singular: compatibility for 4.3.2p10 and before

Add two fallback compatibility `#define`s:
 - `ringorder_ip`
 - `BIGINTVEC_CMD`

Also for old singular:
 - patch the term_order mappings to send `rp` to singular instead of `ip`
 - patch the display of a ring so it prints `ip` instead of `rp`

Author: tornaria

src/sage/interfaces/singular.py

@@ -1402,6 +1402,13 @@ def _repr_(self):
         if self._name in s:
             if self.get_custom_name() is None and self.type() == 'matrix':
                 s = self.parent().eval('pmat(%s,20)' % (self.name()))
+        # compatibility for singular 4.3.2p10 and before
+        if s.startswith("polynomial ring,"):
+            from sage.rings.polynomial.term_order import singular_name_mapping
+            # this is our cue that singular uses `rp` instead of `ip`
+            if singular_name_mapping['invlex'] == 'rp':
+                s = re.sub('^(// .*block.* : ordering )rp$', '\\1ip',
+                           s, 0, re.MULTILINE);
         return s
 
     def __copy__(self):

src/sage/libs/singular/decl.pxd

@@ -49,6 +49,13 @@ cdef extern from "factory/factory.h":
     cdef int SW_USE_NTL_SORT
 
 cdef extern from "singular/Singular/libsingular.h":
+    """
+    // compatibility for singular 4.3.2p10 and before
+    #if SINGULAR_VERSION <= 4330
+    #define ringorder_ip ringorder_rp
+    #define BIGINTVEC_CMD INTVEC_CMD
+    #endif
+    """
 
     #
     # OPTIONS

src/sage/libs/singular/ring.pyx

@@ -17,7 +17,7 @@ AUTHORS:
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-from sage.cpython.string cimport str_to_bytes
+from sage.cpython.string cimport str_to_bytes, bytes_to_str
 
 from sage.libs.gmp.types cimport __mpz_struct
 from sage.libs.gmp.mpz cimport mpz_init_set_ui
@@ -72,6 +72,16 @@ order_dict = {
     "a":  ringorder_a,
 }
 
+cdef extern from "singular/Singular/libsingular.h":
+    cdef char * rSimpleOrdStr(rRingOrder_t)
+
+if bytes_to_str(rSimpleOrdStr(ringorder_ip)) == "rp":
+    # compatibility for singular 4.3.2p10 and before
+    order_dict["rp"] = ringorder_ip
+    # also patch term_order mappings
+    from sage.rings.polynomial import term_order
+    term_order.singular_name_mapping['invlex'] = 'rp'
+    term_order.inv_singular_name_mapping['rp'] = 'invlex'
 
 #############################################################################
 cdef ring *singular_ring_new(base_ring, n, names, term_order) except NULL: