gh-37492: make sagelib work with singular>=4.3.2.p15 (future 4.4)
    
Two major breaking changes:

- The `rp` ordering is renamed to `ip`
- `hilb` now returns a `bigintvec` object (which isn't even exposed in
the C++ API, seems to be an instance of `bigintmat`)

This branch builds and works fine with 4.3.2.p15, but I have no idea how
to make it work with both old and new singular, suggestions welcome.
    
URL: #37492
Reported by: Antonio Rojas
Reviewer(s): Antonio Rojas, Gonzalo Tornaría, Matthias Köppe

Author: Release Manager

src/sage/interfaces/singular.py

@@ -1211,14 +1211,14 @@ def current_ring(self):
             polynomial ring, over a field, global ordering
             //   coefficients: ZZ/127
             //   number of vars : 3
-            //        block   1 : ordering rp
+            //        block   1 : ordering ip
             //                  : names    x y z
             //        block   2 : ordering C
             sage: singular.current_ring()
             polynomial ring, over a field, global ordering
             //   coefficients: ZZ/127
             //   number of vars : 3
-            //        block   1 : ordering rp
+            //        block   1 : ordering ip
             //                  : names    x y z
             //        block   2 : ordering C
         """
@@ -1402,6 +1402,14 @@ 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
+            from sage.repl.rich_output import get_display_manager
+            # this is our cue that singular uses `rp` instead of `ip`
+            if singular_name_mapping['invlex'] == 'rp' and 'doctest' in str(get_display_manager()):
+                s = re.sub('^(// .*block.* : ordering )rp$', '\\1ip',
+                           s, 0, re.MULTILINE);
         return s
 
     def __copy__(self):
@@ -2025,6 +2033,10 @@ def _sage_(self, R=None):
             sage: type(singular(int(5)).sage())
             <class 'sage.rings.integer.Integer'>
 
+        Test that bigintvec can be coerced::
+
+            sage: singular('hilb((ideal(x)), 1)').sage()
+            (1, -1, 0, 0, -1, 1, 0)
         """
         typ = self.type()
         if typ == 'poly':
@@ -2040,6 +2052,9 @@ def _sage_(self, R=None):
         elif typ == 'intvec':
             from sage.modules.free_module_element import vector
             return vector([sage.rings.integer.Integer(str(e)) for e in self])
+        elif typ == 'bigintvec':
+            from sage.modules.free_module_element import vector
+            return vector([sage.rings.rational.Rational(str(e)) for e in self])
         elif typ == 'intmat':
             from sage.matrix.constructor import matrix
             from sage.rings.integer_ring import ZZ

src/sage/libs/singular/decl.pxd

@@ -48,6 +48,13 @@ 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
@@ -243,7 +250,7 @@ cdef extern from "singular/Singular/libsingular.h":
         ringorder_s
         ringorder_lp
         ringorder_dp
-        ringorder_rp
+        ringorder_ip
         ringorder_Dp
         ringorder_wp
         ringorder_Wp
@@ -291,6 +298,10 @@ cdef extern from "singular/Singular/libsingular.h":
         int row
         int col
 
+    cdef cppclass bigintmat:
+        int (*length)()
+        number* (*get)(int i)
+
     # omalloc bins
 
     ctypedef struct omBin "omBin_s"
@@ -921,6 +932,7 @@ cdef extern from "singular/Singular/libsingular.h":
     cdef int MATRIX_CMD
     cdef int LIST_CMD
     cdef int INTVEC_CMD
+    cdef int BIGINTVEC_CMD
     cdef int NONE
     cdef int RESOLUTION_CMD
     cdef int PACKAGE_CMD

src/sage/libs/singular/function.pyx

@@ -98,7 +98,7 @@ from sage.rings.polynomial.multi_polynomial_sequence import PolynomialSequence_g
 from sage.libs.singular.decl cimport *
 from sage.libs.singular.option import opt_ctx
 from sage.libs.singular.polynomial cimport singular_vector_maximal_component
-from sage.libs.singular.singular cimport sa2si, si2sa, si2sa_intvec
+from sage.libs.singular.singular cimport sa2si, si2sa, si2sa_intvec, si2sa_bigintvec
 from sage.libs.singular.singular import error_messages
 
