a5782d..a99c3ba 100644
--- a/src/Vect.h
+++ b/src/Vect.h
@@ -20,6 +20,8 @@ class Vect {
 	 */
 	void Print() const;
 
+	std::size_t GetDimension() const;
+
   private:
 	void Simplify();
 };
\ No newline at end of file

From 4ffeea890028784a1d7685577afe9d855d801703 Mon Sep 17 00:00:00 2001
From: Persson-dev <sim16.prib@gmail.com>
Date: Wed, 14 Feb 2024 21:35:26 +0100
Subject: [PATCH 15/29] image et noyau

---
 src/Solver.cpp | 31 +++++++++++++++++++++++++++++++
 src/Solver.h   | 16 ++++++++++++++++
 src/main.cpp   | 26 ++++++++++----------------
 3 files changed, 57 insertions(+), 16 deletions(-)
 create mode 100644 src/Solver.cpp
 create mode 100644 src/Solver.h

diff --git a/src/Solver.cpp b/src/Solver.cpp
new file mode 100644
index 0000000..5e1634d
--- /dev/null
+++ b/src/Solver.cpp
@@ -0,0 +1,31 @@
+#include "Solver.h"
+
+Solver::Solver(const Matrix& mat) : m_Matrix(mat) {}
+
+Vect Solver::Image() const {
+	Matrix result = m_Matrix;
+	result.Transpose();
+	result.GaussJordan(true);
+	result.Transpose();
+	return {result};
+}
+
+// https://en.wikipedia.org/wiki/Kernel_(linear_algebra)#Computation_by_Gaussian_elimination
+Vect Solver::Noyau() const {
+	Matrix result = m_Matrix;
+	result.Transpose();
+	result.Augmenter(Matrix::Identity(result.GetRawCount()));
+	result.GaussJordan(true);
+	result.Transpose();
+
+	// nombre de colonnes non nulles
+	std::size_t origine_colonne = Vect(result.SubMatrix(0, 0, m_Matrix.GetRawCount(), m_Matrix.GetColumnCount())).GetDimension();
+
+	return {result.SubMatrix(m_Matrix.GetRawCount(), origine_colonne, result.GetRawCount() - m_Matrix.GetRawCount(),
+		result.GetColumnCount() - origine_colonne)};
+}
+
+std::size_t Solver::Rang() const {
+	Vect image = Image();
+	return image.GetDimension();
+}
diff --git a/src/Solver.h b/src/Solver.h
new file mode 100644
index 0000000..aded7b5
--- /dev/null
+++ b/src/Solver.h
@@ -0,0 +1,16 @@
+#pragma once
+
+#include "Vect.h"
+
+class Solver {
+  private:
+	Matrix m_Matrix;
+  public:
+	Solver(const Matrix& mat);
+	~Solver() {}
+
+	Vect Image() const;
+	Vect Noyau() const;
+
+	std::size_t Rang() const;
+};
\ No newline at end of file
diff --git a/src/main.cpp b/src/main.cpp
index 8d66b28..30091d6 100644
--- a/src/main.cpp
+++ b/src/main.cpp
@@ -1,8 +1,8 @@
-#include "Vect.h"
+#include "Solver.h"
 #include <iostream>
 
 void test() {
-	Matrix mat{"matrice4x4.mat"};
+	/* Matrix mat{"matrice4x4.mat"};
 	mat.Print();
 	// mat.Save("matrice3x3.mat");
 	std::cout << "sdfdjiofoseifheoiefhoig\n";
@@ -14,23 +14,17 @@ void test() {
 	mat.Transpose();
 	std::cout << "<<\nTransposée:\n";
 	mat.Print();
-	// mat.Save("matrice4x4echelonne.mat");
+	// mat.Save("matrice4x4echelonne.mat"); */
 
-	Matrix mat2 {"matrice4x4.mat"};
-	mat2.Print();
-	
-	mat2.Transpose();
-	std::cout << "Transposée : \n";
-	mat2.Print();
-	
-	mat2.GaussJordan(true);
-	mat2.Transpose();
-
-	std::cout << "Echelonnée en colonne :\n";
+	Matrix mat2{"matrice4x4.mat"};
 	mat2.Print();
 
-	Vect sol {mat2};
-	sol.Print();
+	Solver solver{mat2};
+
+	std::cout << "\tImage :\n";
+	solver.Image().Print();
+	std::cout << "\tNoyau :\n";
+	solver.Noyau().Print();
 }
 
 void prompt() {

From a1d74ec126a4441f00720af3faa8c379ff2400a9 Mon Sep 17 00:00:00 2001
From: Persson-dev <sim16.prib@gmail.com>
Date: Wed, 14 Feb 2024 22:22:59 +0100
Subject: [PATCH 16/29] vectorial space to linear equation

---
 src/Matrix.cpp |  4 ++--
 src/Vect.cpp   | 12 ++++++++++++
 src/Vect.h     |  2 ++
 src/main.cpp   | 11 +++++++++--
 4 files changed, 25 insertions(+), 4 deletions(-)

diff --git a/src/Matrix.cpp b/src/Matrix.cpp
index a30e09b..465bc55 100644
--- a/src/Matrix.cpp
+++ b/src/Matrix.cpp
@@ -1,11 +1,11 @@
+#include "Matrix.h"
+
 #include <algorithm>
 #include <cassert>
 #include <cmath>
 #include <fstream>
 #include <iostream>
 
-#include "Matrix.h"
-
 Matrix::Matrix(const std::string& fileNameInput) {
 	Load(fileNameInput);
 }
diff --git a/src/Vect.cpp b/src/Vect.cpp
index 1dad13f..5930737 100644
--- a/src/Vect.cpp
+++ b/src/Vect.cpp
@@ -1,4 +1,6 @@
 #include "Vect.h"
+
+#include "Solver.h"
 #include <iostream>
 
 Vect::Vect(const Matrix& mat) : m_Data(mat) {
@@ -21,6 +23,16 @@ void Vect::Simplify() {
 	m_Data = mat;
 }
 
+Matrix Vect::GetLinearSystem() const {
+	Matrix vect = m_Data;
+	vect.Transpose();
+
+	Solver solver {vect};
+	vect = solver.Noyau().m_Data;
+	vect.Transpose();
+	return vect;
+}
+
 void Vect::Print() const {
 	std::cout << "Espace vectoriel de dimension " << GetDimension() << " de base :\n\n";
 	for (std::size_t i = 0; i < m_Data.GetRawCount(); i++) {
diff --git a/src/Vect.h b/src/Vect.h
index a99c3ba..5f89f02 100644
--- a/src/Vect.h
+++ b/src/Vect.h
@@ -22,6 +22,8 @@ class Vect {
 
 	std::size_t GetDimension() const;
 
+	Matrix GetLinearSystem() const;
+
   private:
 	void Simplify();
 };
\ No newline at end of file
diff --git a/src/main.cpp b/src/main.cpp
index 30091d6..39d5061 100644
--- a/src/main.cpp
+++ b/src/main.cpp
@@ -21,10 +21,17 @@ void test() {
 
 	Solver solver{mat2};
 
+	Vect image = solver.Image();
+	Vect noyau = solver.Noyau();
+
 	std::cout << "\tImage :\n";
-	solver.Image().Print();
+	image.Print();
+	std::cout << "Système :\n";
+	image.GetLinearSystem().Print();
 	std::cout << "\tNoyau :\n";
-	solver.Noyau().Print();
+	noyau.Print();
+	std::cout << "Système :\n";
+	noyau.GetLinearSystem().Print();
 }
 
 void prompt() {

From c2fd2805fac5c777b1d2e53b19f22519fafc6313 Mon Sep 17 00:00:00 2001
From: Persson-dev <sim16.prib@gmail.com>
Date: Fri, 16 Feb 2024 10:02:27 +0100
Subject: [PATCH 17/29] matrix stream operators

---
 src/Matrix.cpp | 40 +++++++++++++++++++++++++---------------
 src/Matrix.h   |  3 +++
 2 files changed, 28 insertions(+), 15 deletions(-)

diff --git a/src/Matrix.cpp b/src/Matrix.cpp
index 465bc55..a64fb97 100644
--- a/src/Matrix.cpp
+++ b/src/Matrix.cpp
@@ -74,13 +74,7 @@ void Matrix::Save(const std::string& fileName) {
 		std::cerr << "Impossible de sauvegarder la matrice !\n";
 		return;
 	}
-	out << m_Lignes << " " << m_Colonnes << "\n";
-	for (std::size_t i = 0; i < m_Lignes; i++) {
-		for (std::size_t j = 0; j < m_Colonnes; j++) {
-			out << at(i, j) << " ";
-		}
-		out << "\n";
-	}
+	out << *this;
 }
 
 void Matrix::Load(const std::string& filename) {
@@ -89,13 +83,7 @@ void Matrix::Load(const std::string& filename) {
 		std::cerr << "Impossible de charger la matrice !\n";
 		return;
 	}
-	in >> m_Lignes >> m_Colonnes;
-	m_Data.resize(m_Lignes * m_Colonnes);
-	for (std::size_t i = 0; i < m_Lignes; i++) {
-		for (std::size_t j = 0; j < m_Colonnes; j++) {
-			in >> at(i, j);
-		}
-	}
+	in >> *this;
 }
 
 void Matrix::Transpose() {
@@ -266,4 +254,26 @@ Matrix Matrix::SubMatrix(std::size_t origine_ligne, std::size_t origine_colonne,
 	}
 
 	return result;
-}
\ No newline at end of file
+}
+
+std::ostream& operator<<(std::ostream& stream, const Matrix& mat) {
+	stream << mat.m_Lignes << " " << mat.m_Colonnes << "\n";
+	for (std::size_t i = 0; i < mat.m_Lignes; i++) {
+		for (std::size_t j = 0; j < mat.m_Colonnes; j++) {
+			stream << mat.at(i, j) << " ";
+		}
+		stream << "\n";
+	}
+	return stream;
+}
+
+std::istream& operator>>(std::istream& stream, Matrix& mat) {
+	stream >> mat.m_Lignes >> mat.m_Colonnes;
+	mat.m_Data.resize(mat.m_Lignes * mat.m_Colonnes);
+	for (std::size_t i = 0; i < mat.m_Lignes; i++) {
+		for (std::size_t j = 0; j < mat.m_Colonnes; j++) {
+			stream >> mat.at(i, j);
+		}
+	}
+	return stream;
+}
diff --git a/src/Matrix.h b/src/Matrix.h
index a858f89..4e61977 100644
--- a/src/Matrix.h
+++ b/src/Matrix.h
@@ -55,6 +55,9 @@ class Matrix {
 	long double& at(std::size_t ligne, std::size_t colonne);
 
 	long double at(std::size_t ligne, std::size_t colonne) const;
+
+	friend std::ostream& operator<<(std::ostream& stream, const Matrix& mat);
+	friend std::istream& operator>>(std::istream& stream, Matrix& mat);
 };
 
 template <typename T>

From 46dcad1457f97a94c7908da3e82c0a5faaa0d4f5 Mon Sep 17 00:00:00 2001
From: Persson-dev <sim16.prib@gmail.com>
Date: Fri, 16 Feb 2024 10:39:42 +0100
Subject: [PATCH 18/29] equality of vectorial spaces

---
 src/Solver.cpp |  4 ++--
 src/Vect.cpp   | 36 +++++++++++++++++++++++++++++++++---
 src/Vect.h     | 10 ++++++++++
 3 files changed, 45 insertions(+), 5 deletions(-)

diff --git a/src/Solver.cpp b/src/Solver.cpp
index 5e1634d..336711d 100644
--- a/src/Solver.cpp
+++ b/src/Solver.cpp
@@ -19,7 +19,7 @@ Vect Solver::Noyau() const {
 	result.Transpose();
 
 	// nombre de colonnes non nulles
-	std::size_t origine_colonne = Vect(result.SubMatrix(0, 0, m_Matrix.GetRawCount(), m_Matrix.GetColumnCount())).GetDimension();
+	std::size_t origine_colonne = Vect(result.SubMatrix(0, 0, m_Matrix.GetRawCount(), m_Matrix.GetColumnCount())).GetCardinal();
 
 	return {result.SubMatrix(m_Matrix.GetRawCount(), origine_colonne, result.GetRawCount() - m_Matrix.GetRawCount(),
 		result.GetColumnCount() - origine_colonne)};
@@ -27,5 +27,5 @@ Vect Solver::Noyau() const {
 
 std::size_t Solver::Rang() const {
 	Vect image = Image();
-	return image.GetDimension();
+	return image.GetCardinal();
 }
diff --git a/src/Vect.cpp b/src/Vect.cpp
index 5930737..930a92e 100644
--- a/src/Vect.cpp
+++ b/src/Vect.cpp
@@ -23,18 +23,48 @@ void Vect::Simplify() {
 	m_Data = mat;
 }
 
+std::size_t Vect::GetCardinal() const {
+	return m_Data.GetColumnCount();
+}
+
+bool Vect::operator==(const Vect& other) const {
+	if (GetDimension() != other.GetDimension() || GetCardinal() != other.GetCardinal())
+		return false;
+
+	// on vérifie si chaque vecteur de la deuxième base appartient à la première base
+	for (std::size_t i = 0; i < GetCardinal(); i++) {
+		Vect base = *this;
+		base.AddVector(other.m_Data.SubMatrix(0, i, GetDimension(), 1));
+		if (base.GetCardinal() != GetCardinal())
+			return false;
+	}
+	return true;
+}
+
+void Vect::AddVector(const Matrix& mat) {
+	m_Data.Augmenter(mat);
+	m_Data.Transpose();
+	m_Data.GaussNonJordan(false);
+	m_Data.Transpose();
+	Simplify();
+}
+
+bool Vect::operator!=(const Vect& other) const {
+	return !(*this == other);
+}
+
 Matrix Vect::GetLinearSystem() const {
 	Matrix vect = m_Data;
 	vect.Transpose();
 
-	Solver solver {vect};
+	Solver solver{vect};
 	vect = solver.Noyau().m_Data;
 	vect.Transpose();
 	return vect;
 }
 
 void Vect::Print() const {
-	std::cout << "Espace vectoriel de dimension " << GetDimension() << " de base :\n\n";
+	std::cout << "Espace vectoriel de dimension " << GetCardinal() << " de base :\n\n";
 	for (std::size_t i = 0; i < m_Data.GetRawCount(); i++) {
 		for (std::size_t j = 0; j < m_Data.GetColumnCount(); j++) {
 			printf("[ %.3f ]\t", static_cast<float>(m_Data.at(i, j)));
@@ -44,5 +74,5 @@ void Vect::Print() const {
 }
 
 std::size_t Vect::GetDimension() const {
-	return m_Data.GetColumnCount();
+	return m_Data.GetRawCount();
 }
\ No newline at end of file
diff --git a/src/Vect.h b/src/Vect.h
index 5f89f02..6d5c759 100644
--- a/src/Vect.h
+++ b/src/Vect.h
@@ -21,9 +21,19 @@ class Vect {
 	void Print() const;
 
 	std::size_t GetDimension() const;
+	std::size_t GetCardinal() const;
 
 	Matrix GetLinearSystem() const;
 
+	/**
+	 * \brief Concatène la base actuelle avec un nouveau vecteur
+	 * \param mat Une matrice colonne de taille GetDimension()
+	 */
+	void AddVector(const Matrix& mat);
+
+	bool operator==(const Vect& other) const;
+	bool operator!=(const Vect& other) const;
+
   private:
 	void Simplify();
 };
\ No newline at end of file

From d156602da7c5327a975ad854f9f95d49d569e544 Mon Sep 17 00:00:00 2001
From: Persson-dev <sim16.prib@gmail.com>
Date: Fri, 16 Feb 2024 10:40:26 +0100
Subject: [PATCH 19/29] improve tests

---
 test/{mainTest.cpp => test_jordan.cpp} |  0
 test/test_vect.cpp                     | 31 ++++++++++++++++++++
 xmake.lua                              | 39 ++++++++++++++++++++------
 3 files changed, 61 insertions(+), 9 deletions(-)
 rename test/{mainTest.cpp => test_jordan.cpp} (100%)
 create mode 100644 test/test_vect.cpp

diff --git a/test/mainTest.cpp b/test/test_jordan.cpp
similarity index 100%
rename from test/mainTest.cpp
rename to test/test_jordan.cpp
diff --git a/test/test_vect.cpp b/test/test_vect.cpp
new file mode 100644
index 0000000..66a261b
--- /dev/null
+++ b/test/test_vect.cpp
@@ -0,0 +1,31 @@
+#include "Vect.h"
+#include <cassert>
+
+int main() {
+	Vect vect1 {{3, 2, {
+		1, 2,
+		3, 4,
+		5, 6,
+	}}};
+	Vect vect2 {{3, 2, {
+		1, 0,
+		0, 0,
+		0, 1,
+	}}};
+	Vect vect3 {{3, 2, {
+		1, 3,
+		3, 7,
+		5, 11,
+	}}};
+	Vect vect4 {{3, 2, {
+		1, 0,
+		0, 0,
+		1, 11,
+	}}};
+	assert(vect1 == vect3);
+	assert(vect2 == vect4);
+	assert(vect1 != vect2);
+	assert(vect2 != vect3);
+	assert(vect3 != vect4);
+	return 0;
+}
\ No newline at end of file
diff --git a/xmake.lua b/xmake.lua
index 0cd4b3f..1744eb4 100644
--- a/xmake.lua
+++ b/xmake.lua
@@ -1,22 +1,43 @@
 add_rules("mode.debug", "mode.release")
 
+set_languages("c++17")
+
+-- Solver Library
 target("Pivot")
-    set_kind("binary")
+    set_kind("static")
     add_files("src/*.cpp")
+    remove_files("src/main.cpp")
+
+
+
+
+
+-- Solver Main
+target("PivotMain")
     set_rundir("$(projectdir)/matricies")
-    set_languages("c++17")
+    add_files("src/main.cpp")
+    add_deps("Pivot")
+    set_default(true)
 
 
 
 
 
-target("PivotTest")
-    set_kind("binary")
-    add_files("test/*.cpp", "src/Matrix.cpp")
-    add_includedirs("src")
-    set_default(false)
-    add_tests("compile_and_run")
-    set_rundir("$(projectdir)/matricies")
+-- Solver tests
+for _, file in ipairs(os.files("test/test_*.cpp")) do
+    local name = path.basename(file)
+    target(name)
+        set_kind("binary")
+        add_files("test/" .. name .. ".cpp")
+        set_rundir("$(projectdir)/matricies")
+        add_includedirs("src")
+
+        set_default(false)
+
+        add_deps("Pivot")
+
+        add_tests("compile_and_run")
+end
 
 --
 -- If you want to known more usage about xmake, please see https://xmake.io

From 88cc5290095c2a0108f162d03496bca19aeb8e9e Mon Sep 17 00:00:00 2001
From: Persson-dev <sim16.prib@gmail.com>
Date: Fri, 16 Feb 2024 11:09:27 +0100
Subject: [PATCH 20/29] add solver test

---
 matricies/test/matrice1.test | 12 ++++++++++++
 test/test_solver.cpp         | 26 ++++++++++++++++++++++++++
 2 files changed, 38 insertions(+)
 create mode 100644 matricies/test/matrice1.test
 create mode 100644 test/test_solver.cpp

diff --git a/matricies/test/matrice1.test b/matricies/test/matrice1.test
new file mode 100644
index 0000000..9d63899
--- /dev/null
+++ b/matricies/test/matrice1.test
@@ -0,0 +1,12 @@
+2 3
+1 2 3
+4 5 6
+
+2 2
+0 1
+1 0
+
+3 1
+1
+-2
+1
\ No newline at end of file
diff --git a/test/test_solver.cpp b/test/test_solver.cpp
new file mode 100644
index 0000000..b621d43
--- /dev/null
+++ b/test/test_solver.cpp
@@ -0,0 +1,26 @@
+#include "Solver.h"
+#include <cassert>
+#include <filesystem>
+#include <fstream>
+#include <iostream>
+
+namespace fs = std::filesystem;
+
+int main() {
+	std::string path = "test";
+	for (const auto& entry : fs::directory_iterator(path)) {
+		std::string fileName = entry.path().string();
+		std::cout << "Opening " << fileName << " ...\n";
+		std::ifstream in{fileName};
+		Matrix mat{1, 1}, imageMat{1, 1}, noyauMat{1, 1};
+		in >> mat >> imageMat >> noyauMat;
+
+		Vect image{imageMat};
+		Vect noyau{noyauMat};
+
+		Solver solver{mat};
+		assert(solver.Image() == image);
+		assert(solver.Noyau() == noyau);
+	}
+	return 0;
+}
\ No newline at end of file

From 99467048e2302c0467818cebb0c99478eccf745d Mon Sep 17 00:00:00 2001
From: Persson-dev <sim16.prib@gmail.com>
Date: Wed, 21 Feb 2024 21:59:46 +0100
Subject: [PATCH 21/29] change Vect display

---
 src/Vect.cpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/Vect.cpp b/src/Vect.cpp
index 930a92e..17c06d9 100644
--- a/src/Vect.cpp
+++ b/src/Vect.cpp
@@ -67,7 +67,7 @@ void Vect::Print() const {
 	std::cout << "Espace vectoriel de dimension " << GetCardinal() << " de base :\n\n";
 	for (std::size_t i = 0; i < m_Data.GetRawCount(); i++) {
 		for (std::size_t j = 0; j < m_Data.GetColumnCount(); j++) {
-			printf("[ %.3f ]\t", static_cast<float>(m_Data.at(i, j)));
+			printf("[ %u ]\t", static_cast<float>(m_Data.at(i, j)));
 		}
 		std::cout << "\n";
 	}

From 54798d0ff2889fdecafaa0c72b4b0023fe772e17 Mon Sep 17 00:00:00 2001
From: Persson-dev <sim16.prib@gmail.com>
Date: Wed, 21 Feb 2024 22:01:31 +0100
Subject: [PATCH 22/29] resolve rectangular systems

---
 src/Solver.cpp | 12 ++++++++++++
 src/Solver.h   |  3 +++
 src/Vect.cpp   | 13 ++++++++++++-
 src/Vect.h     | 20 ++++++++++++++++++++
 src/main.cpp   |  3 +++
 5 files changed, 50 insertions(+), 1 deletion(-)

diff --git a/src/Solver.cpp b/src/Solver.cpp
index 336711d..ca71ef7 100644
--- a/src/Solver.cpp
+++ b/src/Solver.cpp
@@ -25,6 +25,18 @@ Vect Solver::Noyau() const {
 		result.GetColumnCount() - origine_colonne)};
 }
 
+VectAffine Solver::SystemeTriangulaire() const {
+	Matrix mat = m_Matrix;
+	mat.GaussJordan(true);
+
+	Solver solver{mat.SubMatrix(0, 0, mat.GetRawCount(), mat.GetColumnCount() - 1)};
+
+	Vect noyau = solver.Noyau();
+	Matrix origin = mat.SubMatrix(0, mat.GetColumnCount() - 1, mat.GetRawCount(), 1);
+
+	return {noyau, origin};
+}
+
 std::size_t Solver::Rang() const {
 	Vect image = Image();
 	return image.GetCardinal();
diff --git a/src/Solver.h b/src/Solver.h
index aded7b5..f299f2e 100644
--- a/src/Solver.h
+++ b/src/Solver.h
@@ -5,6 +5,7 @@
 class Solver {
   private:
 	Matrix m_Matrix;
+
   public:
 	Solver(const Matrix& mat);
 	~Solver() {}
@@ -12,5 +13,7 @@ class Solver {
 	Vect Image() const;
 	Vect Noyau() const;
 
+	VectAffine SystemeTriangulaire() const;
+
 	std::size_t Rang() const;
 };
\ No newline at end of file
diff --git a/src/Vect.cpp b/src/Vect.cpp
index 17c06d9..5ec21af 100644
--- a/src/Vect.cpp
+++ b/src/Vect.cpp
@@ -1,6 +1,7 @@
 #include "Vect.h"
 
 #include "Solver.h"
+#include <cassert>
 #include <iostream>
 
 Vect::Vect(const Matrix& mat) : m_Data(mat) {
@@ -75,4 +76,14 @@ void Vect::Print() const {
 
 std::size_t Vect::GetDimension() const {
 	return m_Data.GetRawCount();
-}
\ No newline at end of file
+}
+
+VectAffine::VectAffine(const Vect& base, const Matrix& origine) :
+	m_Base(base), m_Origin(origine.SubMatrix(0, 0, m_Base.GetDimension(), 1)) {}
+
+void VectAffine::Print() const {
+	std::cout << "\tEspace Affine :\n\n";
+	m_Base.Print();
+	std::cout << "\nOrigine :\n\n";
+	m_Origin.Print();
+}
diff --git a/src/Vect.h b/src/Vect.h
index 6d5c759..9dbee22 100644
--- a/src/Vect.h
+++ b/src/Vect.h
@@ -36,4 +36,24 @@ class Vect {
 
   private:
 	void Simplify();
+};
+
+
+class VectAffine {
+  private:
+	Vect m_Base;
+	Matrix m_Origin;
+
+  public:
+	VectAffine(const Vect& base, const Matrix& origin);
+
+	void Print() const;
+
+	const Vect& GetBase() const {
+		return m_Base;
+	}
+
+	const Matrix& GetOrigin() const {
+		return m_Origin;
+	}
 };
\ No newline at end of file
diff --git a/src/main.cpp b/src/main.cpp
index 39d5061..d4a1693 100644
--- a/src/main.cpp
+++ b/src/main.cpp
@@ -32,6 +32,9 @@ void test() {
 	noyau.Print();
 	std::cout << "Système :\n";
 	noyau.GetLinearSystem().Print();
+
+	std::cout << "\n\n";
+	solver.SystemeTriangulaire().Print();
 }
 
 void prompt() {

From efd0a88868a4f5ec6f5e0a3b2e01411b416ba5e6 Mon Sep 17 00:00:00 2001
From: Persson-dev <sim16.prib@gmail.com>
Date: Wed, 21 Feb 2024 22:06:08 +0100
Subject: [PATCH 23/29] format test_solver

