diff --git a/src/gui/PivotGui.cpp b/src/gui/PivotGui.cpp
index 30ce92b..4f2211d 100644
--- a/src/gui/PivotGui.cpp
+++ b/src/gui/PivotGui.cpp
@@ -1,95 +1,114 @@
 #include "PivotGui.h"
 
+#include "Matrix.h"
+#include "Solver.h"
 #include <imgui.h>
 
-std::vector<std::vector<int>> PivotGui::matrixValues;
-int PivotGui::matrixSizeX = 4;
-int PivotGui::matrixSizeY = 4;
+static Matrix LoadMatrixFromStdVect(const std::vector<std::vector<int>>& data) {
+	Matrix result {data.size(), data.empty() ? 0 : data[0].size()};
+	for (std::size_t i = 0; i < result.GetRawCount(); i++) {
+		for (std::size_t j = 0; j < result.GetColumnCount(); j++) {
+			result.at(i, j) = static_cast<Matrix::Element>(data[i][j]);
+		}
+	}
+    return result;
+}
 
 void PivotGui::Init() {}
 
 void PivotGui::Render() {
-    ImGuiIO& io = ImGui::GetIO();
+	ImGuiIO& io = ImGui::GetIO();
 
-    // divisions des fenetres
-    ImVec2 topLeftWindowSize(io.DisplaySize.x * 0.5f, io.DisplaySize.y * 0.8f);
-    ImVec2 topRightWindowSize(io.DisplaySize.x * 0.5f, io.DisplaySize.y * 0.8f);
-    ImVec2 bottomWindowSize(io.DisplaySize.x, io.DisplaySize.y * 0.2f);
+	static std::vector<std::vector<int>> matrixValues;
+	static int matrixSizeX = 4;
+	static int matrixSizeY = 4;
+	static Solver solver;
 
-    // Begin fenetre top left
-    ImGui::SetNextWindowSize(topLeftWindowSize);
-    ImGui::SetNextWindowPos(ImVec2(0, 0)); // Position at the top-left corner
-    ImGui::Begin("Left Top Window", nullptr, ImGuiWindowFlags_NoResize | ImGuiWindowFlags_NoMove | ImGuiWindowFlags_NoTitleBar | ImGuiWindowFlags_NoScrollbar);
+	// divisions des fenetres
+	ImVec2 topLeftWindowSize(io.DisplaySize.x * 0.5f, io.DisplaySize.y * 0.8f);
+	ImVec2 topRightWindowSize(io.DisplaySize.x * 0.5f, io.DisplaySize.y * 0.8f);
+	ImVec2 bottomWindowSize(io.DisplaySize.x, io.DisplaySize.y * 0.2f);
 
-    // Get window position
-    ImVec2 windowPos = ImGui::GetWindowPos();
+	// Begin fenetre top left
+	ImGui::SetNextWindowSize(topLeftWindowSize);
+	ImGui::SetNextWindowPos(ImVec2(0, 0));	// Position at the top-left corner
+	ImGui::Begin("Left Top Window", nullptr,
+		ImGuiWindowFlags_NoResize | ImGuiWindowFlags_NoMove | ImGuiWindowFlags_NoTitleBar | ImGuiWindowFlags_NoScrollbar);
 
-    ImGui::Text("Matrice initiale:");
+	// Get window position
+	ImVec2 windowPos = ImGui::GetWindowPos();
 
-    ImGui::InputInt("##RowsMatriceInitiale", &matrixSizeY);
-    ImGui::SameLine();
-    ImGui::Text("Lignes");
+	ImGui::Text("Matrice initiale:");
+
+	ImGui::InputInt("##RowsMatriceInitiale", &matrixSizeY);
+	ImGui::SameLine();
+	ImGui::Text("Lignes");
 
 
-    ImGui::InputInt("##ColumnsMatriceInitiale", &matrixSizeX);
-    ImGui::SameLine();
-    ImGui::Text("Colonnes");
+	ImGui::InputInt("##ColumnsMatriceInitiale", &matrixSizeX);
+	ImGui::SameLine();
+	ImGui::Text("Colonnes");
 
-	 ImGui::BeginChild("MatriceInitiale", ImVec2(topLeftWindowSize.x, io.DisplaySize.y * 0.7f), false);
+	ImGui::BeginChild("MatriceInitiale", ImVec2(topLeftWindowSize.x, io.DisplaySize.y * 0.7f), false);
 
-	 // Resize matrixValues and initialize new elements to 0
+	// Resize matrixValues and initialize new elements to 0
 
-		 matrixValues.resize(matrixSizeY);
-	 for(auto& row : matrixValues) {
-		 row.resize(matrixSizeX, 0);
-	 }
-
-	for (int y = 0; y < matrixSizeY; y++) {
-	   for (int x = 0; x < matrixSizeX; x++) {
-		   if (x > 0)
-			   ImGui::SameLine();
-		   ImGui::PushID(y * matrixSizeX + x);
-		   ImGui::PushItemWidth(30); // Adjust this value to change the cell size
-		   ImGui::InputInt("", &matrixValues[y][x], 0, 0, ImGuiInputTextFlags_CharsDecimal);
-		   ImGui::PopItemWidth();
-		   ImGui::PopID();
-	   }
+	matrixValues.resize(matrixSizeY);
+	for (auto& row : matrixValues) {
+		row.resize(matrixSizeX, 0);
 	}
 