 from sage.interfaces.singular import get_docstring
@@ -954,6 +954,8 @@ cdef class Converter(SageObject):
             return si2sa(<number *>to_convert.data, self._singular_ring, self._sage_ring.base_ring())
         elif rtyp == INTVEC_CMD:
             return si2sa_intvec(<intvec *> to_convert.data)
+        elif rtyp == BIGINTVEC_CMD:
+            return si2sa_bigintvec(<bigintmat *> to_convert.data)
         elif rtyp == STRING_CMD:
             # TODO: Need to determine what kind of data can be returned by a
             # STRING_CMD--is it just ASCII strings or can it be an arbitrary
@@ -1048,6 +1050,17 @@ cdef class LibraryCallHandler(BaseCallHandler):
         """
         return False
 
+# mapping int --> string for function arity
+arity_dict = {
+        CMD_1: "CMD_1",
+        CMD_2: "CMD_2",
+        CMD_3: "CMD_3",
+        CMD_12: "CMD_12",
+        CMD_13: "CMD_13",
+        CMD_23: "CMD_23",
+        CMD_123: "CMD_123",
+        CMD_M: "CMD_M"
+}
 
 cdef class KernelCallHandler(BaseCallHandler):
     """
@@ -1125,8 +1138,9 @@ cdef class KernelCallHandler(BaseCallHandler):
 
         errorreported += 1
         error_messages.append(
-                "Wrong number of arguments (got {} arguments, arity code is {})"
-                .format(number_of_arguments, self.arity))
+                "Wrong number of arguments (got {} arguments, arity is {})"
+                .format(number_of_arguments,
+                        arity_dict.get(self.arity) or self.arity))
         return NULL
 
     cdef bint free_res(self) noexcept:
@@ -1231,7 +1245,7 @@ cdef class SingularFunction(SageObject):
             Traceback (most recent call last):
             ...
             RuntimeError: error in Singular function call 'size':
-            Wrong number of arguments (got 2 arguments, arity code is 302)
+            Wrong number of arguments (got 2 arguments, arity is CMD_1)
             sage: size('foobar', ring=P)
             6
 
@@ -1634,17 +1648,17 @@ def singular_function(name):
         Traceback (most recent call last):
         ...
         RuntimeError: error in Singular function call 'factorize':
-        Wrong number of arguments (got 0 arguments, arity code is 305)
+        Wrong number of arguments (got 0 arguments, arity is CMD_12)
         sage: factorize(f, 1, 2)
         Traceback (most recent call last):
         ...
         RuntimeError: error in Singular function call 'factorize':
-        Wrong number of arguments (got 3 arguments, arity code is 305)
+        Wrong number of arguments (got 3 arguments, arity is CMD_12)
         sage: factorize(f, 1, 2, 3)
         Traceback (most recent call last):
         ...
         RuntimeError: error in Singular function call 'factorize':
-        Wrong number of arguments (got 4 arguments, arity code is 305)
+        Wrong number of arguments (got 4 arguments, arity is CMD_12)
 
     The Singular function ``list`` can be called with any number of
     arguments::

