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diff --git a/build/pkgs/singular/checksums.ini b/build/pkgs/singular/checksums.ini
index 2e33a405d3..313463d2fe 100644
--- a/build/pkgs/singular/checksums.ini
+++ b/build/pkgs/singular/checksums.ini
@@ -1,5 +1,5 @@
tarball=singular-VERSION.tar.gz
-sha1=6c2b622d3681e2de3d58d30c654d43d3e32b720c
-md5=abb1e37c794472e7760655358ab66054
-cksum=17455733
+sha1=28bb3ee97ef48d04dfa96de182fd93eebe08426c
+md5=fc0a4f5720dadba45a52ee94324ce00c
+cksum=1573851737
upstream_url=ftp://jim.mathematik.uni-kl.de/pub/Math/Singular/SOURCES/4-3-1/singular-VERSION.tar.gz
diff --git a/build/pkgs/singular/package-version.txt b/build/pkgs/singular/package-version.txt
index 11300c77e7..66e2bede53 100644
--- a/build/pkgs/singular/package-version.txt
+++ b/build/pkgs/singular/package-version.txt
@@ -1 +1 @@
-4.3.1p1
+4.3.1p3
diff --git a/src/sage/libs/singular/decl.pxd b/src/sage/libs/singular/decl.pxd
index 8e3ac314b6..747a6b1e2f 100644
--- a/src/sage/libs/singular/decl.pxd
+++ b/src/sage/libs/singular/decl.pxd
@@ -574,7 +574,7 @@ cdef extern from "singular/Singular/libsingular.h":
# gets a component out of a polynomial vector
- poly *pTakeOutComp1(poly **, int)
+ poly *pTakeOutComp(poly **, int)
# deep copy p
diff --git a/src/sage/libs/singular/singular.pyx b/src/sage/libs/singular/singular.pyx
index d8ea7b07f3..368ee09d50 100644
--- a/src/sage/libs/singular/singular.pyx
+++ b/src/sage/libs/singular/singular.pyx
@@ -1726,20 +1726,17 @@ cdef int overflow_check(unsigned long e, ring *_ring) except -1:
Whether an overflow occurs or not partially depends
on the number of variables in the ring. See trac ticket
- :trac:`11856`. With Singular 4, it is by default optimized
- for at least 4 variables on 64-bit and 2 variables on 32-bit,
- which in both cases makes a maximal default exponent of
- 2^16-1.
+ :trac:`11856`.
EXAMPLES::
sage: P.<x,y> = QQ[]
- sage: y^(2^16-1)
- y^65535
- sage: y^2^16
+ sage: y^(2^30)
+ y^1073741824
+ sage: y^2^32
Traceback (most recent call last):
...
- OverflowError: exponent overflow (65536)
+ OverflowError: exponent overflow (4294967296)
"""
if unlikely(e > _ring.bitmask):
raise OverflowError("exponent overflow (%d)"%(e))
diff --git a/src/sage/rings/polynomial/multi_polynomial_ideal.py b/src/sage/rings/polynomial/multi_polynomial_ideal.py
index 7dc058a22f..71494eddbc 100644
--- a/src/sage/rings/polynomial/multi_polynomial_ideal.py
+++ b/src/sage/rings/polynomial/multi_polynomial_ideal.py
@@ -60,7 +60,7 @@ We compute in a quotient of a polynomial ring over `\ZZ/17\ZZ`::
Note that the result of a computation is not necessarily reduced::
sage: (a+b)^17
- 256*a*b^16 + 256*b^17
+ a*b^16 + b^17
sage: S(17) == 0
True
diff --git a/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx b/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx
index 4dad016b33..1003c45d97 100644
--- a/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx
+++ b/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx
@@ -193,7 +193,7 @@ from sage.libs.singular.decl cimport (
p_IsUnit, p_IsOne, p_Series, p_Head, idInit, fast_map_common_subexp, id_Delete,
p_IsHomogeneous, p_Homogen, p_Totaldegree,pLDeg1_Totaldegree, singclap_pdivide, singclap_factorize,
idLift, IDELEMS, On, Off, SW_USE_CHINREM_GCD, SW_USE_EZGCD,
- p_LmIsConstant, pTakeOutComp1, singclap_gcd, pp_Mult_qq, p_GetMaxExp,
+ p_LmIsConstant, pTakeOutComp, singclap_gcd, pp_Mult_qq, p_GetMaxExp,
pLength, kNF, p_Neg, p_Minus_mm_Mult_qq, p_Plus_mm_Mult_qq,
pDiff, singclap_resultant, p_Normalize,
prCopyR, prCopyR_NoSort)
@@ -1587,7 +1587,7 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_base):
9/4
sage: P.monomial_quotient(x,y) # Note the wrong result
- x*y^65535*z^65535
+ x*y^1048575*z^1048575
sage: P.monomial_quotient(x,P(1))
x
@@ -2247,7 +2247,7 @@ cdef class MPolynomial_libsingular(MPolynomial):
9/4*x^2 - 1/4*y^2 - y - 1
sage: P.<x,y> = PolynomialRing(QQ,order='lex')
- sage: (x^2^15) * x^2^15
+ sage: (x^2^32) * x^2^32
Traceback (most recent call last):
...