-    ImGui::Text("Matrice finale:");
+	for (int y = 0; y < matrixSizeY; y++) {
+		for (int x = 0; x < matrixSizeX; x++) {
+			if (x > 0)
+				ImGui::SameLine();
+			ImGui::PushID(y * matrixSizeX + x);
+			ImGui::PushItemWidth(30);  // Adjust this value to change the cell size
+			ImGui::InputInt("", &matrixValues[y][x], 0, 0, ImGuiInputTextFlags_CharsDecimal);
+			ImGui::PopItemWidth();
+			ImGui::PopID();
+		}
+	}
 
-    ImGui::EndChild(); // End Matrice initiale
+	ImGui::Text("Matrice finale:");
 
-    ImGui::End(); // End fenetre top left
+	ImGui::EndChild();	// End Matrice initiale
 
-    // Begin fenetre top right
-    ImGui::SetNextWindowSize(topRightWindowSize);
-    ImGui::SetNextWindowPos(ImVec2(windowPos.x + topLeftWindowSize.x, 0)); // Position at the top-right corner
-    ImGui::Begin("Right Top Window", nullptr, ImGuiWindowFlags_NoResize | ImGuiWindowFlags_NoMove | ImGuiWindowFlags_NoTitleBar | ImGuiWindowFlags_NoScrollbar);
+	ImGui::End();  // End fenetre top left
 
-    // rajouter le code pour la partie top right
+	// Begin fenetre top right
+	ImGui::SetNextWindowSize(topRightWindowSize);
+	ImGui::SetNextWindowPos(ImVec2(windowPos.x + topLeftWindowSize.x, 0));	// Position at the top-right corner
+	ImGui::Begin("Right Top Window", nullptr,
+		ImGuiWindowFlags_NoResize | ImGuiWindowFlags_NoMove | ImGuiWindowFlags_NoTitleBar | ImGuiWindowFlags_NoScrollbar);
 
-    ImGui::End(); // End fenetre top right
+	// rajouter le code pour la partie top right
 
-    // Begin fenetre bas
-    ImGui::SetNextWindowSize(bottomWindowSize);
-    ImGui::SetNextWindowPos(ImVec2(0, io.DisplaySize.y * 0.8f)); // Position at the bottom-left corner
-    ImGui::Begin("Bottom Part", nullptr, ImGuiWindowFlags_NoResize | ImGuiWindowFlags_NoMove | ImGuiWindowFlags_NoTitleBar | ImGuiWindowFlags_NoScrollbar);
+	ImGui::End();  // End fenetre top right
 
-    // rajouter des boutons clickables
-    if (ImGui::Button("Calcul noyeau")) {
-        // Code de calcul
-    }
-    ImGui::SameLine(); // Align buttons horizontally
-    if (ImGui::Button("Calcul rang")) {
-        // Code de calcul
-    }
-    ImGui::SameLine(); // Align buttons horizontally
-    if (ImGui::Button("Calcul image")) {
-        // Code de calcul
-    }
+	// Begin fenetre bas
+	ImGui::SetNextWindowSize(bottomWindowSize);
+	ImGui::SetNextWindowPos(ImVec2(0, io.DisplaySize.y * 0.8f));  // Position at the bottom-left corner
+	ImGui::Begin("Bottom Part", nullptr,
+		ImGuiWindowFlags_NoResize | ImGuiWindowFlags_NoMove | ImGuiWindowFlags_NoTitleBar | ImGuiWindowFlags_NoScrollbar);
 
-    ImGui::End(); // End fenetre bas
+	// rajouter des boutons clickables
+	if (ImGui::Button("Calcul noyau")) {
+		// Code de calcul
+		Vect kernel = solver.Kernel(LoadMatrixFromStdVect(matrixValues));
+	}
+	ImGui::SameLine();	// Align buttons horizontally
+	if (ImGui::Button("Calcul rang")) {
+		// Code de calcul
+		std::size_t rank = solver.Rank(LoadMatrixFromStdVect(matrixValues));
+	}
+	ImGui::SameLine();	// Align buttons horizontally
+	if (ImGui::Button("Calcul image")) {
+		// Code de calcul
+		Vect image = solver.Image(LoadMatrixFromStdVect(matrixValues));
+	}
+
+	ImGui::End();  // End fenetre bas
 }
 
 void PivotGui::Destroy() {}
\ No newline at end of file
diff --git a/src/gui/PivotGui.h b/src/gui/PivotGui.h
index d02b907..a9245fe 100644
--- a/src/gui/PivotGui.h
+++ b/src/gui/PivotGui.h
@@ -6,7 +6,5 @@ namespace PivotGui {
 void Init();
 void Render();
 void Destroy();
-extern std::vector<std::vector<int>> matrixValues;
-extern int matrixSizeX;
-extern int matrixSizeY;
+
 }  // namespace PivotGui