src/sage/libs/singular/ring.pyx

@@ -16,15 +16,15 @@ 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
 
 from sage.libs.singular.decl cimport ring, currRing
 from sage.libs.singular.decl cimport rChangeCurrRing, rComplete, rDelete, idInit
 from sage.libs.singular.decl cimport omAlloc0, omStrDup, omAlloc
-from sage.libs.singular.decl cimport ringorder_dp, ringorder_Dp, ringorder_lp, ringorder_rp, ringorder_ds, ringorder_Ds, ringorder_ls, ringorder_M, ringorder_c, ringorder_C, ringorder_wp, ringorder_Wp, ringorder_ws, ringorder_Ws, ringorder_a, rRingOrder_t
+from sage.libs.singular.decl cimport ringorder_dp, ringorder_Dp, ringorder_lp, ringorder_ip, ringorder_ds, ringorder_Ds, ringorder_ls, ringorder_M, ringorder_c, ringorder_C, ringorder_wp, ringorder_Wp, ringorder_ws, ringorder_Ws, ringorder_a, rRingOrder_t
 from sage.libs.singular.decl cimport prCopyR
 from sage.libs.singular.decl cimport n_unknown, n_algExt, n_transExt, n_Z, n_Zn,  n_Znm, n_Z2m
 from sage.libs.singular.decl cimport n_coeffType
@@ -60,7 +60,7 @@ order_dict = {
     "dp": ringorder_dp,
     "Dp": ringorder_Dp,
     "lp": ringorder_lp,
-    "rp": ringorder_rp,
+    "ip": ringorder_ip,
     "ds": ringorder_ds,
     "Ds": ringorder_Ds,
     "ls": ringorder_ls,
@@ -71,6 +71,16 @@ 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:

src/sage/libs/singular/singular.pxd

@@ -1,4 +1,4 @@
-from sage.libs.singular.decl cimport ring, poly, number, intvec
+from sage.libs.singular.decl cimport ring, poly, number, intvec, bigintmat
 from sage.libs.singular.function cimport Resolution
 
 from sage.rings.rational cimport Rational
@@ -29,6 +29,7 @@ cdef object   si2sa_ZZmod(number *n, ring *_ring, object base)
 cdef object   si2sa_NF(number *n, ring *_ring, object base)
 
 cdef object si2sa_intvec(intvec *v)
+cdef object si2sa_bigintvec(bigintmat *v)
 
 # dispatches to all the above.
 cdef object si2sa(number *n, ring *_ring, object base)

src/sage/libs/singular/singular.pyx

@@ -1699,6 +1699,25 @@ cdef object si2sa_intvec(intvec *v):
         l.append(v.get(r))
     return tuple(l)
 
+cdef object si2sa_bigintvec(bigintmat *v):
+    r"""
+    create a sage tuple from a singular vector of big integers
+
+    INPUT:
+
+    - ``v`` -- a (pointer to) singular bigintmat
+
+    OUTPUT:
+
+    a sage tuple
+    """
+    cdef int r
+    cdef list l = list()
+    for r in range(v.length()):
+        n = v.get(r)
+        l.append(si2sa_QQ(n, &n, currRing))
+    return tuple(l)
+
 # ==============
 # Initialisation
 # ==============

src/sage/rings/polynomial/multi_polynomial_libsingular.pyx

@@ -1285,7 +1285,7 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_base):
             polynomial ring, over a field, global ordering
             //   coefficients: ZZ/2[a]/(a^8+a^4+a^3+a^2+1)
             //   number of vars : 10
-            //        block   1 : ordering rp
+            //        block   1 : ordering ip
             //                  : names    x0 x1 x2 x3 x4 x5 x6 x7 x8 x9
             //        block   2 : ordering C
 
@@ -1294,7 +1294,7 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_base):
             polynomial ring, over a field, global ordering
             //   coefficients: ZZ/127
             //   number of vars : 2
-            //        block   1 : ordering rp
+            //        block   1 : ordering ip
             //                  : names    x0 x1
             //        block   2 : ordering C
 
@@ -1303,7 +1303,7 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_base):
             polynomial ring, over a field, global ordering
             //   coefficients: QQ
             //   number of vars : 2
-            //        block   1 : ordering rp
+            //        block   1 : ordering ip
             //                  : names    x0 x1
             //        block   2 : ordering C
 

src/sage/rings/polynomial/term_order.py

@@ -388,7 +388,7 @@
 
 singular_name_mapping = {
     'lex'           : 'lp',
-    'invlex'        : 'rp',
+    'invlex'        : 'ip',
     'degrevlex'     : 'dp',
     'deglex'        : 'Dp',
     'neglex'        : 'ls',