Merge branch 'version-11' into f7

2026-01-18 16:27:34 +01:00 · 2019-06-06 10:10:50 +02:00
parent 9985ce7ed0 5015bc231b
commit 22d6cfedda
61 changed files with 412 additions and 177 deletions
--- a/apps/code/base.de.i18n
+++ b/apps/code/base.de.i18n
@@ -1,8 +1,8 @@
 Console = "Interaktive Konsole"
-AddScript = "Skript hinzufuegen"
+AddScript = "Skript hinzufügen"
 ScriptOptions = "Skriptoptionen"
-ExecuteScript = "Skript ausfuehren"
+ExecuteScript = "Skript ausführen"
 AutoImportScript = "Automatischer Import in Konsole"
-DeleteScript = "Skript loeschen"
+DeleteScript = "Skript löschen"
 FunctionsAndVariables = "Funktionen und Variablen"
 AllowedCharactersaz09 = "Erlaubte Zeichen: a-z, 0-9, _"
--- a/apps/code/catalog.de.i18n
+++ b/apps/code/catalog.de.i18n
@@ -1,28 +1,28 @@
 PythonPound = "Kommentar"
 PythonPercent = "Modulo"
-Python1J = "Imaginaeres i"
+Python1J = "Imaginäres i"
 PythonLF = "Zeilenvorschub"
 PythonTab = "Tabulator"
 PythonAmpersand = "Bitweise und"
 PythonSymbolExp = "Bitweise exklusiv oder"
 PythonVerticalBar = "Bitweise oder"
-PythonImag = "Imaginaerteil von z"
+PythonImag = "Imaginärteil von z"
 PythonReal = "Realteil von z"
-PythonSingleQuote = "Einfaches Anfuehrungszeichen"
-PythonAbs = "Absolute/r Wert/Groesse"
+PythonSingleQuote = "Einfaches Anführungszeichen"
+PythonAbs = "Absolute/r Wert/Größe"
 PythonAcos = "Arkuskosinus"
 PythonAcosh = "Hyperbelkosinus"
 PythonAsin = "Arkussinus"
 PythonAsinh = "Hyperbelsinus"
 PythonAtan = "Arkustangens"
-PythonAtan2 = "Gib arctan(y/x)"
+PythonAtan2 = "Gib atan(y/x)"
 PythonAtanh = "Hyperbeltangens"
-PythonBin = "Ganzzahl nach binaer konvertieren"
+PythonBin = "Ganzzahl nach binär konvertieren"
 PythonCeil = "Aufrundung"
 PythonChoice = "Zufallszahl aus der Liste"
-PythonCmathFunction = "cmath-Modul-Funktionspraefix"
+PythonCmathFunction = "cmath-Modul-Funktionspräfix"
 PythonColor = "Definiere eine RGB-Farbe"
-PythonComplex = "a+ib zurueckgeben"
+PythonComplex = "a+ib zurückgeben"
 PythonCopySign = "Return x with the sign of y"
 PythonCos = "Kosinus"
 PythonCosh = "Hyperbolic cosine"
--- a/apps/code/catalog.en.i18n
+++ b/apps/code/catalog.en.i18n
@@ -15,7 +15,7 @@ PythonAcosh = "Arc hyperbolic cosine"
 PythonAsin = "Arc sine"
 PythonAsinh = "Arc hyperbolic sine"
 PythonAtan = "Arc tangent"
-PythonAtan2 = "Return arctan(y/x)"
+PythonAtan2 = "Return atan(y/x)"
 PythonAtanh = "Arc hyperbolic tangent"
 PythonBin = "Convert integer to binary"
 PythonCeil = "Ceiling"
--- a/apps/code/catalog.es.i18n
+++ b/apps/code/catalog.es.i18n
@@ -15,7 +15,7 @@ PythonAcosh = "Arc hyperbolic cosine"
 PythonAsin = "Arc sine"
 PythonAsinh = "Arc hyperbolic sine"
 PythonAtan = "Arc tangent"
-PythonAtan2 = "Return arctan(y/x)"
+PythonAtan2 = "Return atan(y/x)"
 PythonAtanh = "Arc hyperbolic tangent"
 PythonBin = "Convert integer to binary"
 PythonCeil = "Ceiling"
--- a/apps/code/catalog.fr.i18n
+++ b/apps/code/catalog.fr.i18n
@@ -15,7 +15,7 @@ PythonAcosh = "Arc cosinus hyperbolique"
 PythonAsin = "Arc sinus"
 PythonAsinh = "Arc sinus hyperbolique"
 PythonAtan = "Arc tangente"
-PythonAtan2 = "Calcul de arctan(y/x)"
+PythonAtan2 = "Calcul de atan(y/x)"
 PythonAtanh = "Arc tangente hyperbolique"
 PythonBin = "Conversion d'un entier en binaire"
 PythonCeil = "Plafond"
--- a/apps/code/catalog.pt.i18n
+++ b/apps/code/catalog.pt.i18n
@@ -15,7 +15,7 @@ PythonAcosh = "Arc hyperbolic cosine"
 PythonAsin = "Arc sine"
 PythonAsinh = "Arc hyperbolic sine"
 PythonAtan = "Arc tangent"
-PythonAtan2 = "Return arctan(y/x)"
+PythonAtan2 = "Return atan(y/x)"
 PythonAtanh = "Arc hyperbolic tangent"
 PythonBin = "Convert integer to binary"
 PythonCeil = "Ceiling"
--- a/apps/code/editor_controller.cpp
+++ b/apps/code/editor_controller.cpp
@@ -70,9 +70,19 @@ bool EditorController::textAreaDidReceiveEvent(TextArea * textArea, Ion::Events:
    /* If the cursor is on the left of the text of a line, backspace one
     * indentation space at a time. */
    const char * text = textArea->text();
-    const char * firstNonSpace = UTF8Helper::NotCodePointSearch(text, ' ', true, textArea->cursorLocation());
+    const char * cursorLocation = textArea->cursorLocation();
+    const char * firstNonSpace = UTF8Helper::NotCodePointSearch(text, ' ', true, cursorLocation);
    assert(firstNonSpace >= text);
-    if (UTF8Helper::CodePointIs(firstNonSpace, '\n') && ((text - firstNonSpace)/UTF8Decoder::CharSizeOfCodePoint(' ')) >= k_indentationSpacesNumber) {
+    bool cursorIsPrecededOnTheLineBySpacesOnly = false;
+    size_t numberOfSpaces = cursorLocation - firstNonSpace;
+    if (UTF8Helper::CodePointIs(firstNonSpace, '\n')) {
+      cursorIsPrecededOnTheLineBySpacesOnly = true;
+      numberOfSpaces -= UTF8Decoder::CharSizeOfCodePoint('\n');
+    } else if (firstNonSpace == text) {
+      cursorIsPrecededOnTheLineBySpacesOnly = true;
+    }
+    numberOfSpaces = numberOfSpaces / UTF8Decoder::CharSizeOfCodePoint(' ');
+    if (cursorIsPrecededOnTheLineBySpacesOnly && numberOfSpaces >= k_indentationSpacesNumber) {
      for (int i = 0; i < k_indentationSpacesNumber; i++) {
        textArea->removeCodePoint();
      }
--- a/apps/code/python_toolbox.cpp
+++ b/apps/code/python_toolbox.cpp
@@ -95,7 +95,7 @@ const ToolboxMessageTree MathModuleChildren[] = {
 const ToolboxMessageTree KandinskyModuleChildren[] = {
  ToolboxMessageTree::Leaf(I18n::Message::PythonCommandImportKandinsky, I18n::Message::PythonImportKandinsky, false),
  ToolboxMessageTree::Leaf(I18n::Message::PythonCommandImportFromKandinsky, I18n::Message::PythonImportFromKandinsky, false),
-  ToolboxMessageTree::Leaf(I18n::Message::PythonCommandKandinskyFunction, I18n::Message::PythonKandinskyFunction, false),
+  ToolboxMessageTree::Leaf(I18n::Message::PythonCommandKandinskyFunction, I18n::Message::PythonKandinskyFunction, false, I18n::Message::PythonCommandKandinskyFunctionWithoutArg),
  ToolboxMessageTree::Leaf(I18n::Message::PythonCommandGetPixel, I18n::Message::PythonGetPixel),
  ToolboxMessageTree::Leaf(I18n::Message::PythonCommandSetPixel, I18n::Message::PythonSetPixel),
  ToolboxMessageTree::Leaf(I18n::Message::PythonCommandColor, I18n::Message::PythonColor),
--- a/apps/graph/base.de.i18n
+++ b/apps/graph/base.de.i18n
@@ -1,8 +1,8 @@
 FunctionApp = "Funktionen"
 FunctionAppCapital = "FUNKTIONEN"
 FunctionTab = "Funktionen"
-AddFunction = "Funktion hinzufuegen"
-DeleteFunction = "Funktion loeschen"
+AddFunction = "Funktion hinzufügen"
+DeleteFunction = "Funktion löschen"
 FunctionColor = "Farbe der Funktion"
 NoFunction = "Keine Funktion"
 NoActivatedFunction = "Keine aktive Funktion"
--- a/apps/on_boarding/base.de.i18n
+++ b/apps/on_boarding/base.de.i18n
@@ -1,6 +1,6 @@
-UpdateAvailable = "UPDATE VERFUEGBAR"
-UpdateMessage1 = "Wichtige Verbesserungen fuer Ihren"
-UpdateMessage2 = "Rechner stehen zur Verfuegung."
+UpdateAvailable = "UPDATE VERFÜGBAR"
+UpdateMessage1 = "Wichtige Verbesserungen für Ihren"
+UpdateMessage2 = "Rechner stehen zur Verfügung."
 UpdateMessage3 = "Verbinden Sie sich mit Ihrem Computer auf"
 UpdateMessage4 = "www.numworks.com/update."
 BetaVersion = "BETA VERSION"
@@ -10,4 +10,4 @@ BetaVersionMessage3 = "You might run into bugs or glitches."
 BetaVersionMessage4 = ""
 BetaVersionMessage5 = "Please send any feedback to"
 BetaVersionMessage6 = "contact@numworks.com"
-Skip = "Ueberspringen"
+Skip = "Überspringen"
--- a/apps/probability/base.de.i18n
+++ b/apps/probability/base.de.i18n
@@ -1,6 +1,6 @@
 ProbaApp = "Wahrsch."
 ProbaAppCapital = "WAHRSCHEINLICHKEIT"
-ChooseLaw = "Waehlen Sie eine Verteilung"
+ChooseLaw = "Wählen Sie eine Verteilung"
 Binomial = "Binomial"
 Uniforme = "Uniform"
 Normal = "Normal"
@@ -10,7 +10,7 @@ UniformLaw = "Uniformverteilung"
 ExponentialLaw = "Exponentialverteilung"
 NormalLaw = "Normalverteilung"
 PoissonLaw = "Poisson-Verteilung"
-ChooseParameters = "Parameter auswaehlen"
+ChooseParameters = "Parameter auswählen"
 RepetitionNumber = "n: Anzahl der Versuche"
 SuccessProbability = "p: Erfolgswahrscheinlichkeit"
 IntervalDefinition = "[a,b]: Intervall"
--- a/apps/regression/Makefile
+++ b/apps/regression/Makefile
@@ -13,6 +13,7 @@ app_src += $(addprefix apps/regression/,\
  graph_options_controller.cpp \
  graph_view.cpp \
  initialisation_parameter_controller.cpp \
+  linear_model_helper.cpp \
  regression_context.cpp \
  regression_controller.cpp \
  store.cpp \
--- a/apps/regression/linear_model_helper.cpp
+++ b/apps/regression/linear_model_helper.cpp
@@ -0,0 +1,17 @@
+#include "linear_model_helper.h"
+
+namespace Regression {
+
+namespace LinearModelHelper {
+
+double Slope(double covariance, double variance) {
+  return covariance / variance;
+}
+
+double YIntercept(double meanOfY, double meanOfX, double slope) {
+  return meanOfY - slope * meanOfX;
+}
+
+}
+
+}
--- a/apps/regression/linear_model_helper.h
+++ b/apps/regression/linear_model_helper.h
@@ -0,0 +1,15 @@
+#ifndef REGRESSION_LINEAR_MODEL_HELPER
+#define REGRESSION_LINEAR_MODEL_HELPER
+
+namespace Regression {
+
+namespace LinearModelHelper {
+
+double Slope(double covariance, double variance);
+double YIntercept(double meanOfY, double meanOfX, double slope);
+
+}
+
+}
+
+#endif
--- a/apps/regression/model/exponential_model.cpp
+++ b/apps/regression/model/exponential_model.cpp
@@ -1,4 +1,6 @@
 #include "exponential_model.h"
+#include "../store.h"
+#include "../linear_model_helper.h"
 #include <math.h>
 #include <assert.h>
 #include <poincare/code_point_layout.h>
@@ -46,6 +48,45 @@ double ExponentialModel::levelSet(double * modelCoefficients, double xMin, doubl
  return log(y/a)/b;
 }

