diff --git a/Modelica/Math/FastFourierTransform.mo b/Modelica/Math/FastFourierTransform.mo
index c2e3199bd7..06bab8c20c 100644
--- a/Modelica/Math/FastFourierTransform.mo
+++ b/Modelica/Math/FastFourierTransform.mo
@@ -535,7 +535,7 @@ which is a complete example where an FFT is computed during simulation and store
 </html>"));
   end realFFT;
 
-  function realFFTwriteToFile "Write real FFT computation to file"
+  impure function realFFTwriteToFile "Write real FFT computation to file"
     extends Modelica.Icons.Function;
      import Modelica.Utilities.Streams.print;
      import Modelica.Units.Conversions.to_deg;
diff --git a/Modelica/Math/Nonlinear.mo b/Modelica/Math/Nonlinear.mo
index c827dba958..6de6840f00 100644
--- a/Modelica/Math/Nonlinear.mo
+++ b/Modelica/Math/Nonlinear.mo
@@ -5,7 +5,7 @@ package Nonlinear "Library of functions operating on nonlinear equations"
     "Examples demonstrating the usage of the functions in package Nonlinear"
     extends Modelica.Icons.ExamplesPackage;
 
-    function quadratureLobatto1 "Integrate integral with fixed inputs"
+    impure function quadratureLobatto1 "Integrate integral with fixed inputs"
       extends Modelica.Icons.Function;
       import Modelica.Utilities.Streams.print;
 
@@ -87,7 +87,7 @@ The following integrals are computed:
 </html>"));
     end quadratureLobatto1;
 
-    function quadratureLobatto2 "Integrate integral with user dependent inputs"
+    impure function quadratureLobatto2 "Integrate integral with user dependent inputs"
       extends Modelica.Icons.Function;
       import Modelica.Utilities.Streams.print;
 
@@ -159,7 +159,7 @@ The following integrals are computed:
 </html>"));
     end quadratureLobatto2;
 
-    function solveNonlinearEquations1
+    impure function solveNonlinearEquations1
       "Solve nonlinear equations with fixed inputs"
       extends Modelica.Icons.Function;
       import Modelica.Utilities.Streams.print;
@@ -238,7 +238,7 @@ The following nonlinear equations are solved:
 </html>"));
     end solveNonlinearEquations1;
 
-    function solveNonlinearEquations2
+    impure function solveNonlinearEquations2
       "Solve nonlinear equations with user dependent inputs"
       extends Modelica.Icons.Function;
       import Modelica.Utilities.Streams.print;
diff --git a/Modelica/Math/Random.mo b/Modelica/Math/Random.mo
index f85b660349..6d3774a35b 100644
--- a/Modelica/Math/Random.mo
+++ b/Modelica/Math/Random.mo
@@ -1054,7 +1054,7 @@ path is provided.
 </html>"));
     end automaticLocalSeed;
 
-    function initializeImpureRandom
+    impure function initializeImpureRandom
       "Initializes the internal state of the impure random number generator"
       extends Modelica.Icons.Function;
       input Integer seed
diff --git a/Modelica/Math/package.mo b/Modelica/Math/package.mo
index 6a875a6082..c8ba6d2ae4 100644
--- a/Modelica/Math/package.mo
+++ b/Modelica/Math/package.mo
@@ -694,7 +694,7 @@ package Matrices "Library of functions operating on matrices"
   package Examples
     "Examples demonstrating the usage of the Math.Matrices functions"
     extends Modelica.Icons.ExamplesPackage;
-    function solveLinearEquations
+    impure function solveLinearEquations
       "Demonstrate the solution of linear equation systems"
       extends Modelica.Icons.Function;
       import Modelica.Utilities.Streams.print;
diff --git a/Modelica/Mechanics/MultiBody/Visualizers/Colors/colorMapToSvg.mo b/Modelica/Mechanics/MultiBody/Visualizers/Colors/colorMapToSvg.mo
index 4e8a41ea7f..665e74e232 100644
--- a/Modelica/Mechanics/MultiBody/Visualizers/Colors/colorMapToSvg.mo
+++ b/Modelica/Mechanics/MultiBody/Visualizers/Colors/colorMapToSvg.mo
@@ -1,5 +1,5 @@
 within Modelica.Mechanics.MultiBody.Visualizers.Colors;
-function colorMapToSvg
+impure function colorMapToSvg
   "Save a color map on file in svg (scalable vector graphics) format"
   extends Modelica.Icons.Function;
  encapsulated type HeaderType = enumeration(
diff --git a/ModelicaTest/Math.mo b/ModelicaTest/Math.mo
index 26d07b7cc9..75ddd018a0 100644
--- a/ModelicaTest/Math.mo
+++ b/ModelicaTest/Math.mo
@@ -660,7 +660,7 @@ extends Modelica.Icons.ExamplesPackage;
     ok := true;
   end Vectors;
 
-  function colorMapToSvg "Store all predefined color maps in svg"
+  impure function colorMapToSvg "Store all predefined color maps in svg"
     extends Modelica.Icons.Function;
     import Modelica.Mechanics.MultiBody.Visualizers.Colors.colorMapToSvg;
     import Modelica.Mechanics.MultiBody.Visualizers.Colors.ColorMaps.{jet, hot, gray, spring, summer, autumn, winter};
@@ -762,7 +762,7 @@ extends Modelica.Icons.ExamplesPackage;
 
   model TestMatricesExamplesSolveLinearEquations
     extends Modelica.Icons.Example;
-  equation
+  initial equation
       Modelica.Math.Matrices.Examples.solveLinearEquations();
     annotation (experiment(StopTime=0));
   end TestMatricesExamplesSolveLinearEquations;
diff --git a/ModelicaTest/package.mo b/ModelicaTest/package.mo
index 3f79e3e59f..8f17ff8388 100644
--- a/ModelicaTest/package.mo
+++ b/ModelicaTest/package.mo
@@ -4,7 +4,7 @@ extends Modelica.Icons.Package;
 
   import Modelica.Units.SI;
 
-function testAllFunctions "Runs all test cases for functions"
+impure function testAllFunctions "Runs all test cases for functions"
   extends Modelica.Icons.Function;
   import Modelica.Utilities.Streams.print;
   input String logFile = "ModelicaTestLog.txt"