diff --git a/src/bindings/lua/numerics.cpp b/src/bindings/lua/numerics.cpp
index 866717a23..bd9c7fa08 100644
--- a/src/bindings/lua/numerics.cpp
+++ b/src/bindings/lua/numerics.cpp
@@ -7,6 +7,7 @@ Author: Leonardo de Moura
 #include <sstream>
 #include <lua.hpp>
 #include "util/debug.h"
+#include "util/sstream.h"
 #include "util/numerics/mpz.h"
 #include "util/numerics/mpq.h"
 #include "bindings/lua/util.h"
@@ -17,24 +18,20 @@ DECL_UDATA(mpz)
 template<unsigned idx>
 static mpz const & to_mpz(lua_State * L) {
     static thread_local mpz arg;
-    if (lua_isuserdata(L, idx)) {
-        return *static_cast<mpz*>(luaL_checkudata(L, idx, mpz_mt));
-    } else if (lua_isstring(L, idx)) {
-        arg = mpz(luaL_checkstring(L, idx));
-        return arg;
-    } else {
-        arg = static_cast<long int>(luaL_checkinteger(L, 1));
-        return arg;
+    switch (lua_type(L, idx)) {
+    case LUA_TNUMBER:       arg = static_cast<long>(lua_tointeger(L, idx)); return arg;
+    case LUA_TSTRING:       arg = mpz(lua_tostring(L, idx)); return arg;
+    case LUA_TUSERDATA:     return *static_cast<mpz*>(luaL_checkudata(L, idx, mpz_mt));
+    default: throw exception(sstream() << "arg #" << idx << " must be a number, string or mpz");
     }
 }
 
 mpz to_mpz_ext(lua_State * L, int idx) {
-    if (lua_isuserdata(L, idx)) {
-        return *static_cast<mpz*>(luaL_checkudata(L, idx, mpz_mt));
-    } else if (lua_isstring(L, idx)) {
-        return mpz(luaL_checkstring(L, idx));
-    } else {
-        return mpz(static_cast<long int>(luaL_checkinteger(L, 1)));
+    switch (lua_type(L, idx)) {
+    case LUA_TNUMBER:       return mpz(static_cast<long>(lua_tointeger(L, idx)));
+    case LUA_TSTRING:       return mpz(lua_tostring(L, idx));
+    case LUA_TUSERDATA:     return *static_cast<mpz*>(luaL_checkudata(L, idx, mpz_mt));
+    default: throw exception(sstream() << "arg #" << idx << " must be a number, string or mpz");
     }
 }
 
@@ -95,7 +92,7 @@ static const struct luaL_Reg mpz_m[] = {
     {"__eq",       safe_function<mpz_eq>},
     {"__lt",       safe_function<mpz_lt>},
     {"__add",      safe_function<mpz_add>},
-    {"__add",      safe_function<mpz_sub>},
+    {"__sub",      safe_function<mpz_sub>},
     {"__mul",      safe_function<mpz_mul>},
     {"__div",      safe_function<mpz_div>},
     {"__pow",      safe_function<mpz_power>},
@@ -116,31 +113,31 @@ DECL_UDATA(mpq)
 template<unsigned idx>
 static mpq const & to_mpq(lua_State * L) {
     static thread_local mpq arg;
-    if (lua_isuserdata(L, idx)) {
+    switch (lua_type(L, idx)) {
+    case LUA_TNUMBER:       arg = lua_tonumber(L, idx); return arg;
+    case LUA_TSTRING:       arg = mpq(lua_tostring(L, idx)); return arg;
+    case LUA_TUSERDATA:
         if (is_mpz(L, idx)) {
             arg = mpq(to_mpz<idx>(L));
+            return arg;
         } else {
             return *static_cast<mpq*>(luaL_checkudata(L, idx, mpq_mt));
         }
-    } else if (lua_isstring(L, idx)) {
-        arg = mpq(luaL_checkstring(L, idx));
-    } else {
-        arg = static_cast<long int>(luaL_checkinteger(L, 1));
+    default: throw exception(sstream() << "arg #" << idx << " must be a number, string, mpz or mpq");
     }
-    return arg;
 }
 