---
 test/test_solver.cpp | 7 ++++++-
 1 file changed, 6 insertions(+), 1 deletion(-)

diff --git a/test/test_solver.cpp b/test/test_solver.cpp
index b621d43..27cc16b 100644
--- a/test/test_solver.cpp
+++ b/test/test_solver.cpp
@@ -1,17 +1,21 @@
-#include "Solver.h"
 #include <cassert>
 #include <filesystem>
 #include <fstream>
 #include <iostream>
 
+#include "Solver.h"
+
 namespace fs = std::filesystem;
 
 int main() {
 	std::string path = "test";
 	for (const auto& entry : fs::directory_iterator(path)) {
 		std::string fileName = entry.path().string();
+
 		std::cout << "Opening " << fileName << " ...\n";
+
 		std::ifstream in{fileName};
+
 		Matrix mat{1, 1}, imageMat{1, 1}, noyauMat{1, 1};
 		in >> mat >> imageMat >> noyauMat;
 
@@ -19,6 +23,7 @@ int main() {
 		Vect noyau{noyauMat};
 
 		Solver solver{mat};
+
 		assert(solver.Image() == image);
 		assert(solver.Noyau() == noyau);
 	}

From 82ad2e06961b78c433628305b9aa838fca5564e4 Mon Sep 17 00:00:00 2001
From: Persson-dev <sim16.prib@gmail.com>
Date: Fri, 23 Feb 2024 10:14:23 +0100
Subject: [PATCH 24/29] format project

---
 .clang-format        |  2 ++
 src/Matrix.cpp       | 13 +++++++------
 src/NR.h             |  2 ++
 src/Solver.cpp       |  2 +-
 src/Solver.h         |  1 +
 src/Vect.cpp         |  2 +-
 src/Vect.h           |  1 -
 src/main.cpp         |  4 ++--
 test/test_jordan.cpp | 12 ++++++------
 test/test_solver.cpp | 10 +++++-----
 10 files changed, 27 insertions(+), 22 deletions(-)

diff --git a/.clang-format b/.clang-format
index e993027..38e37ec 100644
--- a/.clang-format
+++ b/.clang-format
@@ -7,6 +7,8 @@ ConstructorInitializerAllOnOneLineOrOnePerLine: true
 PointerAlignment: Left
 SortIncludes: true
 SpacesBeforeTrailingComments: 2
+SeparateDefinitionBlocks: Always
+SpaceBeforeCpp11BracedList: true
 UseTab: Always
 MaxEmptyLinesToKeep: 5
 
diff --git a/src/Matrix.cpp b/src/Matrix.cpp
index a64fb97..422a22a 100644
--- a/src/Matrix.cpp
+++ b/src/Matrix.cpp
@@ -13,6 +13,7 @@ Matrix::Matrix(const std::string& fileNameInput) {
 Matrix::Matrix(std::size_t lignes, std::size_t colonnes) : m_Lignes(lignes), m_Colonnes(colonnes) {
 	m_Data.resize(m_Lignes * m_Colonnes);
 }
+
 Matrix::Matrix(std::size_t lignes, std::size_t colonnes, std::initializer_list<long double>&& initList) :
 	m_Lignes(lignes), m_Colonnes(colonnes) {
 	m_Data = initList;
@@ -69,7 +70,7 @@ void Matrix::Insert() {
 }
 
 void Matrix::Save(const std::string& fileName) {
-	std::ofstream out{fileName};
+	std::ofstream out {fileName};
 	if (!out) {
 		std::cerr << "Impossible de sauvegarder la matrice !\n";
 		return;
@@ -78,7 +79,7 @@ void Matrix::Save(const std::string& fileName) {
 }
 
 void Matrix::Load(const std::string& filename) {
-	std::ifstream in{filename};
+	std::ifstream in {filename};
 	if (!in) {
 		std::cerr << "Impossible de charger la matrice !\n";
 		return;
@@ -87,7 +88,7 @@ void Matrix::Load(const std::string& filename) {
 }
 
 void Matrix::Transpose() {
-	Matrix result{m_Colonnes, m_Lignes};
+	Matrix result {m_Colonnes, m_Lignes};
 	for (std::size_t i = 0; i < m_Lignes; i++) {
 		for (std::size_t j = 0; j < m_Colonnes; j++) {
 			result.at(j, i) = at(i, j);
@@ -106,7 +107,7 @@ void Matrix::Identity() {
 }
 
 Matrix Matrix::Identity(std::size_t taille) {
-	Matrix id{taille, taille};
+	Matrix id {taille, taille};
 	id.Identity();
 	return id;
 }
@@ -126,7 +127,7 @@ bool Matrix::IsInversed() const {
 
 void Matrix::Augmenter(const Matrix& droite) {
 	assert(droite.m_Lignes == m_Lignes);
-	Matrix temp{m_Lignes, m_Colonnes + droite.m_Colonnes};
+	Matrix temp {m_Lignes, m_Colonnes + droite.m_Colonnes};
 
 	for (std::size_t i = 0; i < m_Lignes; i++) {
 		for (std::size_t j = 0; j < m_Colonnes; j++) {
@@ -245,7 +246,7 @@ std::size_t Matrix::GetColumnCount() const {
 
 Matrix Matrix::SubMatrix(std::size_t origine_ligne, std::size_t origine_colonne, std::size_t ligne, std::size_t colonne) const {
 	assert(m_Lignes >= ligne && m_Colonnes >= colonne);
-	Matrix result{ligne, colonne};
+	Matrix result {ligne, colonne};
 
 	for (std::size_t i = 0; i < ligne; i++) {
 		for (std::size_t j = 0; j < colonne; j++) {
diff --git a/src/NR.h b/src/NR.h
index 8d6c6ce..b6c32d8 100644
--- a/src/NR.h
+++ b/src/NR.h
@@ -7,6 +7,8 @@ class NR {
 
   public:
 	NR() : m_Numerator(0), m_Denominator(1) {}
+
 	NR(int entier) : m_Numerator(entier), m_Denominator(1) {}
+
 	NR(int numerator, int denominator) : m_Numerator(numerator), m_Denominator(denominator) {}
 };
\ No newline at end of file
diff --git a/src/Solver.cpp b/src/Solver.cpp
index ca71ef7..db4adf3 100644
--- a/src/Solver.cpp
+++ b/src/Solver.cpp
@@ -29,7 +29,7 @@ VectAffine Solver::SystemeTriangulaire() const {
 	Matrix mat = m_Matrix;
 	mat.GaussJordan(true);
 
-	Solver solver{mat.SubMatrix(0, 0, mat.GetRawCount(), mat.GetColumnCount() - 1)};
+	Solver solver {mat.SubMatrix(0, 0, mat.GetRawCount(), mat.GetColumnCount() - 1)};
 
 	Vect noyau = solver.Noyau();
 	Matrix origin = mat.SubMatrix(0, mat.GetColumnCount() - 1, mat.GetRawCount(), 1);
diff --git a/src/Solver.h b/src/Solver.h
index f299f2e..c1d2eb7 100644
--- a/src/Solver.h
+++ b/src/Solver.h
@@ -8,6 +8,7 @@ class Solver {
 
   public:
 	Solver(const Matrix& mat);
+
 	~Solver() {}
 
 	Vect Image() const;
diff --git a/src/Vect.cpp b/src/Vect.cpp
index 5ec21af..936a6fd 100644
--- a/src/Vect.cpp
+++ b/src/Vect.cpp
@@ -58,7 +58,7 @@ Matrix Vect::GetLinearSystem() const {
 	Matrix vect = m_Data;
 	vect.Transpose();
 
-	Solver solver{vect};
+	Solver solver {vect};
 	vect = solver.Noyau().m_Data;
 	vect.Transpose();
 	return vect;
diff --git a/src/Vect.h b/src/Vect.h
index 9dbee22..64b587e 100644
--- a/src/Vect.h
+++ b/src/Vect.h
@@ -38,7 +38,6 @@ class Vect {
 	void Simplify();
 };
 
-
 class VectAffine {
   private:
 	Vect m_Base;
diff --git a/src/main.cpp b/src/main.cpp
index d4a1693..cf4696a 100644
--- a/src/main.cpp
+++ b/src/main.cpp
@@ -16,10 +16,10 @@ void test() {
 	mat.Print();
 	// mat.Save("matrice4x4echelonne.mat"); */
 
-	Matrix mat2{"matrice4x4.mat"};
+	Matrix mat2 {"matrice4x4.mat"};
 	mat2.Print();
 