+void ExponentialModel::fit(Store * store, int series, double * modelCoefficients, Poincare::Context * context) {
+  /* By the change of variable z=ln(y), the equation y=a*exp(b*x) becomes
+   * z=c*x+d with c=b and d=ln(a). Although that change of variable does not
+   * preserve the regression error function, it turns an exponential regression
+   * problem into a linear one and we consider that the solution of the latter
+   * is good enough for our purpose.
+   * That being said, one should check that the y values are all positive. (If
+   * the y values are all negative, one may replace each of them by its
+   * opposite. In the case where y values happen to be zero or of opposite
+   * sign, we call the base class method as a fallback. */
+  double sumOfX = 0;
+  double sumOfY = 0;
+  double sumOfXX = 0;
+  double sumOfXY = 0;
+  const int numberOfPoints = store->numberOfPairsOfSeries(series);
+  const int sign = store->get(series, 1, 0) > 0 ? 1 : -1;
+  for (int p = 0; p < numberOfPoints; p++) {
+    const double x = store->get(series, 0, p);
+    const double z = store->get(series, 1, p) * sign;
+    if (z <= 0) {
+      return Model::fit(store, series, modelCoefficients, context);
+    }
+    const double y = log(z);
+    sumOfX += x;
+    sumOfY += y;
+    sumOfXX += x*x;
+    sumOfXY += x*y;
+  }
+  const double meanOfX = sumOfX / numberOfPoints;
+  const double meanOfY = sumOfY / numberOfPoints;
+  const double meanOfXX = sumOfXX / numberOfPoints;
+  const double meanOfXY = sumOfXY / numberOfPoints;
+  const double variance = meanOfXX - meanOfX * meanOfX;
+  const double covariance = meanOfXY - meanOfX * meanOfY;
+  modelCoefficients[1] = LinearModelHelper::Slope(covariance, variance);
+  modelCoefficients[0] =
+    sign * exp(LinearModelHelper::YIntercept(meanOfY, meanOfX, modelCoefficients[1]));
+}
+
 double ExponentialModel::partialDerivate(double * modelCoefficients, int derivateCoefficientIndex, double x) const {
  double a = modelCoefficients[0];
  double b = modelCoefficients[1];
--- a/apps/regression/model/exponential_model.h
+++ b/apps/regression/model/exponential_model.h
@@ -12,6 +12,7 @@ public:
  I18n::Message formulaMessage() const override { return I18n::Message::ExponentialRegressionFormula; }
  double evaluate(double * modelCoefficients, double x) const override;
  double levelSet(double * modelCoefficients, double xMin, double step, double xMax, double y, Poincare::Context * context) override;
+  void fit(Store * store, int series, double * modelCoefficients, Poincare::Context * context) override;
  double partialDerivate(double * modelCoefficients, int derivateCoefficientIndex, double x) const override;
  int numberOfCoefficients() const override { return 2; }
  int bannerLinesCount() const override { return 2; }
--- a/apps/regression/store.cpp
+++ b/apps/regression/store.cpp
@@ -1,4 +1,5 @@
 #include "store.h"
+#include "linear_model_helper.h"
 #include "apps/apps_container.h"
 #include <poincare/preferences.h>
 #include <assert.h>
@@ -238,11 +239,11 @@ double Store::covariance(int series) const {
 }

 double Store::slope(int series) const {
-  return covariance(series)/varianceOfColumn(series, 0);
+  return LinearModelHelper::Slope(covariance(series), varianceOfColumn(series, 0));
 }

 double Store::yIntercept(int series) const {
-  return meanOfColumn(series, 1) - slope(series)*meanOfColumn(series, 0);
+  return LinearModelHelper::YIntercept(meanOfColumn(series, 1), meanOfColumn(series, 0), slope(series));
 }

 double Store::yValueForXValue(int series, double x, Poincare::Context * globalContext) {
--- a/apps/regression/test/model.cpp
+++ b/apps/regression/test/model.cpp
@@ -76,6 +76,20 @@ QUIZ_CASE(exponential_regression) {
  assert_regression_is(x, y, 6, Model::Type::Exponential, coefficients);
 }