 mpq to_mpq_ext(lua_State * L, int idx) {
-    if (lua_isuserdata(L, idx)) {
+    switch (lua_type(L, idx)) {
+    case LUA_TNUMBER:       return mpq(lua_tonumber(L, idx));
+    case LUA_TSTRING:       return mpq(lua_tostring(L, idx));
+    case LUA_TUSERDATA:
         if (is_mpz(L, idx)) {
-            return mpq(to_mpz(L, idx));
+            return mpq(to_mpz<1>(L));
         } else {
             return *static_cast<mpq*>(luaL_checkudata(L, idx, mpq_mt));
         }
-    } else if (lua_isstring(L, idx)) {
-        return mpq(luaL_checkstring(L, idx));
-    } else {
-        return mpq(static_cast<long int>(luaL_checkinteger(L, 1)));
+    default: throw exception(sstream() << "arg #" << idx << " must be a number, string, mpz or mpq");
     }
 }
 
@@ -201,7 +198,7 @@ static const struct luaL_Reg mpq_m[] = {
     {"__eq",       safe_function<mpq_eq>},
     {"__lt",       safe_function<mpq_lt>},
     {"__add",      safe_function<mpq_add>},
-    {"__add",      safe_function<mpq_sub>},
+    {"__sub",      safe_function<mpq_sub>},
     {"__mul",      safe_function<mpq_mul>},
     {"__div",      safe_function<mpq_div>},
     {"__pow",      safe_function<mpq_power>},
diff --git a/tests/lua/num1.lua b/tests/lua/num1.lua
new file mode 100644
index 000000000..83119a0c6
--- /dev/null
+++ b/tests/lua/num1.lua
@@ -0,0 +1,47 @@
+assert(mpz(10) == mpz("10"))
+assert(mpz(mpz(3)) == mpz("3"))
+print(mpz(10) + mpz(3))
+assert(mpz(10) + mpz(3) == mpz(13))
+assert(mpz(10) + 2 == mpz(12))
+assert(3 + mpz(15) == mpz(18))
+assert(mpz(10) - mpz(3) == mpz(7))
+assert(mpz(10) - 2 == mpz(8))
+assert(3 - mpz(15) == -mpz(12))
+assert(- mpz(15) == mpz("-15"))
+assert(- mpz(15) == -mpz("15"))
+assert(mpz(10) * mpz(3) == mpz(30))
+assert(mpz(10) * 2 == mpz(20))
+assert(3 * mpz(15) == mpz(45))
+assert(mpz(3)^2 == mpz(9))
+local a = -2
+assert(not pcall(function() print(mpz(3)^a) end))
+assert(mpz(3) < mpz(5))
+assert(mpz(3) > mpz(1))
+assert(mpq(3) == mpq("3"))
+assert(mpq(3) == mpq(mpq(3)))
+assert(mpq(3) == mpq(mpz(3)))
+assert(mpq(0.5) == mpq(1)/2)
+assert(mpq(0.4) ~= mpq(1)/2)
+assert(mpq(10) + mpq(3) == mpq(13))
+assert(mpq(10) + 2 == mpq(12))
+assert(3 + mpq(15) == mpq(18))
+assert(mpq(3) + mpz(15) == mpq(18))
+assert(mpq(10) - mpq(3) == mpq(7))
+assert(mpq(10) - 2 == mpq(8))
+assert(3 - mpq(15) == -mpq(12))
+assert(mpq(3) - mpz(15) == -mpq(12))
+assert(mpq(10) * mpq(3) == mpq(30))
+assert(mpq(10) * 2 == mpq(20))
+assert(3 * mpq(15) == mpq(45))
+assert(mpq(3) * mpz(15) == mpq(45))
+assert(mpq(3)^2 == mpq(9))
+print(mpq(0.5)^2)
+assert(mpq(0.5)^2 == mpq(1)/4)
+local a = -2
+assert(not pcall(function() print(mpq(3)^a) end))
+assert(mpq(10) / mpq(3) == mpq("10/3"))
+assert(mpq(10) / 2 == mpq(5))
+assert(3 / mpq(15) == mpq(1)/5)
+assert(mpq(3) / mpz(15) == mpq("1/5"))
+assert(mpq(3) < mpq(5))
+assert(mpq(3) > mpq(1))