-	Solver solver{mat2};
+	Solver solver {mat2};
 
 	Vect image = solver.Image();
 	Vect noyau = solver.Noyau();
diff --git a/test/test_jordan.cpp b/test/test_jordan.cpp
index 43efd2a..6272486 100644
--- a/test/test_jordan.cpp
+++ b/test/test_jordan.cpp
@@ -5,9 +5,9 @@
 #error "Il faut être en debug mode ! xmake f -m debug"
 #endif
 
-struct Test{
-    Matrix mat;
-    Matrix res;
+struct Test {
+	Matrix mat;
+	Matrix res;
 };
 
 static const std::vector<Test> TEST_MATRICES = {
@@ -35,9 +35,9 @@ static const std::vector<Test> TEST_MATRICES = {
 
 void test() {
 	for (Test test : TEST_MATRICES) {
-        test.mat.GaussJordan(true);
-        assert(test.mat == test.res);
-    }
+		test.mat.GaussJordan(true);
+		assert(test.mat == test.res);
+	}
 }
 
 int main(int argc, char** argv) {
diff --git a/test/test_solver.cpp b/test/test_solver.cpp
index 27cc16b..876d7bc 100644
--- a/test/test_solver.cpp
+++ b/test/test_solver.cpp
@@ -14,15 +14,15 @@ int main() {
 
 		std::cout << "Opening " << fileName << " ...\n";
 
-		std::ifstream in{fileName};
+		std::ifstream in {fileName};
 
-		Matrix mat{1, 1}, imageMat{1, 1}, noyauMat{1, 1};
+		Matrix mat {1, 1}, imageMat {1, 1}, noyauMat {1, 1};
 		in >> mat >> imageMat >> noyauMat;
 
-		Vect image{imageMat};
-		Vect noyau{noyauMat};
+		Vect image {imageMat};
+		Vect noyau {noyauMat};
 
-		Solver solver{mat};
+		Solver solver {mat};
 
 		assert(solver.Image() == image);
 		assert(solver.Noyau() == noyau);

From 3b07ae783f34a170135027861f928b709c98b313 Mon Sep 17 00:00:00 2001
From: Persson-dev <sim16.prib@gmail.com>
Date: Fri, 23 Feb 2024 10:48:43 +0100
Subject: [PATCH 25/29] refactor project

---
 src/Gauss.cpp        |  75 ++++++++++++++++++++++++++++++++
 src/Gauss.h          |   9 ++++
 src/Matrix.cpp       | 100 +++----------------------------------------
 src/Matrix.h         |  19 +-------
 src/Solver.cpp       |   8 ++--
 src/Vect.cpp         |   5 ++-
 src/main.cpp         |   3 +-
 test/test_jordan.cpp |   3 +-
 8 files changed, 103 insertions(+), 119 deletions(-)
 create mode 100644 src/Gauss.cpp
 create mode 100644 src/Gauss.h

diff --git a/src/Gauss.cpp b/src/Gauss.cpp
new file mode 100644
index 0000000..60513ee
--- /dev/null
+++ b/src/Gauss.cpp
@@ -0,0 +1,75 @@
+#include "Gauss.h"
+
+#include "Matrix.h"
+
+namespace Gauss {
+
+static void GaussNonJordan(Matrix& mat, bool reduite) {
+	int r = -1;
+	for (std::size_t j = 0; j < mat.GetColumnCount(); j++) {
+		std::size_t indice_ligne_maximum = r + 1;
+
+		// Recherche maximum
+		for (std::size_t i = r + 1; i < mat.GetRawCount(); i++) {
+			if (std::abs(mat.at(i, j)) > std::abs(mat.at(indice_ligne_maximum, j)))
+				indice_ligne_maximum = i;
+		}
+
+		// Si A[k,j]≠0 alors    (A[k,j] désigne la valeur de la ligne k et de la colonne j)
+		if (!IsEqualZero(mat.at(indice_ligne_maximum, j))) {
+			r++;
+
+			// Si k≠r alors
+			if (indice_ligne_maximum != r) {
+				// Échanger les lignes k et r  (On place la ligne du pivot en position r)
+				for (std::size_t k = 0; k < mat.GetColumnCount(); k++) {
+					std::swap(mat.at(indice_ligne_maximum, k), mat.at(r, k));
+				}
+			}
+
+			// Pour i de 1 jusqu'à n               (On simplifie les autres lignes)
+			for (std::size_t i = (reduite ? 0 : j); i < mat.GetRawCount(); i++) {
+				// Si i≠r alors
+				if (i != r) {
+					// Soustraire à la ligne i la ligne r multipliée par A[i,j] (de façon à
+					// annuler A[i,j])
+					for (int k = mat.GetColumnCount() - 1; k >= 0; k--) {
+						long double pivot = mat.at(r, j);
+						long double anul = mat.at(i, j);
+						mat.at(i, k) = mat.at(i, k) * pivot - mat.at(r, k) * anul;
+					}
+				}
+			}
+		}
+	}
+}
+
+static void GaussJordan(Matrix& mat, bool reduite) {
+	GaussNonJordan(mat, reduite);
+	for (std::size_t i = 0; i < mat.GetRawCount(); i++) {
+		int k = -1;
+		for (std::size_t j = 0; j < mat.GetColumnCount(); j++) {
+			if (!IsEqualZero(mat.at(i, j))) {
+				k = j;
+				break;
+			}
+		}
+		// ligne de 0
+		if (k == -1)
+			break;
+		// on divise la ligne par (i, k)
+		long double annul = mat.at(i, k);
+		for (int j = 0; j < mat.GetColumnCount(); j++) {
+			mat.at(i, j) /= annul;
+		}
+	}
+}
+
+void GaussJordan(Matrix& mat, bool reduite, bool normalise) {
+	if (normalise)
+		GaussJordan(mat, reduite);
+	else
+		GaussNonJordan(mat, reduite);
+}
+
+}  // namespace Gauss
\ No newline at end of file
diff --git a/src/Gauss.h b/src/Gauss.h
new file mode 100644
index 0000000..168919a
--- /dev/null
+++ b/src/Gauss.h
@@ -0,0 +1,9 @@
+#pragma once
+
+class Matrix;
+
+namespace Gauss {
+
+void GaussJordan(Matrix& mat, bool reduite, bool normalise);
+
+}  // namespace Gauss
\ No newline at end of file
diff --git a/src/Matrix.cpp b/src/Matrix.cpp
index 422a22a..b289cd3 100644
--- a/src/Matrix.cpp
+++ b/src/Matrix.cpp
@@ -25,6 +25,7 @@ Matrix::~Matrix() {}
 Matrix Matrix::operator*(const Matrix& other) const {
 	if (m_Colonnes != other.m_Lignes) {
 		std::cerr << "Mutiplication impossible car la dimensions des matrices est incompatible" << std::endl;
+		return {1, 1, {0}};
 	}
 
 	Matrix result(m_Lignes, other.m_Colonnes);
@@ -53,13 +54,6 @@ void Matrix::Print() const {
 	}
 }
 
-void Matrix::PrintDebug() {
-#ifndef NDEBUG
-	Print();
-	std::cout << "\n";
-#endif
-}
-
 void Matrix::Insert() {
 	for (size_t i = 0; i < m_Lignes; ++i) {
 		for (size_t j = 0; j < m_Colonnes; ++j) {
@@ -97,32 +91,14 @@ void Matrix::Transpose() {
 	*this = result;
 }
 
-void Matrix::Identity() {
-	assert(m_Lignes == m_Colonnes);
-	for (std::size_t i = 0; i < m_Lignes; i++) {
-		for (std::size_t j = i; j < m_Colonnes; j++) {
-			at(i, j) = i == j;
-		}
-	}
-}
-
 Matrix Matrix::Identity(std::size_t taille) {
 	Matrix id {taille, taille};
-	id.Identity();
-	return id;
-}
-
-bool Matrix::IsInversed() const {
-	for (std::size_t i = 0; i < m_Lignes; ++i) {
-		std::size_t j;
-		for (j = 0; j < m_Colonnes; ++j) {
-			if (!IsEqualZero(at(i, j))) {
-				break;
-			}
-			return false;
+	for (std::size_t i = 0; i < taille; i++) {
+		for (std::size_t j = i; j < taille; j++) {
+			id.at(i, j) = (i == j);
 		}
 	}
-	return true;
+	return id;
 }
 
 void Matrix::Augmenter(const Matrix& droite) {
@@ -158,72 +134,6 @@ bool Matrix::operator==(const Matrix& other) const {
 	return true;
 }
 
