Single template class, with specified types, bind to a Single Python class

[izsahara]

I have a class template Parameter that i would like to bind with python accepting different types

This is the code structure

// in parameters.h


template<typename T>
class BaseParameter {
  /* ....... */
}

template<typename T>
class Parameter;

// Specifying Derived Parameter types
template<>
class Parameter<double> : public BaseParameter<double> {
    /* ....... */
}

template<>
class Parameter<int> : public BaseParameter<int> {
    /* ....... */
}

And binding with pybind

// In parameters.cpp


void wrap_double_parameter(py::module& mod) {
    // Trampoline definition
    class PyDoubleParameter : public Parameter<double> 
    {
      public:
         using Parameter::Parameter;
       /* ....... */
     }

    //
    py::class_<Parameter<double>, PyDoubleParameter> PAR(mod, "Parameter");
    PAR
       .def(/* ....... */)
}

void wrap_int_parameter(py::module& mod) {

    class PyIntParameter : public Parameter<int> 
    {
      public:
         using Parameter::Parameter;
      /* ....... */
    }
    //
    py::class_<Parameter<int>, PyIntParameter> PAR(mod, "Parameter");
    PAR
       .def(/* ....... */)
}

PYBIND11_MODULE(parameters, mod) {
    wrap_double_parameter(mod);
    wrap_int_parameter(mod);
}

I suspect the problem is that both classes share the name "Parameter". However, that is my intention, in that, in Python I would like a single class Parameter that would only accept the specified types. This leads to the error:

'ImportError: generic_type: cannot initialize type "Parameter": an object with that name is already defined'

Is it possible to bind a single class template with multiple types? Rather is there a workaround this?

(NOTE: for the sake of brevity i specified the types int and double however there is also an Eigen::VectorXd that would be an accepted type for Parameter. Also, I wouldnt want BaseParameter to be accesible in Python, hence why i only binded Parameter, unless i have to?)