+QUIZ_CASE(exponential_regression2) {
+  double x[] = {0, 1, 2, 3};
+  double y[] = {3000, 3315.513, 3664.208, 4049.576};
+  double coefficients[] = {3000, .1};
+  assert_regression_is(x, y, 4, Model::Type::Exponential, coefficients);
+}
+
+QUIZ_CASE(exponential_regression3) {
+  double x[] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
+  double y[] = {-1, -.3678794, -.1353353, -.04978707, -.01831564, -.006737947, -.002478752, -.000911882, -.0003354626, -.0001234098, -.00004539993};
+  double coefficients[] = {-1, -1};
+  assert_regression_is(x, y, 11, Model::Type::Exponential, coefficients);
+}
+
 QUIZ_CASE(power_regression) {
  double x[] = {1.0, 50.0, 34.0, 67.0, 20.0};
  double y[] = {71.860, 2775514, 979755.1, 6116830, 233832.9};
--- a/apps/sequence/base.de.i18n
+++ b/apps/sequence/base.de.i18n
@@ -1,15 +1,15 @@
 SequenceApp = "Folge"
 SequenceAppCapital = "FOLGE"
 SequenceTab = "Folgen"
-AddSequence = "Folge hinzufuegen"
-ChooseSequenceType = "Das Bildungsgesetz der Folge auswaehlen"
+AddSequence = "Folge hinzufügen"
+ChooseSequenceType = "Das Bildungsgesetz der Folge auswählen"
 SequenceType = "Bildungsgesetz der Folge"
 Explicit = "Explizit"
 SingleRecurrence = "Rekursion 1. Ordnung"
 DoubleRecurrence = "Rekursion 2. Ordnung"
 SequenceOptions = "Optionen der Folge"
 SequenceColor = "Farbe der Folge"
-DeleteSequence = "Folge loeschen"
+DeleteSequence = "Folge löschen"
 NoSequence = "Keine Folge"
 NoActivatedSequence = "Keine aktive Folge"
 NStart = "Startwert"
--- a/apps/settings/base.de.i18n
+++ b/apps/settings/base.de.i18n
@@ -4,14 +4,14 @@ AngleUnit = "Winkeleinheit"
 DisplayMode = "Zahlenformat"
 EditionMode = "Eingabe"
 EditionLinear = "Linear "
-Edition2D = "Natuerlich "
+Edition2D = "Natürlich "
 ComplexFormat = "Komplex"
 ExamMode = "Testmodus"
 ActivateExamMode = "Start Testmodus"
 ExamModeActive = "Testmodus: aktiv"
-About = "Ueber"
+About = "Über"
 Degres = "Grad "
-Radian = "Bogenmass "
+Radian = "Bogenmaß "
 Decimal = "Dezimal "
 Scientific = "Wissenschaftlich "
 SignificantFigures = "Signifikante Stellen "
--- a/apps/shared.de.i18n
+++ b/apps/shared.de.i18n
@@ -1,10 +1,10 @@
 ActivateDeactivate = "Aktivieren/Deaktivieren"
 ActiveExamModeMessage1 = "Alle Ihre Daten werden "
-ActiveExamModeMessage2 = "geloescht, wenn Sie den "
+ActiveExamModeMessage2 = "gelöscht, wenn Sie den "
 ActiveExamModeMessage3 = "Testmodus einschalten."
 Axis = "Achsen"
 Cancel = "Abbrechen"
-ClearColumn = "Spalte loeschen"
+ClearColumn = "Spalte löschen"
 ColumnOptions = "Optionen der Spalte"
 CopyColumnInList = "Die Spalte in einer Liste kopieren"
 DataNotSuitable = "Daten nicht geeignet"
@@ -14,10 +14,10 @@ Deg = "gra"
 Deviation = "Varianz"
 DisplayValues = "Werte anzeigen"
 Empty = "Leer"
-ExitExamMode1 = "Moechten Sie den Testmodus "
+ExitExamMode1 = "Möchten Sie den Testmodus "
 ExitExamMode2 = "verlassen?"
 Exponential = "Exponentielle"
-FillWithFormula = "Mit einer Formel fuellen"
+FillWithFormula = "Mit einer Formel füllen"
 ForbiddenValue = "Verbotener Wert"
 FunctionColumn = "0(0) Spalte"
 FunctionOptions = "Funktionsoptionen"
@@ -25,22 +25,22 @@ Goto = "Gehe zu"
 GraphTab = "Graph"
 HardwareTestLaunch1 = "Sie sind dabei den Hardwaretest zu"
 HardwareTestLaunch2 = "starten. Um ihn wieder zu verlassen,"
-HardwareTestLaunch3 = "muessen Sie einen Reset durchfuhren,"
-HardwareTestLaunch4 = "der Ihre Daten loeschen wird."
+HardwareTestLaunch3 = "müssen Sie einen Reset durchfuhren,"
+HardwareTestLaunch4 = "der Ihre Daten löschen wird."
 Initialization = "Initialisierung"
 IntervalSet = "Intervall einstellen"
 Language = "Sprache"
-LowBattery = "Batterie erschoepft"
+LowBattery = "Batterie erschöpft"
 Mean = "Mittelwert"
 Move = " Verschieben: "
 NameCannotStartWithNumber = "Ein Name darf nicht mit einer Zahl beginnen"
 NameTaken = "Dieser Name ist bereits vergeben"
 NameTooLong = "Der Name ist zu lang"
-Next = "Naechste"
+Next = "Nächste"
 NoDataToPlot = "Keine Daten zum Zeichnen"
-NoFunctionToDelete = "Keine Funktion zum Loeschen"
-NoValueToCompute = "Keine Groesse zum Berechnen"
-Ok = "Bestaetigen"
+NoFunctionToDelete = "Keine Funktion zum Löschen"
+NoValueToCompute = "Keine Größe zum Berechnen"
+Ok = "Bestätigen"
 Or = " oder "
 Orthonormal = "Orthonormal"
 Plot = "Graphen zeichnen"
--- a/apps/solver/base.de.i18n
+++ b/apps/solver/base.de.i18n
@@ -1,25 +1,25 @@
 SolverApp = "Gleichungen"
 SolverAppCapital = "GLEICHUNGEN"
-AddEquation = "Gleichung hinzufuegen"
-ResolveEquation = "Loesen der Gleichung"
-ResolveSystem = "Loesen des Gleichungssystems"
+AddEquation = "Gleichung hinzufügen"
+ResolveEquation = "Lösen der Gleichung"
+ResolveSystem = "Lösen des Gleichungssystems"
 UseEquationModel = "Verwenden Sie ein Gleichungsmodell"
 RequireEquation = "Die Eingabe muss eine Gleichung sein"
 UndefinedEquation = "Nicht definierte Gleichung"
 UnrealEquation = "Nicht reelle Gleichung"
 TooManyVariables = "Es gibt zu viele Unbekannte"
 NonLinearSystem = "Das System ist nicht linear"
-Solution = "Loesung"
-ApproximateSolution = "Ungefaehre Loesung"
-SearchInverval = "Loesungssuche Intervall"
-NoSolutionSystem = "Das System hat keine Loesung"
-NoSolutionEquation = "Die Gleichung hat keine Loesung"
-NoSolutionInterval = "Keine Loesung im Intervall gefunden"
+Solution = "Lösung"
+ApproximateSolution = "Ungefähre Lösung"
+SearchInverval = "Lösungssuche Intervall"
+NoSolutionSystem = "Das System hat keine Lösung"
+NoSolutionEquation = "Die Gleichung hat keine Lösung"
+NoSolutionInterval = "Keine Lösung im Intervall gefunden"
 EnterEquation = "Geben Sie eine Gleichung ein"
-InfiniteNumberOfSolutions = "Es gibt unendlich viele Loesungen"
-ApproximateSolutionIntervalInstruction0= "Geben Sie das Intervall fuer die Suche"
-ApproximateSolutionIntervalInstruction1= "nach einer ungefaehren Loesung ein"
+InfiniteNumberOfSolutions = "Es gibt unendlich viele Lösungen"
+ApproximateSolutionIntervalInstruction0= "Geben Sie das Intervall für die Suche"
+ApproximateSolutionIntervalInstruction1= "nach einer ungefähren Lösung ein"
 OnlyFirstSolutionsDisplayed0 = "Es werden nur die ersten"
-OnlyFirstSolutionsDisplayed1 = "zehn Loesungen angezeigt."
+OnlyFirstSolutionsDisplayed1 = "zehn Lösungen angezeigt."
 PolynomeHasNoRealSolution0 = "Das Polynom hat"
 PolynomeHasNoRealSolution1 = "keine reelle Nullstelle"
--- a/apps/statistics/base.de.i18n
+++ b/apps/statistics/base.de.i18n
@@ -5,12 +5,12 @@ BoxTab = "Boxplot"
 Values1 = "Werte V1"
 Values2 = "Werte V2"
 Values3 = "Werte V3"
-Sizes1 = "Haeufigkeiten N1"
-Sizes2 = "Haeufigkeiten N2"
-Sizes3 = "Haeufigkeiten N3"
+Sizes1 = "Häufigkeiten N1"
+Sizes2 = "Häufigkeiten N2"
+Sizes3 = "Häufigkeiten N3"
 ImportList = "Laden einer Liste"
 Interval = " Intervall"
-Size = " Haeufigkeit"
+Size = " Häufigkeit"
 Frequency = "Relative"
 HistogramSet = "Einstellung des Histogramms"
 RectangleWidth = "Breite der Rechtecke"
--- a/apps/toolbox.de.i18n
+++ b/apps/toolbox.de.i18n
@@ -19,7 +19,7 @@ Product = "Produkt"
 ComplexAbsoluteValue = "Betrag"
 Agument = "Argument"
 RealPart = "Realteil"
-ImaginaryPart = "Imaginaerteil"
+ImaginaryPart = "Imaginärteil"
 Conjugate = "Konjugiert"
 Combination = "Kombination"
 Permutation = "Permutation"
@@ -31,7 +31,7 @@ Inverse = "Inverse"
 Determinant = "Determinante"
 Transpose = "Transponierte"
 Trace = "Spur"
-Dimension = "Groesse"
+Dimension = "Größe"
 Sort = "Sortieren aufsteigend"
 InvSort = "Sortieren absteigend"
 Maximum = "Maximalwert"
@@ -49,7 +49,7 @@ InverseHyperbolicTangent = "Areatangens hyperbolicus"
 Prediction95 = "Schwankungsbereich 95%"
 Prediction = "Einfacher Schwankungsbereich"
 Confidence = "Konfidenzintervall"
-RandomAndApproximation = "Zufall und Naeherung"
+RandomAndApproximation = "Zufall und Näherung"
 RandomFloat = "Dezimalzahl in [0,1]"
-RandomInteger = "Zufaellige ganze Zahl in [a,b]"
+RandomInteger = "Zufällige ganze Zahl in [a,b]"
 PrimeFactorDecomposition = "Primfaktorzerlegung"
--- a/apps/usb/base.de.i18n
+++ b/apps/usb/base.de.i18n
@@ -1,7 +1,7 @@
 USBConnected = "DER RECHNER IST ANGESCHLOSSEN"
-ConnectedMessage1 = "Um Daten zu uebertragen, verbinden"
+ConnectedMessage1 = "Um Daten zu übertragen, verbinden"
 ConnectedMessage2 = "Sie Sich von Ihrem Computer aus mit"
 ConnectedMessage3 = "workshop.numworks.com."
-ConnectedMessage4 = "Druecken Sie die RETURN-Taste am"
+ConnectedMessage4 = "Drücken Sie die RETURN-Taste am"
 ConnectedMessage5 = "Taschenrechner oder ziehen Sie das Kabel,"
 ConnectedMessage6 = "um die Verbindung zu trennen."
--- a/apps/variables.de.i18n
+++ b/apps/variables.de.i18n
@@ -1,5 +1,5 @@
 Variables = "Variablen"
-Expressions = "Ausdruecke"
+Expressions = "Ausdrücke"
 Functions = "Funktionen"
 EmptyExpressionBox0 = "Sie haben keine Variable definiert."
 EmptyFunctionBox0 = "Sie haben keine Funktion definiert."
--- a/escher/include/escher/layout_field.h
+++ b/escher/include/escher/layout_field.h
@@ -53,7 +53,7 @@ private:
  static_assert(k_maxNumberOfLayouts == TextField::maxBufferSize(), "Maximal number of layouts in a layout field should be equal to max number of char in text field");
  void scrollRightOfLayout(Poincare::Layout layoutR);
  void scrollToBaselinedRect(KDRect rect, KDCoordinate baseline);
-  void insertLayoutAtCursor(Poincare::Layout layoutR, Poincare::Layout pointedLayout, bool forceCursorRightOfLayout = false);
+  void insertLayoutAtCursor(Poincare::Layout layoutR, Poincare::Expression correspondingExpression, bool forceCursorRightOfLayout = false);