-void Matrix::GaussNonJordan(bool reduite) {
-	int r = -1;
-	for (std::size_t j = 0; j < m_Colonnes; j++) {
-		std::size_t indice_ligne_maximum = r + 1;
-
-		// Recherche maximum
-		for (std::size_t i = r + 1; i < m_Lignes; i++) {
-			if (std::abs(at(i, j)) > std::abs(at(indice_ligne_maximum, j)))
-				indice_ligne_maximum = i;
-		}
-
-		// std::cout << "l'indice du maximum est : " << indice_ligne_maximum << "\n\n";
-
-		// Si A[k,j]≠0 alors    (A[k,j] désigne la valeur de la ligne k et de la colonne j)
-		if (!IsEqualZero(at(indice_ligne_maximum, j))) {
-			r++;
-
-			// PrintDebug();
-
-			// Si k≠r alors
-			if (indice_ligne_maximum != r) {
-				// Échanger les lignes k et r  (On place la ligne du pivot en position r)
-				// std::cout << "On échange les lignes " << indice_ligne_maximum << " et " << r << '\n';
-				for (std::size_t k = 0; k < m_Colonnes; k++) {
-					std::swap(at(indice_ligne_maximum, k), at(r, k));
-				}
-			}
-
-			// Pour i de 1 jusqu'à n               (On simplifie les autres lignes)
-			for (std::size_t i = (reduite ? 0 : j); i < m_Lignes; i++) {
-				// Si i≠r alors
-				if (i != r) {
-					// Soustraire à la ligne i la ligne r multipliée par A[i,j] (de façon à
-					// annuler A[i,j])
-					for (int k = m_Colonnes - 1; k >= 0; k--) {
-						long double pivot = at(r, j);
-						long double anul = at(i, j);
-						at(i, k) = at(i, k) * pivot - at(r, k) * anul;
-					}
-				}
-			}
-		}
-	}
-}
-
-void Matrix::GaussJordan(bool reduite) {
-	GaussNonJordan(reduite);
-	for (std::size_t i = 0; i < m_Lignes; i++) {
-		int k = -1;
-		for (std::size_t j = 0; j < m_Colonnes; j++) {
-			if (!IsEqualZero(at(i, j))) {
-				k = j;
-				break;
-			}
-		}
-		// ligne de 0
-		if (k == -1)
-			break;
-		// on divise la ligne par (i, k)
-		long double annul = at(i, k);
-		for (int j = 0; j < m_Colonnes; j++) {
-			at(i, j) /= annul;
-		}
-	}
-}
-
 long double& Matrix::operator[](std::size_t indice) {
 	return m_Data[indice];
 }
diff --git a/src/Matrix.h b/src/Matrix.h
index 4e61977..c6fbb56 100644
--- a/src/Matrix.h
+++ b/src/Matrix.h
@@ -20,40 +20,25 @@ class Matrix {
 	std::size_t GetRawCount() const;
 	std::size_t GetColumnCount() const;
 
-	Matrix operator*(const Matrix& other) const;
-
-	void GaussNonJordan(bool reduite);
-
-	void GaussJordan(bool reduite);
-
+	void Insert();
 	void Print() const;
 
-	void PrintDebug();
-
-	void Insert();
-
 	void Save(const std::string& fileName);
-
 	void Load(const std::string& filename);
 
 	void Transpose();
 
-	void Identity();
-
 	static Matrix Identity(std::size_t taille);
 
-	bool IsInversed() const;
-
 	void Augmenter(const Matrix& droite);
 
 	Matrix SubMatrix(std::size_t origine_ligne, std::size_t origine_colonne, std::size_t ligne, std::size_t colonne) const;
 
 	bool operator==(const Matrix& other) const;
-
+	Matrix operator*(const Matrix& other) const;
 	long double& operator[](std::size_t indice);
 
 	long double& at(std::size_t ligne, std::size_t colonne);
-
 	long double at(std::size_t ligne, std::size_t colonne) const;
 
 	friend std::ostream& operator<<(std::ostream& stream, const Matrix& mat);
diff --git a/src/Solver.cpp b/src/Solver.cpp
index db4adf3..69fed58 100644
--- a/src/Solver.cpp
+++ b/src/Solver.cpp
@@ -1,11 +1,13 @@
 #include "Solver.h"
 
+#include "Gauss.h"
+
 Solver::Solver(const Matrix& mat) : m_Matrix(mat) {}
 
 Vect Solver::Image() const {
 	Matrix result = m_Matrix;
 	result.Transpose();
-	result.GaussJordan(true);
+	Gauss::GaussJordan(result, true, true);
 	result.Transpose();
 	return {result};
 }
@@ -15,7 +17,7 @@ Vect Solver::Noyau() const {
 	Matrix result = m_Matrix;
 	result.Transpose();
 	result.Augmenter(Matrix::Identity(result.GetRawCount()));
-	result.GaussJordan(true);
+	Gauss::GaussJordan(result, true, true);
 	result.Transpose();
 
 	// nombre de colonnes non nulles
@@ -27,7 +29,7 @@ Vect Solver::Noyau() const {
 
 VectAffine Solver::SystemeTriangulaire() const {
 	Matrix mat = m_Matrix;
-	mat.GaussJordan(true);
+	Gauss::GaussJordan(mat, true, true);
 
 	Solver solver {mat.SubMatrix(0, 0, mat.GetRawCount(), mat.GetColumnCount() - 1)};
 
diff --git a/src/Vect.cpp b/src/Vect.cpp
index 936a6fd..f56bb08 100644
--- a/src/Vect.cpp
+++ b/src/Vect.cpp
@@ -1,5 +1,6 @@
 #include "Vect.h"
 
+#include "Gauss.h"
 #include "Solver.h"
 #include <cassert>
 #include <iostream>
@@ -45,7 +46,7 @@ bool Vect::operator==(const Vect& other) const {
 void Vect::AddVector(const Matrix& mat) {
 	m_Data.Augmenter(mat);
 	m_Data.Transpose();
-	m_Data.GaussNonJordan(false);
+	Gauss::GaussJordan(m_Data, false, false);
 	m_Data.Transpose();
 	Simplify();
 }
@@ -68,7 +69,7 @@ void Vect::Print() const {
 	std::cout << "Espace vectoriel de dimension " << GetCardinal() << " de base :\n\n";
 	for (std::size_t i = 0; i < m_Data.GetRawCount(); i++) {
 		for (std::size_t j = 0; j < m_Data.GetColumnCount(); j++) {
-			printf("[ %u ]\t", static_cast<float>(m_Data.at(i, j)));
+			printf("[ %d ]\t", static_cast<float>(m_Data.at(i, j)));
 		}
 		std::cout << "\n";
 	}
diff --git a/src/main.cpp b/src/main.cpp
index cf4696a..a662fbc 100644
--- a/src/main.cpp
+++ b/src/main.cpp
@@ -1,3 +1,4 @@
+#include "Gauss.h"
 #include "Solver.h"
 #include <iostream>
 
@@ -52,7 +53,7 @@ void prompt() {
 
 	mat.Print();
 
-	mat.GaussJordan(true);
+	Gauss::GaussJordan(mat, true, true);
 
 	mat.Print();
 }
diff --git a/test/test_jordan.cpp b/test/test_jordan.cpp
index 6272486..d61e51a 100644
--- a/test/test_jordan.cpp
+++ b/test/test_jordan.cpp
@@ -1,3 +1,4 @@
+#include "Gauss.h"
 #include "Matrix.h"
 #include <cassert>
 
@@ -35,7 +36,7 @@ static const std::vector<Test> TEST_MATRICES = {
 
 void test() {
 	for (Test test : TEST_MATRICES) {
-		test.mat.GaussJordan(true);
+		Gauss::GaussJordan(test.mat, true, true);
 		assert(test.mat == test.res);
 	}
 }

From 99eca82b3a2980b3e0579e530dceb280c82c3ab3 Mon Sep 17 00:00:00 2001
From: Persson-dev <sim16.prib@gmail.com>
Date: Fri, 23 Feb 2024 11:02:49 +0100
Subject: [PATCH 26/29] fix Vect display

---
 src/Vect.cpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/Vect.cpp b/src/Vect.cpp
index f56bb08..1947141 100644
--- a/src/Vect.cpp
+++ b/src/Vect.cpp
@@ -69,7 +69,7 @@ void Vect::Print() const {
 	std::cout << "Espace vectoriel de dimension " << GetCardinal() << " de base :\n\n";
 	for (std::size_t i = 0; i < m_Data.GetRawCount(); i++) {
 		for (std::size_t j = 0; j < m_Data.GetColumnCount(); j++) {
-			printf("[ %d ]\t", static_cast<float>(m_Data.at(i, j)));
+			std::cout << "[ " << m_Data.at(i, j) << " ]\t";
 		}
 		std::cout << "\n";
 	}