OverflowError: exponent overflow (...)
@@ -2371,7 +2371,7 @@ cdef class MPolynomial_libsingular(MPolynomial):
ValueError: not a 2nd power
sage: P.<x,y> = PolynomialRing(QQ,order='lex')
- sage: (x+y^2^15)^10
+ sage: (x+y^2^32)^10
Traceback (most recent call last):
....
OverflowError: exponent overflow (...)
@@ -3452,16 +3452,16 @@ cdef class MPolynomial_libsingular(MPolynomial):
We are catching overflows::
sage: R.<x,y> = QQ[]
- sage: n=100; f = x^n
+ sage: n=10000; f = x^n
sage: try:
....: f.subs(x = x^n)
....: print("no overflow")
....: except OverflowError:
....: print("overflow")
- x^10000
+ x^100000000
no overflow
- sage: n = 1000
+ sage: n = 100000
sage: try:
....: f = x^n
....: f.subs(x = x^n)
@@ -4567,7 +4567,7 @@ cdef class MPolynomial_libsingular(MPolynomial):
l = []
for i from 0 <= i < IDELEMS(res):
for j from 1 <= j <= IDELEMS(_I):
- l.append( new_MP(parent, pTakeOutComp1(&res.m[i], j)) )
+ l.append( new_MP(parent, pTakeOutComp(&res.m[i], 1)) )
id_Delete(&fI, r)
id_Delete(&_I, r)
@@ -4635,7 +4635,7 @@ cdef class MPolynomial_libsingular(MPolynomial):
sage: f = 3*x
sage: f.reduce([2*x,y])
- 3*x
+ x
The reduction is not canonical when ``I`` is not a Groebner
basis::
diff --git a/src/sage/rings/polynomial/plural.pyx b/src/sage/rings/polynomial/plural.pyx
index 1c9f35e56b..587511c388 100644
--- a/src/sage/rings/polynomial/plural.pyx
+++ b/src/sage/rings/polynomial/plural.pyx
@@ -1619,10 +1619,10 @@ cdef class NCPolynomial_plural(RingElement):
sage: P = A.g_algebra(relations={y*x:-x*y + z}, order='lex')
sage: P.inject_variables()
Defining x, z, y
- sage: (x^2^15) * x^2^15
+ sage: (x^2^31) * x^2^31
Traceback (most recent call last):
...
- OverflowError: exponent overflow (65536)
+ OverflowError: exponent overflow (2147483648)
"""
# all currently implemented rings are commutative
cdef poly *_p
@@ -1689,10 +1689,10 @@ cdef class NCPolynomial_plural(RingElement):
sage: P = A.g_algebra(relations={y*x:-x*y + z}, order='lex')
sage: P.inject_variables()
Defining x, z, y
- sage: (x+y^2^15)^10
+ sage: (x+y^2^31)^10
Traceback (most recent call last):
....
- OverflowError: exponent overflow (327680)
+ OverflowError: exponent overflow (2147483648)
"""
if type(exp) is not Integer:
try:
diff --git a/src/sage/structure/element.pyx b/src/sage/structure/element.pyx
index b5d83ef71b..f1dc37cad0 100644
--- a/src/sage/structure/element.pyx
+++ b/src/sage/structure/element.pyx
@@ -2705,10 +2705,10 @@ cdef class RingElement(ModuleElement):
with Singular 4::
sage: K.<x,y> = ZZ[]
- sage: (x^12345)^54321
+ sage: (x^123456)^654321
Traceback (most recent call last):
...
- OverflowError: exponent overflow (670592745)
+ OverflowError: exponent overflow (80779853376)
"""
return arith_generic_power(self, n)
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