  class ContentView : public View {
  public:
--- a/escher/src/layout_field.cpp
+++ b/escher/src/layout_field.cpp
@@ -1,5 +1,4 @@
 #include <escher/layout_field.h>
-#include <apps/i18n.h>
 #include <escher/clipboard.h>
 #include <escher/text_field.h>
 #include <poincare/expression.h>
@@ -91,6 +90,10 @@ void LayoutField::reload(KDSize previousSize) {
 }

 bool LayoutField::handleEventWithText(const char * text, bool indentation, bool forceCursorRightOfText) {
+  /* The text here can be:
+   * - the result of a key pressed, such as "," or "cos(•)"
+   * - the text added after a toolbox selection
+   * - the result of a copy-paste. */
  if (text[0] == 0) {
    // The text is empty
    return true;
@@ -122,31 +125,18 @@ bool LayoutField::handleEventWithText(const char * text, bool indentation, bool
  } else {
    Expression resultExpression = Expression::Parse(text);
    if (resultExpression.isUninitialized()) {
+      // The text is not parsable (for instance, ",") and is added char by char.
      KDSize previousLayoutSize = minimalSizeForOptimalDisplay();
      m_contentView.cursor()->insertText(text);
      reload(previousLayoutSize);
-    } else {
-      Layout resultLayout = resultExpression.createLayout(Poincare::Preferences::sharedPreferences()->displayMode(), Poincare::PrintFloat::k_numberOfStoredSignificantDigits);
-      if (currentNumberOfLayouts + resultLayout.numberOfDescendants(true) >= k_maxNumberOfLayouts) {
-        return true;
-      }
-      // Find the pointed layout.
-      Layout pointedLayout;
-      if (!forceCursorRightOfText) {
-        if (strcmp(text, I18n::translate(I18n::Message::RandomCommandWithArg)) == 0) {
-          /* Special case: if the text is "random()", the cursor should not be set
-           * inside the parentheses. */
-          pointedLayout = resultLayout;
-        } else if (resultLayout.type() == LayoutNode::Type::HorizontalLayout) {
-          pointedLayout = resultLayout.recursivelyMatches(
-              [](Poincare::Layout layout) {
-              return layout.type() == LayoutNode::Type::LeftParenthesisLayout || layout.isEmpty();});
-        }
-      }
-      /* Insert the layout. If pointedLayout is uninitialized, the cursor will
-       * be on the right of the inserted layout. */
-      insertLayoutAtCursor(resultLayout, pointedLayout, forceCursorRightOfText);
+      return true;
    }
+    // The text is parsable, we create its layout an insert it.
+    Layout resultLayout = resultExpression.createLayout(Poincare::Preferences::sharedPreferences()->displayMode(), Poincare::PrintFloat::k_numberOfStoredSignificantDigits);
+    if (currentNumberOfLayouts + resultLayout.numberOfDescendants(true) >= k_maxNumberOfLayouts) {
+      return true;
+    }
+    insertLayoutAtCursor(resultLayout, resultExpression, forceCursorRightOfText);
  }
  return true;
 }
@@ -285,42 +275,44 @@ void LayoutField::scrollToBaselinedRect(KDRect rect, KDCoordinate baseline) {
  scrollToContentRect(balancedRect, true);
 }

-void LayoutField::insertLayoutAtCursor(Layout layoutR, Layout pointedLayoutR, bool forceCursorRightOfLayout) {
+void LayoutField::insertLayoutAtCursor(Layout layoutR, Poincare::Expression correspondingExpression, bool forceCursorRightOfLayout) {
  if (layoutR.isUninitialized()) {
    return;
  }

  KDSize previousSize = minimalSizeForOptimalDisplay();
+  Poincare::LayoutCursor * cursor = m_contentView.cursor();

  // Handle empty layouts
-  m_contentView.cursor()->showEmptyLayoutIfNeeded();
+  cursor->showEmptyLayoutIfNeeded();

  bool layoutWillBeMerged = layoutR.type() == LayoutNode::Type::HorizontalLayout;
  Layout lastMergedLayoutChild = layoutWillBeMerged ? layoutR.childAtIndex(layoutR.numberOfChildren()-1) : Layout();

-  // Add the layout
-  m_contentView.cursor()->addLayoutAndMoveCursor(layoutR);
+  // Find the layout where the cursor will point
+  assert(!correspondingExpression.isUninitialized());
+  Layout cursorLayout = forceCursorRightOfLayout ? layoutR : layoutR.layoutToPointWhenInserting(&correspondingExpression);
+  assert(!cursorLayout.isUninitialized());

-  // Move the cursor if needed
-  if(!forceCursorRightOfLayout) {
-    if (!pointedLayoutR.isUninitialized() && (!layoutWillBeMerged || pointedLayoutR != layoutR)) {
-      // Make sure the layout was inserted (its parent is not uninitialized)
-      m_contentView.cursor()->setLayout(pointedLayoutR);
-      m_contentView.cursor()->setPosition(LayoutCursor::Position::Right);
-    } else if (!layoutWillBeMerged) {
-      m_contentView.cursor()->setLayout(layoutR.layoutToPointWhenInserting());
-      m_contentView.cursor()->setPosition(LayoutCursor::Position::Right);
-    }
-  } else if (!layoutWillBeMerged) {
-    m_contentView.cursor()->setLayout(layoutR);
-    m_contentView.cursor()->setPosition(LayoutCursor::Position::Right);
+  // Add the layout. This puts the cursor at the right of the added layout
+  cursor->addLayoutAndMoveCursor(layoutR);
+
+  /* Move the cursor if needed.
+   * If the layout to point to has been merged, it means that only its children
+   * have been inserted in the layout, so we must not move the cursor to the
+   * parent. In this case, addLayoutAndMoveCursor made the cursor point to the
+   * last merged child, which is what is wanted.
+   * For other cases, move the cursor to the computed layout. */
+  if (!(layoutWillBeMerged && cursorLayout == layoutR)) {
+    cursor->setLayout(cursorLayout);
+    cursor->setPosition(LayoutCursor::Position::Right);
  }

  // Handle matrices
-  m_contentView.cursor()->layoutReference().addGreySquaresToAllMatrixAncestors();
+  cursor->layoutReference().addGreySquaresToAllMatrixAncestors();

  // Handle empty layouts
-  m_contentView.cursor()->hideEmptyLayoutIfNeeded();
+  cursor->hideEmptyLayoutIfNeeded();

  // Reload
  reload(previousSize);
--- a/ion/include/ion/keyboard/layout_B2/layout_events.h
+++ b/ion/include/ion/keyboard/layout_B2/layout_events.h
@@ -24,7 +24,7 @@ static constexpr EventData s_dataForEvent[4*Event::PageSize] = {
  U(), U(), U(), U(), U(), U(),
  U(), U(), TL(), TL(), TL(), TL(),
  T("["), T("]"), T("{"), T("}"), T("_"), T("→"),
-  T("arcsin(\x11)"), T("arccos(\x11)"), T("arctan(\x11)"), T("="), T("<"), T(">"),
+  T("asin(\x11)"), T("acos(\x11)"), T("atan(\x11)"), T("="), T("<"), T(">"),
  U(), U(), U(), U(), U(), U(),
  U(), U(), U(), U(), U(), U(),
  U(), U(), U(), U(), U(), U(),
--- a/ion/include/ion/keyboard/layout_B3/layout_events.h
+++ b/ion/include/ion/keyboard/layout_B3/layout_events.h
@@ -24,7 +24,7 @@ static constexpr EventData s_dataForEvent[4*Event::PageSize] = {
  U(), U(), U(), U(), U(), U(),
  U(), U(), TL(), TL(), TL(), TL(),
  T("["), T("]"), T("{"), T("}"), T("_"), T("→"),
-  T("arcsin(\x11)"), T("arccos(\x11)"), T("arctan(\x11)"), T("="), T("<"), T(">"),
+  T("asin(\x11)"), T("acos(\x11)"), T("atan(\x11)"), T("="), T("<"), T(">"),
  U(), U(), U(), U(), U(), U(),
  U(), U(), U(), U(), U(), U(),
  U(), U(), U(), U(), U(), U(),
--- a/kandinsky/Makefile
+++ b/kandinsky/Makefile
@@ -16,8 +16,8 @@ src += $(addprefix kandinsky/src/,\
 )

 src += $(addprefix kandinsky/fonts/, \
-  LargeSourcePixel.ttf \
-  SmallSourcePixel.ttf \
+  LargeFont.ttf \
+  SmallFont.ttf \
 )

 tests += $(addprefix kandinsky/test/,\
@@ -26,13 +26,13 @@ tests += $(addprefix kandinsky/test/,\
  rect.cpp\
 )

-RASTERIZER_CFLAGS := -std=c99 `pkg-config freetype2 --cflags`
-RASTERIZER_LDFLAGS := `pkg-config freetype2 --libs`
+RASTERIZER_CFLAGS := -std=c99 $(shell pkg-config freetype2 --cflags)
+RASTERIZER_LDFLAGS := $(shell pkg-config freetype2 --libs)

-ifdef LIBPNG_PATH
-  small_font_files += kandinsky/src/small_font.png
-  large_font_files += kandinsky/src/large_font.png
-  RASTERIZER_CFLAGS += -I$(LIBPNG_PATH)/include -DGENERATE_PNG=1 -L$(LIBPNG_PATH)/lib -lpng
+HAS_LIBPNG := $(shell pkg-config libpng --exists && echo 1)
+ifeq ($(HAS_LIBPNG),1)
+  RASTERIZER_CFLAGS += $(shell pkg-config libpng --cflags) -DGENERATE_PNG=1
+  RASTERIZER_LDFLAGS += $(shell pkg-config libpng --libs)
 endif