From 5a5c247019bda016e3fe11dbc3e81172120fe083 Mon Sep 17 00:00:00 2001
From: Persson-dev <sim16.prib@gmail.com>
Date: Fri, 23 Feb 2024 11:03:38 +0100
Subject: [PATCH 27/29] english name for symbols

---
 src/Matrix.cpp       | 80 ++++++++++++++++++++++----------------------
 src/Matrix.h         | 20 +++++------
 src/Solver.cpp       | 10 +++---
 src/Solver.h         |  6 ++--
 src/Vect.cpp         |  4 +--
 src/main.cpp         |  4 +--
 test/test_solver.cpp |  2 +-
 7 files changed, 63 insertions(+), 63 deletions(-)

diff --git a/src/Matrix.cpp b/src/Matrix.cpp
index b289cd3..596a55f 100644
--- a/src/Matrix.cpp
+++ b/src/Matrix.cpp
@@ -10,30 +10,30 @@ Matrix::Matrix(const std::string& fileNameInput) {
 	Load(fileNameInput);
 }
 
-Matrix::Matrix(std::size_t lignes, std::size_t colonnes) : m_Lignes(lignes), m_Colonnes(colonnes) {
-	m_Data.resize(m_Lignes * m_Colonnes);
+Matrix::Matrix(std::size_t lignes, std::size_t colonnes) : m_Raws(lignes), m_Columns(colonnes) {
+	m_Data.resize(m_Raws * m_Columns);
 }
 
 Matrix::Matrix(std::size_t lignes, std::size_t colonnes, std::initializer_list<long double>&& initList) :
-	m_Lignes(lignes), m_Colonnes(colonnes) {
+	m_Raws(lignes), m_Columns(colonnes) {
 	m_Data = initList;
-	m_Data.resize(m_Lignes * m_Colonnes);
+	m_Data.resize(m_Raws * m_Columns);
 }
 
 Matrix::~Matrix() {}
 
 Matrix Matrix::operator*(const Matrix& other) const {
-	if (m_Colonnes != other.m_Lignes) {
+	if (m_Columns != other.m_Raws) {
 		std::cerr << "Mutiplication impossible car la dimensions des matrices est incompatible" << std::endl;
 		return {1, 1, {0}};
 	}
 
-	Matrix result(m_Lignes, other.m_Colonnes);
+	Matrix result(m_Raws, other.m_Columns);
 
-	for (std::size_t i = 0; i < m_Lignes; ++i) {
-		for (std::size_t j = 0; j < other.m_Colonnes; ++j) {
+	for (std::size_t i = 0; i < m_Raws; ++i) {
+		for (std::size_t j = 0; j < other.m_Columns; ++j) {
 			long double sum = 0;
-			for (std::size_t k = 0; k < m_Colonnes; k++) {
+			for (std::size_t k = 0; k < m_Columns; k++) {
 				sum += at(i, k) * other.at(k, j);
 			}
 			result.at(i, j) = sum;
@@ -43,10 +43,10 @@ Matrix Matrix::operator*(const Matrix& other) const {
 }
 
 void Matrix::Print() const {
-	for (size_t i = 0; i < m_Lignes; ++i) {
+	for (size_t i = 0; i < m_Raws; ++i) {
 		std::cout << "[ ";
-		for (size_t j = 0; j < m_Colonnes; ++j) {
-			std::size_t indice = i * m_Lignes + j;
+		for (size_t j = 0; j < m_Columns; ++j) {
+			std::size_t indice = i * m_Raws + j;
 			std::cout << at(i, j) << " ";
 		}
 		std::cout << "]";
@@ -55,8 +55,8 @@ void Matrix::Print() const {
 }
 
 void Matrix::Insert() {
-	for (size_t i = 0; i < m_Lignes; ++i) {
-		for (size_t j = 0; j < m_Colonnes; ++j) {
+	for (size_t i = 0; i < m_Raws; ++i) {
+		for (size_t j = 0; j < m_Columns; ++j) {
 			std::cin >> at(i, j);
 		}
 		std::cout << std::endl;
@@ -82,9 +82,9 @@ void Matrix::Load(const std::string& filename) {
 }
 
 void Matrix::Transpose() {
-	Matrix result {m_Colonnes, m_Lignes};
-	for (std::size_t i = 0; i < m_Lignes; i++) {
-		for (std::size_t j = 0; j < m_Colonnes; j++) {
+	Matrix result {m_Columns, m_Raws};
+	for (std::size_t i = 0; i < m_Raws; i++) {
+		for (std::size_t j = 0; j < m_Columns; j++) {
 			result.at(j, i) = at(i, j);
 		}
 	}
@@ -101,19 +101,19 @@ Matrix Matrix::Identity(std::size_t taille) {
 	return id;
 }
 
-void Matrix::Augmenter(const Matrix& droite) {
-	assert(droite.m_Lignes == m_Lignes);
-	Matrix temp {m_Lignes, m_Colonnes + droite.m_Colonnes};
+void Matrix::Augment(const Matrix& droite) {
+	assert(droite.m_Raws == m_Raws);
+	Matrix temp {m_Raws, m_Columns + droite.m_Columns};
 
-	for (std::size_t i = 0; i < m_Lignes; i++) {
-		for (std::size_t j = 0; j < m_Colonnes; j++) {
+	for (std::size_t i = 0; i < m_Raws; i++) {
+		for (std::size_t j = 0; j < m_Columns; j++) {
 			temp.at(i, j) = at(i, j);
 		}
 	}
 
-	for (std::size_t i = 0; i < m_Lignes; i++) {
-		for (std::size_t j = 0; j < droite.m_Colonnes; j++) {
-			temp.at(i, j + m_Colonnes) = droite.at(i, j);
+	for (std::size_t i = 0; i < m_Raws; i++) {
+		for (std::size_t j = 0; j < droite.m_Columns; j++) {
+			temp.at(i, j + m_Columns) = droite.at(i, j);
 		}
 	}
 
@@ -121,11 +121,11 @@ void Matrix::Augmenter(const Matrix& droite) {
 }
 
 bool Matrix::operator==(const Matrix& other) const {
-	if (m_Lignes != other.m_Lignes || m_Colonnes != other.m_Colonnes)
+	if (m_Raws != other.m_Raws || m_Columns != other.m_Columns)
 		return false;
 
-	for (std::size_t i = 0; i < m_Lignes; i++) {
-		for (std::size_t j = 0; j < m_Colonnes; j++) {
+	for (std::size_t i = 0; i < m_Raws; i++) {
+		for (std::size_t j = 0; j < m_Columns; j++) {
 			if (!IsEqualZero(at(i, j) - other.at(i, j)))
 				return false;
 		}
@@ -139,23 +139,23 @@ long double& Matrix::operator[](std::size_t indice) {
 }
 
 long double& Matrix::at(std::size_t ligne, std::size_t colonne) {
-	return m_Data[ligne * m_Colonnes + colonne];
+	return m_Data[ligne * m_Columns + colonne];
 }
 
 long double Matrix::at(std::size_t ligne, std::size_t colonne) const {
-	return m_Data[ligne * m_Colonnes + colonne];
+	return m_Data[ligne * m_Columns + colonne];
 }
 
 std::size_t Matrix::GetRawCount() const {
-	return m_Lignes;
+	return m_Raws;
 }
 
 std::size_t Matrix::GetColumnCount() const {
-	return m_Colonnes;
+	return m_Columns;
 }
 
 Matrix Matrix::SubMatrix(std::size_t origine_ligne, std::size_t origine_colonne, std::size_t ligne, std::size_t colonne) const {
-	assert(m_Lignes >= ligne && m_Colonnes >= colonne);
+	assert(m_Raws >= ligne && m_Columns >= colonne);
 	Matrix result {ligne, colonne};
 
 	for (std::size_t i = 0; i < ligne; i++) {
@@ -168,9 +168,9 @@ Matrix Matrix::SubMatrix(std::size_t origine_ligne, std::size_t origine_colonne,
 }
 
 std::ostream& operator<<(std::ostream& stream, const Matrix& mat) {
-	stream << mat.m_Lignes << " " << mat.m_Colonnes << "\n";
-	for (std::size_t i = 0; i < mat.m_Lignes; i++) {
-		for (std::size_t j = 0; j < mat.m_Colonnes; j++) {
+	stream << mat.m_Raws << " " << mat.m_Columns << "\n";
+	for (std::size_t i = 0; i < mat.m_Raws; i++) {
+		for (std::size_t j = 0; j < mat.m_Columns; j++) {
 			stream << mat.at(i, j) << " ";
 		}
 		stream << "\n";
@@ -179,10 +179,10 @@ std::ostream& operator<<(std::ostream& stream, const Matrix& mat) {
 }
 
