Trac #33160: update Singular to 4.3.1

The previous update was on #32907

See https://www.singular.uni-kl.de/Manual/4-3-0/sing_2998.htm -
in particular,  Flint 2.8 is supported.

This ticket also serves as the new target ticket for Singular's ci-sage
after Singular/Singular#1131

URL: https://trac.sagemath.org/33160
Reported by: dimpase
Ticket author(s): Matthias Koeppe, Michael Orlitzky, Dima Pasechnik
Reviewer(s): Dima Pasechnik, Matthias Koeppe

build/pkgs/singular/checksums.ini

@@ -1,5 +1,5 @@
 tarball=singular-VERSION.tar.gz
-sha1=f257a0ef23cedb2c8f9514bbc5f292ca3660a244
-md5=8b9142f42cb73aede3940ef3c5f9586d
-cksum=2019987428
-upstream_url=ftp://jim.mathematik.uni-kl.de/pub/Math/Singular/SOURCES/4-2-1/singular-VERSION.tar.gz
+sha1=6c2b622d3681e2de3d58d30c654d43d3e32b720c
+md5=abb1e37c794472e7760655358ab66054
+cksum=17455733
+upstream_url=ftp://jim.mathematik.uni-kl.de/pub/Math/Singular/SOURCES/4-3-1/singular-VERSION.tar.gz

build/pkgs/singular/package-version.txt

@@ -1 +1 @@
-4.2.1p3
+4.3.1p1

src/sage/rings/polynomial/hilbert.pyx

@@ -576,11 +576,13 @@ def hilbert_poincare_series(I, grading=None):
         sage: hilbert_poincare_series(J).denominator().factor()
         (t - 1)^14
 
-    This example exceeded the capabilities of Singular before version 4.2.1p2::
+    This example exceeded the capabilities of Singular before version 4.2.1p2.
+    In Singular 4.3.1, it works correctly on 64-bit, but on 32-bit, it prints overflow warnings
+    and omits some terms.
 
         sage: J.hilbert_numerator(algorithm='singular')
-        120*t^33 - 3465*t^32 + 48180*t^31 - 429374*t^30 + 2753520*t^29 - 13522410*t^28 + 52832780*t^27 - 168384150*t^26 + 445188744*t^25 - 987193350*t^24 + 1847488500*t^23 + 1372406746*t^22 - 403422496*t^21 - 8403314*t^20 - 471656596*t^19 + 1806623746*t^18 + 752776200*t^17 + 752776200*t^16 - 1580830020*t^15 + 1673936550*t^14 - 1294246800*t^13 + 786893250*t^12 - 382391100*t^11 + 146679390*t^10 - 42299400*t^9 + 7837830*t^8 - 172260*t^7 - 468930*t^6 + 183744*t^5 - 39270*t^4 + 5060*t^3 - 330*t^2 + 1
-
+        120*t^33 - 3465*t^32 + 48180*t^31 - 429374*t^30 + 2753520*t^29 - 13522410*t^28 + 52832780*t^27 - 168384150*t^26 + 445188744*t^25 - 987193350*t^24 + 1847488500*t^23 + 1372406746*t^22 - 403422496*t^21 - 8403314*t^20 - 471656596*t^19 + 1806623746*t^18 + 752776200*t^17 + 752776200*t^16 - 1580830020*t^15 + 1673936550*t^14 - 1294246800*t^13 + 786893250*t^12 - 382391100*t^11 + 146679390*t^10 - 42299400*t^9 + 7837830*t^8 - 172260*t^7 - 468930*t^6 + 183744*t^5 - 39270*t^4 + 5060*t^3 - 330*t^2 + 1  # 64-bit
+        ...120*t^33 - 3465*t^32 + 48180*t^31 - ...  # 32-bit
     """
     cdef Polynomial_integer_dense_flint HP
     HP, grading = first_hilbert_series(I, grading=grading, return_grading=True)

src/sage/rings/polynomial/multi_polynomial_ideal.py

@@ -2902,6 +2902,20 @@ def hilbert_numerator(self, grading = None, algorithm = 'sage'):
             sage: I = Ideal([x^3*y^2 + 3*x^2*y^2*z + y^3*z^2 + z^5])
             sage: I.hilbert_numerator()
             -t^5 + 1
+
+        Our two algorithms should always agree; not tested until
+        :trac:`33178` is fixed::
+
+            sage: m = ZZ.random_element(2,8)                      # not tested
+            sage: nvars = m^2                                     # not tested
+            sage: R = PolynomialRing(QQ, "x", nvars)              # not tested
+            sage: M = matrix(R, m, R.gens())                      # not tested
+            sage: I = R.ideal(M.minors(2))                        # not tested
+            sage: n1 = I.hilbert_numerator()                      # not tested
+            sage: n2 = I.hilbert_numerator(algorithm='singular')  # not tested
+            sage: n1 == n2                                        # not tested
+            True
+
         """
         if not self.is_homogeneous():
             raise TypeError("Ideal must be homogeneous.")