 $(eval $(call rule_for, \
@@ -44,16 +44,15 @@ $(eval $(call rule_for, \

 RASTERIZER := $(BUILD_DIR)/kandinsky/fonts/rasterizer

-$(eval $(call rule_for, \
+# Define a rasterizing recipe. Parameters : font name, size, packed_width, packed_height
+define raster_font
+$(call rule_for, \
  RASTER, \
-  kandinsky/fonts/SmallSourcePixel.cpp, \
-  kandinsky/fonts/SmallSourcePixel.otf $$(RASTERIZER), \
-  $$(RASTERIZER) $$< 12 12 SmallFont $$@ \
-))
+  kandinsky/fonts/$(1).cpp, \
+  kandinsky/fonts/$(1).ttf $$(RASTERIZER), \
+  $$(RASTERIZER) $$< $(2) $(2) $(3) $(4) $(1) $$@ $(if $(HAS_LIBPNG),$$(basename $$@).png) \
+)
+endef

-$(eval $(call rule_for, \
-  RASTER, \
-  kandinsky/fonts/LargeSourcePixel.cpp, \
-  kandinsky/fonts/LargeSourcePixel.otf $$(RASTERIZER), \
-  $$(RASTERIZER) $$< 16 16 LargeFont $$@ \
-))
+$(eval $(call raster_font,SmallFont,12,7,14))
+$(eval $(call raster_font,LargeFont,16,10,18))
--- a/kandinsky/fonts/LargeFont.ttf
+++ b/kandinsky/fonts/LargeFont.ttf
--- a/kandinsky/fonts/LargeSourcePixel.otf
+++ b/kandinsky/fonts/LargeSourcePixel.otf
--- a/kandinsky/fonts/SmallFont.ttf
+++ b/kandinsky/fonts/SmallFont.ttf
--- a/kandinsky/fonts/SmallSourcePixel.otf
+++ b/kandinsky/fonts/SmallSourcePixel.otf
--- a/kandinsky/fonts/rasterizer.c
+++ b/kandinsky/fonts/rasterizer.c
@@ -36,6 +36,7 @@ typedef struct {
 } image_t;

 #ifdef GENERATE_PNG
+#define PNG_SKIP_SETJMP_CHECK
 #include <png.h>
 void writeImageToPNGFile(image_t * image, char * filename);
 #endif
@@ -48,9 +49,9 @@ int main(int argc, char * argv[]) {
  FT_Face face;
  image_t bitmap_image;

-  int expectedNumberOfArguments = 6;
+  int expectedNumberOfArguments = 8;
 #ifdef GENERATE_PNG
-  expectedNumberOfArguments = 7;
+  expectedNumberOfArguments = 9;
 #endif
  if (argc != expectedNumberOfArguments) {
 #ifdef GENERATE_PNG
@@ -61,6 +62,8 @@ int main(int argc, char * argv[]) {
    fprintf(stderr, "  font_file: Path of the font file to load\n");
    fprintf(stderr, "  glyph_width: Width of bitmap glyphs, in pixels\n");
    fprintf(stderr, "  glyph_height: Height of bitmap glyphs, in pixels\n");
+    fprintf(stderr, "  packed_glyph_width: Minimal glyph width in pixels. Pass 0 if unsure.\n");
+    fprintf(stderr, "  packed_glyph_height: Minimal glyph height in pixels. Pass 0 if unsure.\n");
    fprintf(stderr, "  font_name: name of the loaded font\n");
    fprintf(stderr, "  output_cpp: Name of the generated C source file\n");
 #ifdef GENERATE_PNG
@@ -72,10 +75,12 @@ int main(int argc, char * argv[]) {
  char * font_file = argv[1];
  int requested_glyph_width = atoi(argv[2]);
  int requested_glyph_height = atoi(argv[3]);
-  char * font_name = argv[4];
-  char * output_cpp = argv[5];
+  int packed_glyph_width = atoi(argv[4]);
+  int packed_glyph_height = atoi(argv[5]);
+  char * font_name = argv[6];
+  char * output_cpp = argv[7];
 #ifdef GENERATE_PNG
-  char * output_png = argv[6];
+  char * output_png = argv[8];
 #endif

  ENSURE(!FT_Init_FreeType(&library), "Initializing library");
@@ -108,11 +113,21 @@ int main(int argc, char * argv[]) {
    if (belowBaseline > maxBelowBaseline) {
      maxBelowBaseline = belowBaseline;
    }
+    // printf("Codepoint %04x : %dx%d\n", codePoint, width, aboveBaseline+belowBaseline);
  }

  int glyph_width = maxWidth-1;
+  if (packed_glyph_width != 0) {
+    ENSURE(glyph_width == packed_glyph_width, "Expecting a packed glyph width of %d but got %d instead", packed_glyph_width, glyph_width);
+  } else {
+    printf("Computed packed_glyph_width = %d\n", glyph_width);
+  }
  int glyph_height = maxAboveBaseline+maxBelowBaseline;
-  //printf("Actual glyph size = %dx%d\n", glyph_width, glyph_height);
+  if (packed_glyph_height != 0) {
+    ENSURE(glyph_height == packed_glyph_height, "Expecting a packed glyph height of %d but got %d instead", packed_glyph_height, glyph_height);
+  } else {
+    printf("Computed packed_glyph_height = %d\n", glyph_height);
+  }

  int grid_size = 1;
  int grid_width = 20;
@@ -192,6 +207,7 @@ int main(int argc, char * argv[]) {
  int greyscaleBitsPerPixel = 4;

  int sizeOfUncompressedGlyphBuffer = glyph_width * glyph_height * greyscaleBitsPerPixel/8;
+  ENSURE(8*sizeOfUncompressedGlyphBuffer == glyph_width * glyph_height * greyscaleBitsPerPixel, "Error: the glyph size (%dx%d@%dbpp) cannot fit in an integral number of bytes", glyph_width, glyph_height, greyscaleBitsPerPixel);
  uint8_t * uncompressedGlyphBuffer = (uint8_t *)malloc(sizeOfUncompressedGlyphBuffer);

  uint16_t glyphDataOffset[NumberOfCodePoints+1];
@@ -218,8 +234,8 @@ int main(int argc, char * argv[]) {
        }
      }
    }
-    ENSURE(accumulator == 0, "Discarded accumulator data");
-    ENSURE(numberOfValuesAccumulated == 0, "Discarded accumulator data");
+    ENSURE(accumulator == 0, "Discarded accumulator data (accumulator = %d)", accumulator);
+    ENSURE(numberOfValuesAccumulated == 0, "Discarded accumulator data (numberOfValuesAccumulated = %d)", numberOfValuesAccumulated);
    ENSURE(uncompressedGlyphBufferIndex == sizeOfUncompressedGlyphBuffer, "Error filling uncompressed buffer, only %d out of %d", uncompressedGlyphBufferIndex, sizeOfUncompressedGlyphBuffer);

    int sizeOfCompressedGlyphBuffer = LZ4_compress_HC(
--- a/kandinsky/include/kandinsky/font.h
+++ b/kandinsky/include/kandinsky/font.h
@@ -26,6 +26,7 @@
 class KDFont {
 private:
  static constexpr int k_bitsPerPixel = 4; // TODO: Should be generated by the rasterizer
+  static constexpr int k_maxGlyphPixelCount = 180; //TODO: Should be generated by the rasterizer
  static const KDFont privateLargeFont;
  static const KDFont privateSmallFont;
 public:
@@ -44,7 +45,6 @@ public:
    uint8_t * greyscaleBuffer() { return m_greyscales; }
    uint8_t * secondaryGreyscaleBuffer() { return m_greyscales + k_maxGlyphPixelCount; }
  private:
-    static constexpr int k_maxGlyphPixelCount = 180; //TODO: Should be generated by the rasterizer
    uint8_t m_greyscales[2*k_maxGlyphPixelCount];
    KDColor m_colors[k_maxGlyphPixelCount];
  };
--- a/poincare/Makefile
+++ b/poincare/Makefile
@@ -159,6 +159,7 @@ tests += $(addprefix poincare/test/,\
  infinity.cpp\
  integer.cpp\
  layouts.cpp\
+  layout_cursor.cpp\
  logarithm.cpp\
  matrix.cpp\
  multiplication.cpp\
--- a/poincare/include/poincare/condensed_sum_layout.h
+++ b/poincare/include/poincare/condensed_sum_layout.h
@@ -26,9 +26,9 @@ public:
    return SerializationHelper::Prefix(this, buffer, bufferSize, floatDisplayMode, numberOfSignificantDigits, Sum::s_functionHelper.name());
  }

-  LayoutNode * layoutToPointWhenInserting() override {
+  LayoutNode * layoutToPointWhenInserting(Expression * correspondingExpression) override {
    assert(false);
-    return nullptr;
+    return this;
  }

  // TreeNode
--- a/poincare/include/poincare/fraction_layout.h
+++ b/poincare/include/poincare/fraction_layout.h
@@ -27,7 +27,7 @@ public:
  int leftCollapsingAbsorbingChildIndex() const override { return 0; }
  int rightCollapsingAbsorbingChildIndex() const override { return 1; }
  void didCollapseSiblings(LayoutCursor * cursor) override;
-  LayoutNode * layoutToPointWhenInserting() override;
+  LayoutNode * layoutToPointWhenInserting(Expression * correspondingExpression) override;
  bool canBeOmittedMultiplicationRightFactor() const override { return false; }
  /* WARNING: We need to override this function, else 1/2 3/4 would be
   * serialized as 1/2**3/4, as the two Fraction layouts think their sibling is
--- a/poincare/include/poincare/horizontal_layout.h
+++ b/poincare/include/poincare/horizontal_layout.h
@@ -26,6 +26,7 @@ public:
  void moveCursorRight(LayoutCursor * cursor, bool * shouldRecomputeLayout) override;
  LayoutCursor equivalentCursor(LayoutCursor * cursor) override;
  void deleteBeforeCursor(LayoutCursor * cursor) override;
+  LayoutNode * layoutToPointWhenInserting(Expression * correspondingExpression) override;
  int serialize(char * buffer, int bufferSize, Preferences::PrintFloatMode floatDisplayMode, int numberOfSignificantDigits) const override;

  bool isEmpty() const override { return m_numberOfChildren == 1 && const_cast<HorizontalLayoutNode *>(this)->childAtIndex(0)->isEmpty(); }
--- a/poincare/include/poincare/integral.h
+++ b/poincare/include/poincare/integral.h
@@ -41,7 +41,7 @@ private:
    T integral;
    T absoluteError;
  };
-  constexpr static int k_maxNumberOfIterations = 10;
+  constexpr static int k_maxNumberOfIterations = 20;
 #ifdef LAGRANGE_METHOD
  template<typename T> T lagrangeGaussQuadrature(T a, T b, Context Context & context, Preferences::AngleUnit angleUnit context, Preferences::ComplexFormat complexFormat, Preferences::AngleUnit angleUnit) const;
 #else
--- a/poincare/include/poincare/integral_layout.h
+++ b/poincare/include/poincare/integral_layout.h
@@ -24,7 +24,7 @@ public:
  void moveCursorDown(LayoutCursor * cursor, bool * shouldRecomputeLayout, bool equivalentPositionVisited = false) override;
  void deleteBeforeCursor(LayoutCursor * cursor) override;
  int serialize(char * buffer, int bufferSize, Preferences::PrintFloatMode floatDisplayMode, int numberOfSignificantDigits) const override;
-  LayoutNode * layoutToPointWhenInserting() override { return lowerBoundLayout(); }
+  LayoutNode * layoutToPointWhenInserting(Expression * correspondingExpression) override { return lowerBoundLayout(); }
  CodePoint XNTCodePoint() const override { return 'x'; }

  // TreeNode
--- a/poincare/include/poincare/layout.h
+++ b/poincare/include/poincare/layout.h
@@ -8,6 +8,7 @@
 namespace Poincare {

 class LayoutCursor;
+class Expression;

 class Layout : public TreeHandle {
  friend class GridLayoutNode;
@@ -59,7 +60,11 @@ public:
  void deleteBeforeCursor(LayoutCursor * cursor) { return node()->deleteBeforeCursor(cursor); }
  bool removeGreySquaresFromAllMatrixAncestors() { return node()->removeGreySquaresFromAllMatrixAncestors(); }
  bool addGreySquaresToAllMatrixAncestors() { return node()->addGreySquaresToAllMatrixAncestors(); }
-  Layout layoutToPointWhenInserting() { return Layout(node()->layoutToPointWhenInserting()); }
+  Layout layoutToPointWhenInserting(Expression * correspondingExpression) {
+    // Pointer to correspondingExpr because expression.h includes layout.h
+    assert(correspondingExpression != nullptr);
+    return Layout(node()->layoutToPointWhenInserting(correspondingExpression));
+  }

  // Cursor
  LayoutCursor cursor() const;
--- a/poincare/include/poincare/layout_node.h
+++ b/poincare/include/poincare/layout_node.h
@@ -6,6 +6,7 @@

 namespace Poincare {

+class Expression;
 class LayoutCursor;
 class Layout;

@@ -102,9 +103,7 @@ public:
  virtual void deleteBeforeCursor(LayoutCursor * cursor);

  // Other
-  virtual LayoutNode * layoutToPointWhenInserting() {
-    return numberOfChildren() > 0 ? childAtIndex(0) : this;
-  }
+  virtual LayoutNode * layoutToPointWhenInserting(Expression * correspondingExpression);
  bool removeGreySquaresFromAllMatrixAncestors() { return changeGreySquaresOfAllMatrixAncestors(false); }
  bool addGreySquaresToAllMatrixAncestors() { return changeGreySquaresOfAllMatrixAncestors(true); }
  /* A layout has text if it is not empty and it is not an horizontal layout
--- a/poincare/include/poincare/sequence_layout.h
+++ b/poincare/include/poincare/sequence_layout.h
@@ -19,7 +19,7 @@ public:
  void moveCursorUp(LayoutCursor * cursor, bool * shouldRecomputeLayout, bool equivalentPositionVisited = false) override;
  void moveCursorDown(LayoutCursor * cursor, bool * shouldRecomputeLayout, bool equivalentPositionVisited = false) override;
  void deleteBeforeCursor(LayoutCursor * cursor) override;
-  LayoutNode * layoutToPointWhenInserting() override { return lowerBoundLayout(); }
+  LayoutNode * layoutToPointWhenInserting(Expression * correspondingExpression) override { return lowerBoundLayout(); }
  CodePoint XNTCodePoint() const override { return 'n'; }

  // TreeNode
--- a/poincare/src/arc_cosine.cpp
+++ b/poincare/src/arc_cosine.cpp
@@ -39,7 +39,7 @@ Complex<T> ArcCosineNode::computeOnComplex(const std::complex<T> c, Preferences:
     * this cut. We followed the convention chosen by the lib c++ of llvm on
     * ]-inf+0i, -1+0i[ (warning: acos takes the other side of the cut values on
     * ]-inf-0i, -1-0i[) and choose the values on ]1+0i, +inf+0i[ to comply with
-     * acos(-x) = Pi - acos(x) and tan(arccos(x)) = sqrt(1-x^2)/x. */
+     * acos(-x) = π - acos(x) and tan(acos(x)) = sqrt(1-x^2)/x. */
    if (c.imag() == 0 && c.real() > 1) {
      result.imag(-result.imag()); // other side of the cut
    }
--- a/poincare/src/arc_sine.cpp
+++ b/poincare/src/arc_sine.cpp
@@ -39,7 +39,7 @@ Complex<T> ArcSineNode::computeOnComplex(const std::complex<T> c, Preferences::C
     * this cut. We followed the convention chosen by the lib c++ of llvm on
     * ]-inf+0i, -1+0i[ (warning: asin takes the other side of the cut values on
     * ]-inf-0i, -1-0i[) and choose the values on ]1+0i, +inf+0i[ to comply with
-     * asin(-x) = -asin(x) and tan(arcsin(x)) = x/sqrt(1-x^2). */
+     * asin(-x) = -asin(x) and tan(asin(x)) = x/sqrt(1-x^2). */
    if (c.imag() == 0 && c.real() > 1) {
      result.imag(-result.imag()); // other side of the cut
    }
--- a/poincare/src/arc_tangent.cpp
+++ b/poincare/src/arc_tangent.cpp
@@ -35,7 +35,7 @@ Complex<T> ArcTangentNode::computeOnComplex(const std::complex<T> c, Preferences
     * on this cut. We followed the convention chosen by the lib c++ of llvm on
     * ]-i+0, -i*inf+0[ (warning: atan takes the other side of the cut values on
     * ]-i+0, -i*inf+0[) and choose the values on ]-inf*i, -i[ to comply with
-     * atan(-x) = -atan(x) and sin(arctan(x)) = x/sqrt(1+x^2). */
+     * atan(-x) = -atan(x) and sin(atan(x)) = x/sqrt(1+x^2). */
    if (c.real() == 0 && c.imag() < -1) {
      result.real(-result.real()); // other side of the cut
    }
--- a/poincare/src/complex_cartesian.cpp
+++ b/poincare/src/complex_cartesian.cpp
@@ -140,8 +140,8 @@ Expression ComplexCartesian::argument(Context & context, Preferences::ComplexFor
  Expression a = real();
  Expression b = imag();
  if (!b.isRationalZero()) {
-    // if b != 0, argument = sign(b) * Pi/2 - arctan(a/b)
-    // First, compute arctan(a/b) or (Pi/180)*arctan(a/b)
+    // if b != 0, argument = sign(b) * π/2 - atan(a/b)
+    // First, compute atan(a/b) or (π/180)*atan(a/b)
    Expression divab = Division::Builder(a, b.clone());
    Expression arcTangent = ArcTangent::Builder(divab);
    divab.shallowReduce(context, complexFormat, angleUnit, target);
@@ -150,7 +150,7 @@ Expression ComplexCartesian::argument(Context & context, Preferences::ComplexFor
      arcTangent.shallowReduce(context, complexFormat, angleUnit, target);
      arcTangent = temp;
    }
-    // Then, compute sign(b) * Pi/2 - arctan(a/b)
+    // Then, compute sign(b) * π/2 - atan(a/b)
    Expression signb = SignFunction::Builder(b);
    Expression signbPi2 = Multiplication::Builder(Rational::Builder(1,2), signb, Constant::Builder(UCodePointGreekSmallLetterPi));
    signb.shallowReduce(context, complexFormat, angleUnit, target);
@@ -159,7 +159,7 @@ Expression ComplexCartesian::argument(Context & context, Preferences::ComplexFor
    arcTangent.shallowReduce(context, complexFormat, angleUnit, target);
    return sub;
  } else {
-    // if b == 0, argument = (1-sign(a))*Pi/2
+    // if b == 0, argument = (1-sign(a))*π/2
    Expression signa = SignFunction::Builder(a).shallowReduce(context, complexFormat, angleUnit, target);
    Subtraction sub = Subtraction::Builder(Rational::Builder(1), signa);
    signa.shallowReduce(context, complexFormat, angleUnit, target);
--- a/poincare/src/decimal.cpp
+++ b/poincare/src/decimal.cpp
@@ -287,6 +287,13 @@ Decimal Decimal::Builder(const char * integralPart, int integralPartLength, cons
  }
  //TODO: set a FLAG to tell that a rounding happened?
  bool rounding = integralPartLength > PrintFloat::k_numberOfStoredSignificantDigits && integralPart[PrintFloat::k_numberOfStoredSignificantDigits] >= '5';
+  /* At this point, the exponent has already been computed. In the very special
+   * case where all the significant digits of the mantissa are 9, rounding up
+   * must increment the exponent. For instance, rounding up 0.99...9 (whose
+   * exponent is -1) yields 1 (whose exponent is 0). To that end, the
+   * significant digits will be scanned successively to determine whether the
+   * exponent should be incremented. */
+  bool incrementExponentAfterRoundingUp = true;
  // Cap the length of the integralPart
  integralPartLength = integralPartLength > PrintFloat::k_numberOfStoredSignificantDigits ? PrintFloat::k_numberOfStoredSignificantDigits : integralPartLength;
  Integer numerator(integralPart, integralPartLength, false);
@@ -301,13 +308,22 @@ Decimal Decimal::Builder(const char * integralPart, int integralPartLength, cons
  }
  rounding |= integralPartLength+fractionalPartLength > PrintFloat::k_numberOfStoredSignificantDigits && fractionalPart[PrintFloat::k_numberOfStoredSignificantDigits-integralPartLength] >= '5';
  fractionalPartLength = integralPartLength+fractionalPartLength > PrintFloat::k_numberOfStoredSignificantDigits ? PrintFloat::k_numberOfStoredSignificantDigits - integralPartLength : fractionalPartLength;
+  while (incrementExponentAfterRoundingUp && integralPartLength-- > 0) {
+    incrementExponentAfterRoundingUp = (*(integralPart++) == '9');
+  }
  for (int i = 0; i < fractionalPartLength; i++) {
    numerator = Integer::Multiplication(numerator, base);
    assert(*fractionalPart >= '0' && *fractionalPart <= '9');
    numerator = Integer::Addition(numerator, Integer(*fractionalPart-'0'));
+    incrementExponentAfterRoundingUp &= (*fractionalPart == '9');
    fractionalPart++;
  }
-  numerator = rounding ? Integer::Addition(numerator, Integer(1)) : numerator;
+  if (rounding) {
+    numerator = Integer::Addition(numerator, Integer(1));
+    if (incrementExponentAfterRoundingUp) {
+      exponent++;
+    }
+  }
  exponent = numerator.isZero() ? 0 : exponent;
  return Decimal::Builder(numerator, exponent);
 }
--- a/poincare/src/expression.cpp
+++ b/poincare/src/expression.cpp
@@ -446,7 +446,7 @@ void Expression::simplifyAndApproximate(Expression * simplifiedExpression, Expre
      /* Step 2: Approximation
       * We compute the approximate expression from the Cartesian form to avoid
       * unprecision. For example, if the result is the ComplexCartesian(a,b),
-       * the final expression is goind to be sqrt(a^2+b^2)*exp(i*arctan(b/a)...
+       * the final expression is going to be sqrt(a^2+b^2)*exp(i*atan(b/a)...
       * in Polar ComplexFormat. If we approximate this expression instead of
       * ComplexCartesian(a,b), we are going to loose precision on the resulting
       * complex.*/
--- a/poincare/src/fraction_layout.cpp
+++ b/poincare/src/fraction_layout.cpp
@@ -166,7 +166,7 @@ int FractionLayoutNode::serialize(char * buffer, int bufferSize, Preferences::Pr
  return numberOfChar;
 }