 std::istream& operator>>(std::istream& stream, Matrix& mat) {
-	stream >> mat.m_Lignes >> mat.m_Colonnes;
-	mat.m_Data.resize(mat.m_Lignes * mat.m_Colonnes);
-	for (std::size_t i = 0; i < mat.m_Lignes; i++) {
-		for (std::size_t j = 0; j < mat.m_Colonnes; j++) {
+	stream >> mat.m_Raws >> mat.m_Columns;
+	mat.m_Data.resize(mat.m_Raws * mat.m_Columns);
+	for (std::size_t i = 0; i < mat.m_Raws; i++) {
+		for (std::size_t j = 0; j < mat.m_Columns; j++) {
 			stream >> mat.at(i, j);
 		}
 	}
diff --git a/src/Matrix.h b/src/Matrix.h
index c6fbb56..2d34ded 100644
--- a/src/Matrix.h
+++ b/src/Matrix.h
@@ -7,14 +7,14 @@
 
 class Matrix {
   private:
-	std::size_t m_Lignes;
-	std::size_t m_Colonnes;
+	std::size_t m_Raws;
+	std::size_t m_Columns;
 	std::vector<long double> m_Data;
 
   public:
 	Matrix(const std::string& fileNameInput);
-	Matrix(std::size_t lignes, std::size_t colonnes);
-	Matrix(std::size_t lignes, std::size_t colonnes, std::initializer_list<long double>&& initList);
+	Matrix(std::size_t raws, std::size_t columns);
+	Matrix(std::size_t raws, std::size_t columns, std::initializer_list<long double>&& initList);
 	~Matrix();
 
 	std::size_t GetRawCount() const;
@@ -28,18 +28,18 @@ class Matrix {
 
 	void Transpose();
 
-	static Matrix Identity(std::size_t taille);
+	static Matrix Identity(std::size_t size);
 
-	void Augmenter(const Matrix& droite);
+	void Augment(const Matrix& right);
 
-	Matrix SubMatrix(std::size_t origine_ligne, std::size_t origine_colonne, std::size_t ligne, std::size_t colonne) const;
+	Matrix SubMatrix(std::size_t raw_origin, std::size_t column_origin, std::size_t raw, std::size_t column) const;
 
 	bool operator==(const Matrix& other) const;
 	Matrix operator*(const Matrix& other) const;
-	long double& operator[](std::size_t indice);
+	long double& operator[](std::size_t index);
 
-	long double& at(std::size_t ligne, std::size_t colonne);
-	long double at(std::size_t ligne, std::size_t colonne) const;
+	long double& at(std::size_t raw, std::size_t column);
+	long double at(std::size_t raw, std::size_t column) const;
 
 	friend std::ostream& operator<<(std::ostream& stream, const Matrix& mat);
 	friend std::istream& operator>>(std::istream& stream, Matrix& mat);
diff --git a/src/Solver.cpp b/src/Solver.cpp
index 69fed58..5f05d14 100644
--- a/src/Solver.cpp
+++ b/src/Solver.cpp
@@ -13,10 +13,10 @@ Vect Solver::Image() const {
 }
 
 // https://en.wikipedia.org/wiki/Kernel_(linear_algebra)#Computation_by_Gaussian_elimination
-Vect Solver::Noyau() const {
+Vect Solver::Kernel() const {
 	Matrix result = m_Matrix;
 	result.Transpose();
-	result.Augmenter(Matrix::Identity(result.GetRawCount()));
+	result.Augment(Matrix::Identity(result.GetRawCount()));
 	Gauss::GaussJordan(result, true, true);
 	result.Transpose();
 
@@ -27,19 +27,19 @@ Vect Solver::Noyau() const {
 		result.GetColumnCount() - origine_colonne)};
 }
 
-VectAffine Solver::SystemeTriangulaire() const {
+VectAffine Solver::TriangularSystem() const {
 	Matrix mat = m_Matrix;
 	Gauss::GaussJordan(mat, true, true);
 
 	Solver solver {mat.SubMatrix(0, 0, mat.GetRawCount(), mat.GetColumnCount() - 1)};
 
-	Vect noyau = solver.Noyau();
+	Vect noyau = solver.Kernel();
 	Matrix origin = mat.SubMatrix(0, mat.GetColumnCount() - 1, mat.GetRawCount(), 1);
 
 	return {noyau, origin};
 }
 
-std::size_t Solver::Rang() const {
+std::size_t Solver::Rank() const {
 	Vect image = Image();
 	return image.GetCardinal();
 }
diff --git a/src/Solver.h b/src/Solver.h
index c1d2eb7..2d6bbf5 100644
--- a/src/Solver.h
+++ b/src/Solver.h
@@ -12,9 +12,9 @@ class Solver {
 	~Solver() {}
 
 	Vect Image() const;
-	Vect Noyau() const;
+	Vect Kernel() const;
 
-	VectAffine SystemeTriangulaire() const;
+	VectAffine TriangularSystem() const;
 
-	std::size_t Rang() const;
+	std::size_t Rank() const;
 };
\ No newline at end of file
diff --git a/src/Vect.cpp b/src/Vect.cpp
index 1947141..e3a2368 100644
--- a/src/Vect.cpp
+++ b/src/Vect.cpp
@@ -44,7 +44,7 @@ bool Vect::operator==(const Vect& other) const {
 }
 
 void Vect::AddVector(const Matrix& mat) {
-	m_Data.Augmenter(mat);
+	m_Data.Augment(mat);
 	m_Data.Transpose();
 	Gauss::GaussJordan(m_Data, false, false);
 	m_Data.Transpose();
@@ -60,7 +60,7 @@ Matrix Vect::GetLinearSystem() const {
 	vect.Transpose();
 
 	Solver solver {vect};
-	vect = solver.Noyau().m_Data;
+	vect = solver.Kernel().m_Data;
 	vect.Transpose();
 	return vect;
 }
diff --git a/src/main.cpp b/src/main.cpp
index a662fbc..c45d706 100644
--- a/src/main.cpp
+++ b/src/main.cpp
@@ -23,7 +23,7 @@ void test() {
 	Solver solver {mat2};
 
 	Vect image = solver.Image();
-	Vect noyau = solver.Noyau();
+	Vect noyau = solver.Kernel();
 
 	std::cout << "\tImage :\n";
 	image.Print();
@@ -35,7 +35,7 @@ void test() {
 	noyau.GetLinearSystem().Print();
 
 	std::cout << "\n\n";
-	solver.SystemeTriangulaire().Print();
+	solver.TriangularSystem().Print();
 }
 
 void prompt() {
diff --git a/test/test_solver.cpp b/test/test_solver.cpp
index 876d7bc..cfe6e7e 100644
--- a/test/test_solver.cpp
+++ b/test/test_solver.cpp
@@ -25,7 +25,7 @@ int main() {
 		Solver solver {mat};
 
 		assert(solver.Image() == image);
-		assert(solver.Noyau() == noyau);
+		assert(solver.Kernel() == noyau);
 	}
 	return 0;
 }
\ No newline at end of file

From a35f45015b1e7fdd5306e5e005a798c6e107431e Mon Sep 17 00:00:00 2001
From: Simon Pribylski <sim16.prib@gmail.com>
Date: Fri, 23 Feb 2024 11:16:58 +0100
Subject: [PATCH 28/29] Use fixed xmake version for action

---
 .gitea/workflows/ubuntu.yaml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.gitea/workflows/ubuntu.yaml b/.gitea/workflows/ubuntu.yaml
index e4d31e4..2b37b66 100644
--- a/.gitea/workflows/ubuntu.yaml
+++ b/.gitea/workflows/ubuntu.yaml
@@ -13,7 +13,7 @@ jobs:
       - name: Prepare XMake
         uses: xmake-io/github-action-setup-xmake@v1
         with:
-          xmake-version: branch@master
+          xmake-version: '2.8.6'
           actions-cache-folder: '.xmake-cache'
           actions-cache-key: 'ubuntu'
 

From 6b03fab302019fb14f75fda8cd052960db00661e Mon Sep 17 00:00:00 2001
From: Persson-dev <sim16.prib@gmail.com>
Date: Sat, 24 Feb 2024 13:05:29 +0100
Subject: [PATCH 29/29] action: use xmake latest

---
 .gitea/workflows/ubuntu.yaml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.gitea/workflows/ubuntu.yaml b/.gitea/workflows/ubuntu.yaml
index 2b37b66..4f37a72 100644
--- a/.gitea/workflows/ubuntu.yaml
+++ b/.gitea/workflows/ubuntu.yaml
@@ -13,7 +13,7 @@ jobs:
       - name: Prepare XMake
         uses: xmake-io/github-action-setup-xmake@v1
         with:
-          xmake-version: '2.8.6'
+          xmake-version: latest
           actions-cache-folder: '.xmake-cache'
           actions-cache-key: 'ubuntu'