[MathMore] allow using several methods of Polynomial.h in const context

    - Remove unused `fRoots` data member (it was cleared before each root
      computation and provided no persistent state).
    - Return polynomial roots by value instead of via internal storage.
    - Mark the affected query/utility methods as `const` to make the class
      usable in const contexts.
    - Apply clang-format to the modified sections.

Author: meiyasan

math/mathmore/inc/Math/Polynomial.h

@@ -116,20 +116,20 @@ class Polynomial : public ParamFunction<IParamGradFunction>,
       equation is very small. In that case it might be more robust to use the numerical method, by calling directly FindNumRoots()
 
    */
-   const std::vector<std::complex <double> > & FindRoots();
+   const std::vector<std::complex<double>> &FindRoots() const;
 
    /**
       Find the only the real polynomial roots.
       For n <= 4, the roots are found analytically while for larger order an iterative numerical method is used
       The numerical method used is from GSL (see <A HREF="https://www.gnu.org/software/gsl/doc/html/poly.html">documentation</A> )
    */
-   std::vector<double > FindRealRoots();
+   std::vector<double> FindRealRoots() const;
 
    /**
       Find the polynomial roots using always an iterative numerical methods
       The numerical method used is from GSL (see <A HREF="https://www.gnu.org/software/gsl/doc/html/poly.html">documentation</A> )
    */
-   const std::vector<std::complex <double> > & FindNumRoots();
+   const std::vector<std::complex<double>> &FindNumRoots() const;
 
    /**
       Order of Polynomial
@@ -166,9 +166,7 @@ class Polynomial : public ParamFunction<IParamGradFunction>,
    mutable std::vector<double> fDerived_params;
 
    // roots
-
-   std::vector< std::complex < double > > fRoots;
-
+   mutable std::vector<std::complex<double>> fRoots;
 };
 
 } // namespace Math

math/mathmore/src/Polynomial.cxx

@@ -147,13 +147,12 @@ IGenFunction * Polynomial::Clone() const {
     return f;
 }
 
+const std::vector<std::complex<double>> &Polynomial::FindRoots() const
+{
 
-const std::vector< std::complex <double> > &  Polynomial::FindRoots(){
-
-
-    // check if order is correct
-    unsigned int n = fOrder;
-    while ( Parameters()[n] == 0 ) {
+   // check if order is correct
+   unsigned int n = fOrder;
+   while (Parameters()[n] == 0) {
       n--;
     }
 
@@ -230,26 +229,25 @@ const std::vector< std::complex <double> > &  Polynomial::FindRoots(){
     }
 
     return fRoots;
-
-  }
-
-
-std::vector< double >  Polynomial::FindRealRoots(){
-  FindRoots();
-  std::vector<double> roots;
-  roots.reserve(fOrder);
-  for (unsigned int i = 0; i < fOrder; ++i) {
-    if (fRoots[i].imag() == 0)
-      roots.push_back( fRoots[i].real() );
-  }
-  return roots;
 }
-const std::vector< std::complex <double> > &  Polynomial::FindNumRoots(){
 
+std::vector<double> Polynomial::FindRealRoots() const
+{
+   FindRoots();
+   std::vector<double> roots;
+   roots.reserve(fOrder);
+   for (unsigned int i = 0; i < fOrder; ++i) {
+      if (fRoots[i].imag() == 0)
+         roots.push_back(fRoots[i].real());
+   }
+   return roots;
+}
+const std::vector<std::complex<double>> &Polynomial::FindNumRoots() const
+{
 
-    // check if order is correct
-    unsigned int n = fOrder;
-    while ( Parameters()[n] == 0 ) {
+   // check if order is correct
+   unsigned int n = fOrder;
+   while (Parameters()[n] == 0) {
       n--;
     }
     fRoots.clear();
@@ -271,6 +269,5 @@ const std::vector< std::complex <double> > &  Polynomial::FindNumRoots(){
     return fRoots;
 }
 
-
 } // namespace Math
 } // namespace ROOT