-LayoutNode * FractionLayoutNode::layoutToPointWhenInserting() {
+LayoutNode * FractionLayoutNode::layoutToPointWhenInserting(Expression * correspondingExpression) {
  if (numeratorLayout()->isEmpty()){
    return numeratorLayout();
  }
--- a/poincare/src/horizontal_layout.cpp
+++ b/poincare/src/horizontal_layout.cpp
@@ -164,6 +164,21 @@ void HorizontalLayoutNode::deleteBeforeCursor(LayoutCursor * cursor) {
  LayoutNode::deleteBeforeCursor(cursor);
 }

+LayoutNode * HorizontalLayoutNode::layoutToPointWhenInserting(Expression * correspondingExpression) {
+  assert(correspondingExpression != nullptr);
+  if (correspondingExpression->numberOfChildren() > 0) {
+    Layout layoutToPointTo = Layout(this).recursivelyMatches(
+      [](Poincare::Layout layout) {
+        return layout.type() == LayoutNode::Type::LeftParenthesisLayout || layout.isEmpty();
+      }
+    );
+    if (!layoutToPointTo.isUninitialized()) {
+      return layoutToPointTo.node();
+    }
+  }
+  return this;
+}
+
 int HorizontalLayoutNode::serialize(char * buffer, int bufferSize, Preferences::PrintFloatMode floatDisplayMode, int numberOfSignificantDigits) const {
  if (numberOfChildren() == 0) {
    if (bufferSize == 0) {
--- a/poincare/src/layout_node.cpp
+++ b/poincare/src/layout_node.cpp
@@ -110,6 +110,11 @@ void LayoutNode::deleteBeforeCursor(LayoutCursor * cursor) {
  // WARNING: Do no use "this" afterwards
 }

+LayoutNode * LayoutNode::layoutToPointWhenInserting(Expression * correspondingExpression) {
+  assert(correspondingExpression != nullptr);
+  return numberOfChildren() > 0 ? childAtIndex(0) : this;
+}
+
 bool LayoutNode::willRemoveChild(LayoutNode * l, LayoutCursor * cursor, bool force) {
  if (!force) {
    Layout(this).replaceChildWithEmpty(Layout(l), cursor);
--- a/poincare/src/trigonometry.cpp
+++ b/poincare/src/trigonometry.cpp
@@ -99,14 +99,14 @@ Expression Trigonometry::shallowReduceDirectFunction(Expression & e, Context& co
    return lookup;
  }

-  // Step 2. Look for an expression of type "cos(arccos(x))", return x
+  // Step 2. Look for an expression of type "cos(acos(x))", return x
  if (AreInverseFunctions(e, e.childAtIndex(0))) {
    Expression result = e.childAtIndex(0).childAtIndex(0);
    e.replaceWithInPlace(result);
    return result;
  }

-  // Step 3. Look for an expression of type "cos(arcsin(x))" or "sin(arccos(x)), return sqrt(1-x^2)
+  // Step 3. Look for an expression of type "cos(asin(x))" or "sin(acos(x)), return sqrt(1-x^2)
  // These equalities are true on complexes
  if ((e.type() == ExpressionNode::Type::Cosine && e.childAtIndex(0).type() == ExpressionNode::Type::ArcSine) || (e.type() == ExpressionNode::Type::Sine && e.childAtIndex(0).type() == ExpressionNode::Type::ArcCosine)) {
    Expression sqrt =
@@ -131,9 +131,9 @@ Expression Trigonometry::shallowReduceDirectFunction(Expression & e, Context& co
    return sqrt.shallowReduce(context, complexFormat, angleUnit, target);
  }

-  // Step 4. Look for an expression of type "cos(arctan(x))" or "sin(arctan(x))"
-  // cos(arctan(x)) --> 1/sqrt(1+x^2)
-  // sin(arctan(x)) --> x/sqrt(1+x^2)
+  // Step 4. Look for an expression of type "cos(atan(x))" or "sin(atan(x))"
+  // cos(atan(x)) --> 1/sqrt(1+x^2)
+  // sin(atan(x)) --> x/sqrt(1+x^2)
  // These equalities are true on complexes
  if ((e.type() == ExpressionNode::Type::Cosine || e.type() == ExpressionNode::Type::Sine) && e.childAtIndex(0).type() == ExpressionNode::Type::ArcTangent) {
    Expression x = e.childAtIndex(0).childAtIndex(0);
@@ -252,7 +252,7 @@ Expression Trigonometry::shallowReduceInverseFunction(Expression & e, Context& c
  assert(isInverseTrigonometryFunction(e));
  float pi = angleUnit == Preferences::AngleUnit::Radian ? M_PI : 180;

-  // Step 1. Look for an expression of type "arccos(cos(x))", return x
+  // Step 1. Look for an expression of type "acos(cos(x))", return x
  if (AreInverseFunctions(e.childAtIndex(0), e)) {
    float trigoOp = e.childAtIndex(0).childAtIndex(0).node()->approximate(float(), context, complexFormat, angleUnit).toScalar();
    if ((e.type() == ExpressionNode::Type::ArcCosine && trigoOp >= 0.0f && trigoOp <= pi) ||
@@ -264,7 +264,7 @@ Expression Trigonometry::shallowReduceInverseFunction(Expression & e, Context& c
    }
  }

-  // Step 2. Special case for arctan(sin(x)/cos(x))
+  // Step 2. Special case for atan(sin(x)/cos(x))
  if (e.type() == ExpressionNode::Type::ArcTangent && ExpressionIsEquivalentToTangent(e.childAtIndex(0))) {
    float trigoOp = e.childAtIndex(0).childAtIndex(1).childAtIndex(0).node()->approximate(float(), context, complexFormat, angleUnit).toScalar();
    if (trigoOp >= -pi/2.0f && trigoOp <= pi/2.0f) {
@@ -274,7 +274,7 @@ Expression Trigonometry::shallowReduceInverseFunction(Expression & e, Context& c
    }
  }

-  // Step 3. Look for an expression of type "arctan(1/x), return sign(x)*π/2-arctan(x)
+  // Step 3. Look for an expression of type "atan(1/x), return sign(x)*π/2-atan(x)
  if (e.type() == ExpressionNode::Type::ArcTangent && e.childAtIndex(0).type() == ExpressionNode::Type::Power && e.childAtIndex(0).childAtIndex(1).type() == ExpressionNode::Type::Rational && e.childAtIndex(0).childAtIndex(1).convert<Rational>().isMinusOne()) {
    Expression x = e.childAtIndex(0).childAtIndex(0);
    /* This equality is not true if x = 0. We apply it under certain conditions:
@@ -310,8 +310,8 @@ Expression Trigonometry::shallowReduceInverseFunction(Expression & e, Context& c
   */
  Expression p = e.parent();
  bool letArcFunctionAtRoot = !p.isUninitialized() && isDirectTrigonometryFunction(p);
-  /* Step 5. Handle opposite argument: arccos(-x) = π-arcos(x),
-   * arcsin(-x) = -arcsin(x), arctan(-x)= -arctan(x) *
+  /* Step 5. Handle opposite argument: acos(-x) = π-acos(x),
+   * asin(-x) = -asin(x), atan(-x)= -atan(x) *
   */
  if (!letArcFunctionAtRoot) {
    Expression positiveArg = e.childAtIndex(0).makePositiveAnyNegativeNumeralFactor(context, complexFormat, angleUnit, target);
--- a/poincare/test/helper.cpp
+++ b/poincare/test/helper.cpp
@@ -193,6 +193,11 @@ void assert_parsed_expression_layout_serialize_to_self(const char * expressionLa
  quiz_assert(strcmp(expressionLayout, buffer) == 0);
 }

+void assert_expression_layouts_as(Poincare::Expression expression, Poincare::Layout layout) {
+  Layout l = expression.createLayout(DecimalMode, PrintFloat::k_numberOfStoredSignificantDigits);
+  quiz_assert(l.isIdenticalTo(layout));
+}
+
 void assert_expression_layout_serialize_to(Poincare::Layout layout, const char * serialization) {
  constexpr int bufferSize = 255;
  char buffer[bufferSize];
--- a/poincare/test/helper.h
+++ b/poincare/test/helper.h
@@ -39,6 +39,7 @@ void assert_parsed_expression_approximates_with_value_for_symbol(Poincare::Expre

 void assert_parsed_expression_simplify_to(const char * expression, const char * simplifiedExpression, Poincare::ExpressionNode::ReductionTarget target = Poincare::ExpressionNode::ReductionTarget::User, Poincare::Preferences::AngleUnit angleUnit = Poincare::Preferences::AngleUnit::Radian, Poincare::Preferences::ComplexFormat complexFormat = Poincare::Preferences::ComplexFormat::Cartesian);
 void assert_parsed_expression_serialize_to(Poincare::Expression expression, const char * serializedExpression, Poincare::Preferences::PrintFloatMode mode = DecimalMode, int numberOfSignifiantDigits = 7);
+void assert_expression_layouts_as(Poincare::Expression expression, Poincare::Layout layout);


 // Layouts
--- a/poincare/test/layout_cursor.cpp
+++ b/poincare/test/layout_cursor.cpp
@@ -0,0 +1,74 @@
+#include <quiz.h>
+#include <poincare_layouts.h>
+#include "helper.h"
+
+using namespace Poincare;
+
+void assert_inserted_layout_points_to(Layout layoutToInsert, Expression * correspondingExpression, Layout layoutToPoint) {
+  quiz_assert(correspondingExpression != nullptr);
+  assert_expression_layouts_as(*correspondingExpression, layoutToInsert);
+  Layout layoutToPointComputed = layoutToInsert.layoutToPointWhenInserting(correspondingExpression);
+  quiz_assert(layoutToPointComputed.identifier() == layoutToPoint.identifier());
+}
+
+QUIZ_CASE(poincare_layout_cursor_computation) {
+  Layout l;
+  Expression e;
+
+  // 1+2
+  l = HorizontalLayout::Builder(
+      CodePointLayout::Builder('1'),
+      CodePointLayout::Builder('+'),
+      CodePointLayout::Builder('2'));
+  e = Addition::Builder(Rational::Builder(1), Rational::Builder(2));
+  assert_inserted_layout_points_to(l, &e, l);
+
+  // random()
+  HorizontalLayout hl = HorizontalLayout::Builder();
+  hl.addChildAtIndex(CodePointLayout::Builder('r'), hl.numberOfChildren(),  hl.numberOfChildren(), nullptr);
+  hl.addChildAtIndex(CodePointLayout::Builder('a'), hl.numberOfChildren(),  hl.numberOfChildren(), nullptr);
+  hl.addChildAtIndex(CodePointLayout::Builder('n'), hl.numberOfChildren(),  hl.numberOfChildren(), nullptr);
+  hl.addChildAtIndex(CodePointLayout::Builder('d'), hl.numberOfChildren(),  hl.numberOfChildren(), nullptr);
+  hl.addChildAtIndex(CodePointLayout::Builder('o'), hl.numberOfChildren(),  hl.numberOfChildren(), nullptr);
+  hl.addChildAtIndex(CodePointLayout::Builder('m'), hl.numberOfChildren(),  hl.numberOfChildren(), nullptr);
+  hl.addChildAtIndex(LeftParenthesisLayout::Builder(), hl.numberOfChildren(), hl.numberOfChildren(), nullptr);
+  hl.addChildAtIndex(RightParenthesisLayout::Builder(), hl.numberOfChildren(), hl.numberOfChildren(), nullptr);
+  l = hl;
+  e = Random::Builder();
+  assert_inserted_layout_points_to(l, &e, l);
+
+  // cos(\x11)
+  hl = HorizontalLayout::Builder();
+  hl.addChildAtIndex(CodePointLayout::Builder('c'), hl.numberOfChildren(),  hl.numberOfChildren(), nullptr);
+  hl.addChildAtIndex(CodePointLayout::Builder('o'), hl.numberOfChildren(),  hl.numberOfChildren(), nullptr);
+  hl.addChildAtIndex(CodePointLayout::Builder('s'), hl.numberOfChildren(),  hl.numberOfChildren(), nullptr);
+  hl.addChildAtIndex(LeftParenthesisLayout::Builder(), hl.numberOfChildren(), hl.numberOfChildren(), nullptr);
+  hl.addChildAtIndex(RightParenthesisLayout::Builder(), hl.numberOfChildren(), hl.numberOfChildren(), nullptr);
+  l = hl;
+  e = Cosine::Builder(EmptyExpression::Builder());
+  assert_inserted_layout_points_to(l, &e, l.childAtIndex(3));
+
+  // •^•
+  l = HorizontalLayout::Builder(
+      EmptyLayout::Builder(),
+      VerticalOffsetLayout::Builder(
+        EmptyLayout::Builder(),
+        VerticalOffsetLayoutNode::Position::Superscript)
+      );
+  e = Power::Builder(EmptyExpression::Builder(), EmptyExpression::Builder());
+  assert_inserted_layout_points_to(l, &e, l.childAtIndex(0));
+
+  // int(•, x, •, •)
+  l = IntegralLayout::Builder(
+      EmptyLayout::Builder(),
+      HorizontalLayout::Builder(
+        CodePointLayout::Builder('x')),
+      EmptyLayout::Builder(),
+      EmptyLayout::Builder());
+  e = Integral::Builder(
+      EmptyExpression::Builder(),
+      Symbol::Builder('x'),
+      EmptyExpression::Builder(),
+      EmptyExpression::Builder());
+  assert_inserted_layout_points_to(l, &e, l.childAtIndex(2));
+}
--- a/poincare/test/number.cpp
+++ b/poincare/test/number.cpp
@@ -27,6 +27,12 @@ QUIZ_CASE(poincare_number_parser) {
  assert_parsed_expression_is("123456789012345.2", Decimal::Builder(Integer("12345678901235"), 14));
  assert_parsed_expression_is("123456789012341.2", Decimal::Builder(Integer("12345678901234"), 14));
  assert_parsed_expression_is("12.34567", Decimal::Builder(Integer("1234567"), 1));
+  assert_parsed_expression_is(".999999999999990", Decimal::Builder(Integer("99999999999999"), -1));
+  assert_parsed_expression_is("9.99999999999994", Decimal::Builder(Integer("99999999999999"), 0));
+  assert_parsed_expression_is("99.9999999999995", Decimal::Builder(Integer("100000000000000"), 2));
+  assert_parsed_expression_is("999.999999999999", Decimal::Builder(Integer("100000000000000"), 3));
+  assert_parsed_expression_is("9999.99199999999", Decimal::Builder(Integer("99999920000000"), 3));
+  assert_parsed_expression_is("99299.9999999999", Decimal::Builder(Integer("99300000000000"), 4));

  // Infinity
  assert_parsed_expression_is("23ᴇ1000", Infinity::Builder(false));
--- a/poincare/test/trigo.cpp
+++ b/poincare/test/trigo.cpp
@@ -513,22 +513,22 @@ QUIZ_CASE(poincare_trigo_simplify) {
  assert_parsed_expression_simplify_to("atan(√(3))", "60", User, Degree);
  assert_parsed_expression_simplify_to("atan(1/x)", "(π×sign(x)-2×atan(x))/2", User, Degree);

-  // cos(arcsin)
+  // cos(asin)
  assert_parsed_expression_simplify_to("cos(asin(x))", "√(-x^2+1)", User, Degree);
  assert_parsed_expression_simplify_to("cos(asin(-x))", "√(-x^2+1)", User, Degree);
-  // cos(arctan)
+  // cos(atan)
  assert_parsed_expression_simplify_to("cos(atan(x))", "1/√(x^2+1)", User, Degree);
  assert_parsed_expression_simplify_to("cos(atan(-x))", "1/√(x^2+1)", User, Degree);
-  // sin(arccos)
+  // sin(acos)
  assert_parsed_expression_simplify_to("sin(acos(x))", "√(-x^2+1)", User, Degree);
  assert_parsed_expression_simplify_to("sin(acos(-x))", "√(-x^2+1)", User, Degree);
-  // sin(arctan)
+  // sin(atan)
  assert_parsed_expression_simplify_to("sin(atan(x))", "x/√(x^2+1)", User, Degree);
  assert_parsed_expression_simplify_to("sin(atan(-x))", "-x/√(x^2+1)", User, Degree);
-  // tan(arccos)
+  // tan(acos)
  assert_parsed_expression_simplify_to("tan(acos(x))", "√(-x^2+1)/x", User, Degree);
  assert_parsed_expression_simplify_to("tan(acos(-x))", "-√(-x^2+1)/x", User, Degree);
-  // tan(arcsin)
+  // tan(asin)
  assert_parsed_expression_simplify_to("tan(asin(x))", "x/√(-x^2+1)", User, Degree);
  assert_parsed_expression_simplify_to("tan(asin(-x))", "-x/√(-x^2+1)", User, Degree);
 }