I have this code for my C extension in a seal_diff_cpp.cpp file:
extern "C" { // C Headers must be inside exter "C" { } block.
#include <postgres.h>
#include <utils/rel.h>
#include <fmgr.h>
#include <utils/array.h>
#include <utils/builtins.h>
#include <catalog/pg_type.h>
#include <stdlib.h>
#include <stdint.h>
PG_MODULE_MAGIC;
}
// CPP Header must be outside extern "C" { } block.
#include <string>
#include <vector>
#include <iostream>
#include <fstream>
#include <sstream>
#include <iterator> // For the ostream_iterator
// External projects c++ libraries compiled and linked on running 'make'.
#include <seal/seal.h>
#include <cppcodec/base64_rfc4648.hpp>
// CPP function can be declared and used inside or outside extern "C" { } block.
std::stringstream dec(std::string st){
        // Decode the base64 string into a stringstream 
        auto decodeBase64 = cppcodec::base64_rfc4648::decode(st);
        std::stringstream decodeBase64SS;
        std::move(decodeBase64.begin(), decodeBase64.end(), std::ostream_iterator<unsigned char>(decodeBase64SS));
        return decodeBase64SS;
}
std::string enc(std::string st){
        // Create a vector to hold the raw data
        std::vector<uint8_t> encodeStream;
        // Push all the characters from the raw data string into the vector
        for (auto &ch : st){
                encodeStream.push_back((unsigned char&&)(ch));
        }
        // Encode the vector as base64 string
        std::string encodeBase64 = cppcodec::base64_rfc4648::encode(encodeStream);
        encodeStream.clear();
        return encodeBase64;
}
std::string seal_diff_operation(std::string decodedLocalEncParamTmp, std::string decodedLocalTmp, std::string decodedLocalTmp){
        std::stringstream decodedLocalEncParam;
        decodedLocalEncParam.str(decodedLocalEncParamTmp);
        std::stringstream decodedLocalT1;
        decodedLocalT1.str(decodedLocalTmp);
        std::stringstream decodedLocalT2;
        decodedLocalT2.str(decodedLocalTmp);
        // Execute seal library operations
        // Load the ecryption parameters
        seal::EncryptionParameters IntegerEncryptorParms;
        IntegerEncryptorParms.load(decodedLocalEncParam);
        // Set Context and evaluator objects
        seal::SEALContext context(IntegerEncryptorParms);
        seal::Evaluator evaluator(context);
        // Set the Encoder parameters
        seal::IntegerEncoder encoder(context.plain_modulus());
        // Create Ciphertexts and load Chipertext information into them
        seal::Ciphertext number1Encoded;
        seal::Ciphertext number2Encoded;
        seal::Ciphertext diffEncodedResult;
        number1Encoded.load(decodedLocalT1);
        number2Encoded.load(decodedLocalT2);
        // Do the diff operation on the Ciphertexts and prepare the result for output
        evaluator.sub(number1Encoded, number2Encoded, diffEncodedResult);
        std::stringstream encResult;
        diffEncodedResult.save(encResult);
        std::string output = enc(encResult.str());
        return output;
}
extern "C" { // PostgreSQL functions be inside extern "C" { } block. 
