Add exercise 4

ex4/problem1/z2_group_skeleton.cpp

+/* Programming Techniques for Scientific Simulations, HS 2021
+ * Exercise 4.1
+ */
+
+#include <iostream>
+
+enum Z2 { Plus, Minus };
+
+template<class T>
+T identity_element() { return T(1); }
+
+template <>
+Z2 identity_element() {return Plus; }
+
+Z2 operator*(const Z2 a, const Z2 b) {
+  if (a == b) {
+    return Plus;
+  }
+  else {
+    return Minus;
+  }
+}
+
+std::ostream& operator<<(std::ostream& os, const Z2 a) {
+  if (a == Plus) {
+    os << "Plus";
+  }
+  else if (a == Minus) {
+    os << "Minus";
+  }
+  return os;
+}
+
+template<class T>
+T operator*(const T a, const Z2 b) {
+  return b == Plus ? a : -a;
+}
+
+template<class T>
+T operator*(const Z2 b, const T a) {
+  return b == Plus ? a : -a;
+}
+
+template<class T>
+T mypow(T a, const unsigned int n)  {
+  T temp = identity_element<T>();
+  for (unsigned int i = 0; i < n; i++) {
+    temp = temp * a;
+  }
+  return temp;
+}
+
+int main()
+{
+  // some testing: feel free to add your own!
+  std::cout << Plus*Plus << std::endl;
+  std::cout << Plus*Minus << std::endl;
+  std::cout << Plus*-1*Minus << std::endl;
+  std::cout << (1.+3.)*mypow(Minus,4) << std::endl;
+  for (unsigned i=0; i<7; i++)
+    std::cout << "Plus^" << i << " = " << mypow(Plus,i) << std::endl;
+  for (unsigned i=0; i<7; i++)
+    std::cout << "Minus^" << i << " = " << mypow(Minus,i) << std::endl;
+  for (unsigned i=0; i<7; i++)
+    std::cout << "2^" << i << " = " << mypow(2.0,i) << std::endl;
+  return 0;
+}

ex4/problem2/CMakeLists.txt

+# require minimum version of CMake
+cmake_minimum_required(VERSION 3.21) 
+
+# set name of project
+project(Square)
+
+# set warning compile flags
+add_compile_options(-Wall -Wextra -Wpedantic)
+
+# option to build STATIC or SHARED library
+option(BUILD_SQUARE_SHARED "Build the square library shared." OFF)
+if(BUILD_SQUARED_SHARED)
+    set(SQUARE_LIBRARY_TYPE SHARED)
+else()
+    set(SQUARE_LIBRARY_TYPE STATIC)
+endif()
+
+# tell CMake that there is another CMakeLists.txt in this subdirectory
+add_subdirectory(integrator)
+
+# add executable to the project
+add_executable(print_integrals main.cpp)
+
+# specify that we need the library
+target_link_libraries(print_integrals integratorLib)
+
+# specify install rules
+install(TARGETS print_integrals DESTINATION bin)
+
+

ex4/problem2/build/CMakeCache.txt

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