Update tests for singular 4.2.1p2

src/sage/modular/modform_hecketriangle/abstract_space.py

@@ -1161,8 +1161,8 @@ def F_basis_pol(self, m, order_1=ZZ(0)):
 
             sage: MF.F_basis_pol(2)
             x^13*y*d^2 - 2*x^8*y^3*d^2 + x^3*y^5*d^2
-            sage: MF.F_basis_pol(1)
-            (-81*x^13*y*d + 62*x^8*y^3*d + 19*x^3*y^5*d)/(-100)
+            sage: MF.F_basis_pol(1) * 100
+            81*x^13*y*d - 62*x^8*y^3*d - 19*x^3*y^5*d
             sage: MF.F_basis_pol(0)
             (141913*x^13*y + 168974*x^8*y^3 + 9113*x^3*y^5)/320000
 

src/sage/modular/modform_hecketriangle/readme.py

@@ -757,8 +757,8 @@
 
   General Eisenstein series in some arithmetic cases::
 
-      sage: ModularFormsRing(n=4).EisensteinSeries(k=8)
-      (-25*f_rho^4 - 9*f_i^2)/(-34)
+      sage: ModularFormsRing(n=4).EisensteinSeries(k=8) * 34
+      25*f_rho^4 + 9*f_i^2
       sage: ModularForms(n=3, k=12).EisensteinSeries()
       1 + 65520/691*q + 134250480/691*q^2 + 11606736960/691*q^3 + 274945048560/691*q^4 + O(q^5)
       sage: ModularForms(n=6, k=12).EisensteinSeries()

src/sage/rings/asymptotic/asymptotics_multivariate_generating_functions.py

@@ -1578,7 +1578,7 @@ def asymptotics(self, p, alpha, N, asy_var=None, numerical=0,
             (1, [(x*y + x + y - 1, 2)])
             sage: alpha = [4, 3]
             sage: decomp = F.asymptotic_decomposition(alpha); decomp
-            (0, []) + (-2*r*(1/x + 1) - 1/2/x - 1/2, [(x*y + x + y - 1, 1)])
+            (0, []) + (... - 1/2, [(x*y + x + y - 1, 1)])
             sage: F1 = decomp[1]
             sage: p = {y: 1/3, x: 1/2}
             sage: asy = F1.asymptotics(p, alpha, 2, verbose=True)

src/sage/rings/polynomial/hilbert.pyx

@@ -576,13 +576,10 @@ def hilbert_poincare_series(I, grading=None):
         sage: hilbert_poincare_series(J).denominator().factor()
         (t - 1)^14
 
-    This example exceeds the current capabilities of Singular::
+    This example exceeded the capabilities of Singular before version 4.2.1p2
 
         sage: J.hilbert_numerator(algorithm='singular')
-        Traceback (most recent call last):
-        ...
-        RuntimeError: error in Singular function call 'hilb':
-         int overflow in hilb 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
 
     """
     cdef Polynomial_integer_dense_flint HP

src/sage/rings/polynomial/multi_polynomial_ideal.py

@@ -154,7 +154,7 @@
     which is not 1. ::
 
         sage: I.groebner_basis()
-        [x + y + 57119*z + 4, y^2 + 3*y + 17220, y*z + y + 26532, 2*y + 158864, z^2 + 17223, 2*z + 41856, 164878]
+        [x + y + 57119*z + 4, y^2 + 3*y + 17220, y*z + ..., 2*y + 158864, z^2 + 17223, 2*z + 41856, 164878]
 
     Now for each prime `p` dividing this integer 164878, the Groebner
     basis of I modulo `p` will be non-trivial and will thus give a

src/sage/rings/polynomial/multi_polynomial_libsingular.pyx

@@ -4920,7 +4920,8 @@ cdef class MPolynomial_libsingular(MPolynomial):
 
             sage: Pol.<x,y,z> = ZZ[]
             sage: p = -x*y + x*z + 54*x - 2
-            sage: (5*p^2).lcm(3*p) == 15*p^2
+            sage: q = (5*p^2).lcm(3*p)
+            sage: q * q.lc().sign() == 15*p^2
             True
             sage: lcm(2*x, 2*y)
             2*x*y