Datum seal_diff_cpp(PG_FUNCTION_ARGS){
        // Get the Parameters
        text *t1 = PG_GETARG_TEXT_PP(0);
        text *t2 = PG_GETARG_TEXT_PP(1);
        text *encParam = PG_GETARG_TEXT_PP(2);
        std::string localT1;
        std::string localT2;
        std::string localEncParam;
        localT1 = text_to_cstring(t1);
        localT2 = text_to_cstring(t2);
        localEncParam = text_to_cstring(encParam);
        // Decode the parameters 
        std::stringstream decodedLocalT1 = dec(localT1);
        std::stringstream decodedLocalT2 = dec(localT2);
        std::stringstream decodedLocalEncParam = dec(localEncParam);
        // Encode the parameters
        std::string encodedLocalT1 = enc(decodedLocalT1.str());
        //std::string encodedLocalT1 = enc(encResult.str());
        std::string encodedLocalT2 = enc(decodedLocalT2.str());
        //std::string outputParam = seal_diff_operation(decodedLocalEncParam.str(), decodedLocalT1.str(), decodedLocalT2.str());
        // Returns Text 
        PG_RETURN_TEXT_P(cstring_to_text_with_len(localT1.c_str(), localT1.size()));
};
PG_FUNCTION_INFO_V1(seal_diff_cpp);
}
And I use this quick and dirty Makefile to create my .so file:
MODULES = seal_diff_cpp
PG_CONFIG = /usr/pgsql-10/bin/pg_config
PGXS = $(shell $(PG_CONFIG) --pgxs)
INCLUDEDIR = $(shell $(PG_CONFIG) --includedir-server)
INCLUDE_SEAL = /usr/local/include/seal
INCLUDE_SEAL_LIB = /usr/local/lib
INCLUDE_CPPCODEC = /usr/local/include/cppcodec
CXX = g++
CXXFLAGS = -std=c++17 -fPIC -Wall -Werror -g -O0 -pthread \
        -I$(INCLUDEDIR) -L$(INCLUDE_SEAL_LIB) -l libseal.a -I$(INCLUDE_SEAL) -I$(INCLUDE_CPPCODEC)
include $(PGXS)
seal_diff_cpp.so: seal_diff_cpp.o
        $(CXX) -shared -o seal_diff_cpp.so seal_diff_cpp.o
seal_diff_cpp.o: seal_diff_cpp.cpp
         $(CXX) $(CXXFLAGS) -o seal_diff_cpp.o -c seal_diff_cpp.cpp
When I try to add my C extension after copying it to the /usr/pgsql-10/lib/ folder with
-- Drop the function first, needed when changing return type
DROP FUNCTION IF EXISTS public.seal_diff_cpp(CHARACTER VARYING, CHARACTER VARYING, CHARACTER VARYING);
-- Create the new function
CREATE OR REPLACE FUNCTION 
   seal_diff_cpp(CHARACTER VARYING, CHARACTER VARYING, CHARACTER VARYING) RETURNS CHARACTER VARYING AS 'seal_diff_cpp' 
LANGUAGE C STRICT;
I get the error:
ERROR: could not load library "/usr/pgsql-10/lib/seal_diff_cpp.so": /usr/pgsql-10/lib/seal_diff_cpp.so: undefined symbol: _ZN4seal9Evaluator3subERNS_10CiphertextERKS1_ SQL state: XX000
This _ZN4seal9Evaluator3subERNS_10CiphertextERKS1_ is created because of using the seal::<some parameter>, the #include <seal/seal.h> is there so such errors won't happen. The SEAL library is an external library installed to /usr/local/include/seal and its libseal.a into /usr/local/lib/. 
The error occurs with the first declaration of a seal:: object, I have no problems/errors compiling it into the needed seal_diff_cpp.so file with my Makefile. When I comment all the SEAL code the extension runs perfectly with the second external library (#include <cppcodec/base64_rfc4648.hpp>) which is under /usr/local/include/cppcodec.
Am I doing something wrong with the seal library in the .cpp file or in Makefile? Do I need to install the external SEAL and cppcodec libraries into /usr/pgsql-10/include/ or some other pgsql-10 path? I have the feeling that #include <seal/seal.h> doesn't work.
UPDATE
After changing my Makefile as suggested by Alan Britles and and running make gave me this output, showing no errors with linking:
g++ -Wl,--no-undefined -std=c++17 -fPIC -Wall -Werror -g -O0 -pthread -I/usr/pgsql-10/include/server -I/usr/local/include/seal -I/usr/local/include/cppcodec -o seal_diff_cpp.o -c seal_diff_cpp.cpp g++ -L/usr/pgsql-10/lib -L/usr/lib64 -Wl,--as-needed -Wl,-rpath,'/usr/pgsql-10/lib',--enable-new-dtags -shared -o seal_diff_cpp.so seal_diff_cpp.o
With nm -gC seal_diff_cpp.so | grep "seal": I get this output:
000000000000e641 T pg_finfo_seal_diff_cpp
000000000000e26c T seal_diff_cpp
000000000000de73 T seal_diff_operation(std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> >, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> >, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> >)
                 U seal::Ciphertext::load(std::istream&)
                 U seal::Ciphertext::operator=(seal::Ciphertext const&)
000000000000f3b0 W seal::Ciphertext::Ciphertext()
000000000000f3b0 W seal::Ciphertext::Ciphertext()
000000000000f42c W seal::Ciphertext::~Ciphertext()
000000000000f42c W seal::Ciphertext::~Ciphertext()
                 U seal::SEALContext::SEALContext(seal::EncryptionParameters const&)
000000000000f1e6 W seal::SEALContext::~SEALContext()
000000000000f1e6 W seal::SEALContext::~SEALContext()
                 U seal::IntegerEncoder::IntegerEncoder(seal::SmallModulus const&, unsigned long)
                 U seal::IntegerEncoder::~IntegerEncoder()
000000000000eb80 W seal::MemoryPoolHandle::MemoryPoolHandle()
000000000000eb80 W seal::MemoryPoolHandle::MemoryPoolHandle()
000000000000eabe W seal::MemoryPoolHandle::~MemoryPoolHandle()
000000000000eabe W seal::MemoryPoolHandle::~MemoryPoolHandle()
                 U seal::EncryptionParameters::load(std::istream&)
                 U seal::EncryptionParameters::EncryptionParameters()
000000000000ebd2 W seal::EncryptionParameters::~EncryptionParameters()
000000000000ebd2 W seal::EncryptionParameters::~EncryptionParameters()
000000000000effc W seal::util::BaseConverter::~BaseConverter()
000000000000effc W seal::util::BaseConverter::~BaseConverter()
000000000000f166 W seal::util::SmallNTTTables::~SmallNTTTables()
000000000000f166 W seal::util::SmallNTTTables::~SmallNTTTables()
000000000000eba0 W seal::util::Modulus::~Modulus()
000000000000eba0 W seal::util::Modulus::~Modulus()
000000000000e9bc W seal::util::Pointer::release()
000000000000e986 W seal::util::Pointer::Pointer()
000000000000e986 W seal::util::Pointer::Pointer()
000000000000ea66 W seal::util::Pointer::~Pointer()
000000000000ea66 W seal::util::Pointer::~Pointer()
                 U seal::BigPoly::~BigPoly()
                 U seal::BigUInt::~BigUInt()
000000000000ec1c W seal::Evaluator::sub(seal::Ciphertext const&, seal::Ciphertext const&, seal::Ciphertext&)
                 U seal::Evaluator::sub(seal::Ciphertext&, seal::Ciphertext const&)
                 U seal::Evaluator::Evaluator(seal::SEALContext const&)
000000000000f276 W seal::Evaluator::~Evaluator()
000000000000f276 W seal::Evaluator::~Evaluator()
0000000000011c16 W __gnu_cxx::new_allocator<seal::SmallModulus>::deallocate(seal::SmallModulus*, unsigned long)
0000000000010afe W __gnu_cxx::new_allocator<seal::SmallModulus>::~new_allocator()
0000000000010afe W __gnu_cxx::new_allocator<seal::SmallModulus>::~new_allocator()
0000000000013e54 W __gnu_cxx::new_allocator<seal::util::SmallNTTTables>::deallocate(seal::util::SmallNTTTables*, unsigned long)
000000000001383a W __gnu_cxx::new_allocator<seal::util::SmallNTTTables>::~new_allocator()
000000000001383a W __gnu_cxx::new_allocator<seal::util::SmallNTTTables>::~new_allocator()
                 U seal::Ciphertext::save(std::ostream&) const
000000000000ebfe W seal::SEALContext::plain_modulus() const
000000000000ebc0 W seal::EncryptionParameters::plain_modulus() const
000000000000ff92 W std::allocator<seal::SmallModulus>::~allocator()
000000000000ff92 W std::allocator<seal::SmallModulus>::~allocator()
00000000000114fe W std::allocator<seal::util::SmallNTTTables>::~allocator()
00000000000114fe W std::allocator<seal::util::SmallNTTTables>::~allocator()
000000000000eb20 W std::shared_ptr<seal::util::MemoryPool>::shared_ptr(decltype(nullptr))
000000000000eb04 W std::shared_ptr<seal::util::MemoryPool>::shared_ptr()
000000000000eaa2 W std::shared_ptr<seal::util::MemoryPool>::~shared_ptr()
000000000000eaa2 W std::shared_ptr<seal::util::MemoryPool>::~shared_ptr()
0000000000013881 W void std::_Destroy_aux<false>::__destroy<seal::util::SmallNTTTables*>(seal::util::SmallNTTTables*, seal::util::SmallNTTTables*)
0000000000011c06 W void std::_Destroy_aux<true>::__destroy<seal::SmallModulus*>(seal::SmallModulus*, seal::SmallModulus*)
000000000000eb40 W std::__shared_ptr<seal::util::MemoryPool, (__gnu_cxx::_Lock_policy)2>::__shared_ptr()
000000000000ea82 W std::__shared_ptr<seal::util::MemoryPool, (__gnu_cxx::_Lock_policy)2>::~__shared_ptr()
000000000000ea82 W std::__shared_ptr<seal::util::MemoryPool, (__gnu_cxx::_Lock_policy)2>::~__shared_ptr()
000000000000ffae W std::_Vector_base<seal::SmallModulus, std::allocator<seal::SmallModulus> >::_Vector_impl::~_Vector_impl()
000000000000ffae W std::_Vector_base<seal::SmallModulus, std::allocator<seal::SmallModulus> >::_Vector_impl::~_Vector_impl()
0000000000010060 W std::_Vector_base<seal::SmallModulus, std::allocator<seal::SmallModulus> >::_M_deallocate(seal::SmallModulus*, unsigned long)
0000000000010028 W std::_Vector_base<seal::SmallModulus, std::allocator<seal::SmallModulus> >::_M_get_Tp_allocator()
000000000000ffca W std::_Vector_base<seal::SmallModulus, std::allocator<seal::SmallModulus> >::~_Vector_base()
000000000000ffca W std::_Vector_base<seal::SmallModulus, std::allocator<seal::SmallModulus> >::~_Vector_base()
000000000001073a W std::_Vector_base<seal::util::SmallNTTTables, std::allocator<seal::util::SmallNTTTables> >::_Vector_impl::~_Vector_impl()
000000000001073a W std::_Vector_base<seal::util::SmallNTTTables, std::allocator<seal::util::SmallNTTTables> >::_Vector_impl::~_Vector_impl()
000000000001151a W std::_Vector_base<seal::util::SmallNTTTables, std::allocator<seal::util::SmallNTTTables> >::_M_deallocate(seal::util::SmallNTTTables*, unsigned long)
00000000000107b4 W std::_Vector_base<seal::util::SmallNTTTables, std::allocator<seal::util::SmallNTTTables> >::_M_get_Tp_allocator()
0000000000010756 W std::_Vector_base<seal::util::SmallNTTTables, std::allocator<seal::util::SmallNTTTables> >::~_Vector_base()
0000000000010756 W std::_Vector_base<seal::util::SmallNTTTables, std::allocator<seal::util::SmallNTTTables> >::~_Vector_base()
0000000000010b2f W std::allocator_traits<std::allocator<seal::SmallModulus> >::deallocate(std::allocator<seal::SmallModulus>&, seal::SmallModulus*, unsigned long)
0000000000013845 W std::allocator_traits<std::allocator<seal::util::SmallNTTTables> >::deallocate(std::allocator<seal::util::SmallNTTTables>&, seal::util::SmallNTTTables*, unsigned long)
000000000000f574 W std::vector<seal::SmallModulus, std::allocator<seal::SmallModulus> >::~vector()
000000000000f574 W std::vector<seal::SmallModulus, std::allocator<seal::SmallModulus> >::~vector()
000000000000fbbe W std::vector<seal::util::SmallNTTTables, std::allocator<seal::util::SmallNTTTables> >::~vector()
000000000000fbbe W std::vector<seal::util::SmallNTTTables, std::allocator<seal::util::SmallNTTTables> >::~vector()
0000000000013873 W seal::util::SmallNTTTables* std::__addressof<seal::util::SmallNTTTables>(seal::util::SmallNTTTables&)
0000000000013e76 W void std::_Destroy<seal::util::SmallNTTTables>(seal::util::SmallNTTTables*)
0000000000010b09 W void std::_Destroy<seal::SmallModulus*>(seal::SmallModulus*, seal::SmallModulus*)
0000000000010036 W void std::_Destroy<seal::SmallModulus*, seal::SmallModulus>(seal::SmallModulus*, seal::SmallModulus*, std::allocator<seal::SmallModulus>&)
000000000001154f W void std::_Destroy<seal::util::SmallNTTTables*>(seal::util::SmallNTTTables*, seal::util::SmallNTTTables*)
00000000000107c2 W void std::_Destroy<seal::util::SmallNTTTables*, seal::util::SmallNTTTables>(seal::util::SmallNTTTables*, seal::util::SmallNTTTables*, std::allocator<seal::util::SmallNTTTables>&)
So I guess that the SEAL library is getting linked correctly, but I do have some important symbols mared with undefined (U) and therefore I'm still getting the same error from PostgreSQL. But why are those symbols get marked as undefined?
 
    