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nixpkgs/pkgs/applications/science/math/sage/patches/pynac-0.7.22.patch
Timo Kaufmann 398dad270a sage, arb: update sage dependencies arb and pynac 
Removes the version pinning for arb and pynac by backporting the
upstream (sage) package upgrades. This necessitates a new patch for arb,
which was however already proposed and accepted upstream.
2018-06-30 17:05:56 +02:00

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diff --git a/src/sage/calculus/calculus.py b/src/sage/calculus/calculus.py
index 3a417d9d5c..fadaadbaf6 100644
--- a/src/sage/calculus/calculus.py
+++ b/src/sage/calculus/calculus.py
@@ -231,7 +231,7 @@ Another example::
sage: f(x=3)
arcsinh(1)
sage: f.derivative(x)
- 1/3/sqrt(1/9*x^2 + 1)
+ 1/sqrt(x^2 + 9)
We compute the length of the parabola from 0 to 2::
@@ -1509,8 +1509,8 @@ def laplace(ex, t, s, algorithm='maxima'):
Testing SymPy::
sage: laplace(t^n, t, s, algorithm='sympy')
- (s^(-n)*gamma(n + 1)/s, 0, -re(n) < 1)
-
+ (gamma(n + 1)/(s*s^n), 0, -re(n) < 1)
+
Testing Maxima::
sage: laplace(t^n, t, s, algorithm='maxima')
diff --git a/src/sage/functions/hypergeometric.py b/src/sage/functions/hypergeometric.py
index 1fc2db5c94..f3e49b9cdb 100644
--- a/src/sage/functions/hypergeometric.py
+++ b/src/sage/functions/hypergeometric.py
@@ -34,7 +34,7 @@ Simplification (note that ``simplify_full`` does not yet call
sage: a.simplify_hypergeometric()
1/((-e^x + 1)^e^x)
sage: a.simplify_hypergeometric(algorithm='sage')
- (-e^x + 1)^(-e^x)
+ 1/((-e^x + 1)^e^x)
Equality testing::
@@ -145,7 +145,7 @@ Series expansions of confluent hypergeometric functions::
sage: hypergeometric_M(2, 2, x).series(x, 3)
1 + 1*x + 1/2*x^2 + Order(x^3)
- sage: hypergeometric_U(2, 2, x).series(x == 3, 100).subs(x=1).n()
+ sage: hypergeometric_U(2, 2, x).series(x == 3, 100).subs(x=1).n() # known bug (see :trac:`25688`)
0.403652637676806
sage: hypergeometric_U(2, 2, 1).n()
0.403652637676806
@@ -773,7 +773,7 @@ def closed_form(hyp):
sage: closed_form(hypergeometric([], [], z))
e^z
sage: closed_form(hypergeometric([a], [], z))
- (-z + 1)^(-a)
+ 1/((-z + 1)^a)
sage: closed_form(hypergeometric([1, 1, 2], [1, 1], z))
(z - 1)^(-2)
sage: closed_form(hypergeometric([2, 3], [1], x))
@@ -1121,7 +1121,7 @@ class Hypergeometric_U(BuiltinFunction):
sage: var('a b z')
(a, b, z)
sage: hypergeometric_U(a, b, z).generalized()
- z^(-a)*hypergeometric((a, a - b + 1), (), -1/z)
+ hypergeometric((a, a - b + 1), (), -1/z)/z^a
sage: hypergeometric_U(1, 3, 1/2).generalized()
2*hypergeometric((1, -1), (), -2)
sage: hypergeometric_U(3, I, 2).generalized()
diff --git a/src/sage/functions/log.py b/src/sage/functions/log.py
index 75d1bf8060..61968582af 100644
--- a/src/sage/functions/log.py
+++ b/src/sage/functions/log.py
@@ -518,17 +518,17 @@ class Function_polylog(GinacFunction):
sage: BF = RealBallField(100)
sage: polylog(2, BF(1/3))
- [0.36621322997706348761674629766 +/- 4.51e-30]
+ [0.36621322997706348761674629766... +/- ...]
sage: polylog(2, BF(4/3))
- nan
+ [2.27001825336107090380391448586 +/- 5.64e-30] + [-0.90377988538400159956755721265 +/- 8.39e-30]*I
sage: parent(_)
- Real ball field with 100 bits of precision
+ Complex ball field with 100 bits of precision
sage: polylog(2, CBF(1/3))
- [0.366213229977063 +/- 5.85e-16]
+ [0.366213229977063 +/- ...]
sage: parent(_)
Complex ball field with 53 bits of precision
sage: polylog(2, CBF(1))
- [1.644934066848226 +/- 6.59e-16]
+ [1.644934066848226 +/- ...]
sage: parent(_)
Complex ball field with 53 bits of precision
"""
diff --git a/src/sage/functions/trig.py b/src/sage/functions/trig.py
index e7e7a311cd..1f2926d6c9 100644
--- a/src/sage/functions/trig.py
+++ b/src/sage/functions/trig.py
@@ -529,13 +529,8 @@ class Function_arcsin(GinacFunction):
arcsin
sage: asin(complex(1,1))
(0.6662394324925152+1.0612750619050357j)
-
- Check that :trac:`22823` is fixed::
-
- sage: bool(asin(SR(2.1)) == NaN)
- True
- sage: asin(SR(2.1)).is_real()
- False
+ sage: asin(SR(2.1))
+ 1.57079632679490 - 1.37285914424258*I
"""
GinacFunction.__init__(self, 'arcsin', latex_name=r"\arcsin",
conversions=dict(maxima='asin', sympy='asin', fricas="asin", giac="asin"))
@@ -595,13 +590,8 @@ class Function_arccos(GinacFunction):
arccos
sage: acos(complex(1,1))
(0.9045568943023814-1.0612750619050357j)
-
- Check that :trac:`22823` is fixed::
-
- sage: bool(acos(SR(2.1)) == NaN)
- True
- sage: acos(SR(2.1)).is_real()
- False
+ sage: acos(SR(2.1))
+ 1.37285914424258*I
"""
GinacFunction.__init__(self, 'arccos', latex_name=r"\arccos",
conversions=dict(maxima='acos', sympy='acos', fricas='acos', giac='acos'))
@@ -807,7 +797,7 @@ class Function_arcsec(GinacFunction):
sage: arcsec(2).n(100)
1.0471975511965977461542144611
sage: arcsec(1/2).n(100)
- NaN
+ 1.3169578969248167086250463473*I
sage: RDF(arcsec(2)) # abs tol 1e-15
1.0471975511965976
sage: arcsec(1 + I)
@@ -958,7 +948,9 @@ class Function_arctan2(GinacFunction):
sage: atan2(0,0,hold=True)
arctan2(0, 0)
sage: atan2(0,0,hold=True).n()
- NaN
+ Traceback (most recent call last):
+ ...
+ RuntimeError: atan2(): division by zero
Check if :trac:`10062` is fixed, this was caused by
``(I*I).is_positive()`` returning ``True``::
diff --git a/src/sage/geometry/hyperbolic_space/hyperbolic_geodesic.py b/src/sage/geometry/hyperbolic_space/hyperbolic_geodesic.py
index 3b5c8d1729..1c6b73a16c 100644
--- a/src/sage/geometry/hyperbolic_space/hyperbolic_geodesic.py
+++ b/src/sage/geometry/hyperbolic_space/hyperbolic_geodesic.py
@@ -1422,8 +1422,10 @@ class HyperbolicGeodesicUHP(HyperbolicGeodesic):
expressions do not generate runtime errors. ::
sage: g=HyperbolicPlane().UHP().get_geodesic(-1+I,1+I)
- sage: g.midpoint()
- Point in UHP 1/2*(sqrt(2)*e^(1/2*arccosh(3)) - sqrt(2) + (I - 1)*e^(1/2*arccosh(3)) + I - 1)/((1/4*I - 1/4)*sqrt(2)*e^(1/2*arccosh(3)) - (1/4*I - 1/4)*sqrt(2) + 1/2*e^(1/2*arccosh(3)) + 1/2)
+ sage: point = g.midpoint(); point
+ Point in UHP -1/2*(sqrt(2)*...
+ sage: QQbar(point.coordinates()).radical_expression()
+ I*sqrt(2)
Check that floating points remain floating points
in :meth:`midpoint` ::
diff --git a/src/sage/interfaces/fricas.py b/src/sage/interfaces/fricas.py
index 82aae78e37..8501ea2a18 100644
--- a/src/sage/interfaces/fricas.py
+++ b/src/sage/interfaces/fricas.py
@@ -1084,14 +1084,14 @@ class FriCASElement(ExpectElement):
0.451026811796262,
0.732815101786507,
0.837981225008390,
- NaN,
- NaN,
+ 1.57079632679490 - 0.467145308103262*I,
+ 0.467145308103262*I,
1.11976951499863,
0.451026811796262,
0.732815101786507,
0.837981225008390,
- NaN,
- NaN]
+ 1.57079632679490 - 0.467145308103262*I,
+ 0.467145308103262*I]
sage: l = [tanh, sinh, cosh, coth, sech, csch, asinh, acosh, atanh, acoth, asech, acsch, arcsinh, arccosh, arctanh, arccoth, arcsech, arccsch]
sage: [f(x)._fricas_().sage().subs(x=0.9) for f in l] # optional - fricas
[0.716297870199024,
diff --git a/src/sage/libs/pynac/pynac.pyx b/src/sage/libs/pynac/pynac.pyx
index 9e9d8f664b..e3406f007e 100644
--- a/src/sage/libs/pynac/pynac.pyx
+++ b/src/sage/libs/pynac/pynac.pyx
@@ -1824,7 +1824,7 @@ cdef py_atan2(x, y):
sage: atan2(CC(I), CC(I+1))
0.553574358897045 + 0.402359478108525*I
sage: atan2(CBF(I), CBF(I+1))
- [0.55357435889705 +/- 5.58e-15] + [0.402359478108525 +/- 7.11e-16]*I
+ [0.55357435889705 +/- ...] + [0.402359478108525 +/- ...]*I
Check that :trac:`23776` is fixed and RDF input gives real output::
diff --git a/src/sage/matrix/matrix_symbolic_dense.pyx b/src/sage/matrix/matrix_symbolic_dense.pyx
index 46a15e53eb..7a0beb437b 100644
--- a/src/sage/matrix/matrix_symbolic_dense.pyx
+++ b/src/sage/matrix/matrix_symbolic_dense.pyx
@@ -200,7 +200,7 @@ cdef class Matrix_symbolic_dense(Matrix_generic_dense):
sage: eval, [evec], mult = es[0]
sage: delta = eval*evec - evec*A
sage: abs(abs(delta)) < 1e-10
- sqrt(9/25*((2*sqrt(6) - 3)*(sqrt(6) - 2) + 7*sqrt(6) - 18)^2 + 9/25*((sqrt(6) - 2)*(sqrt(6) - 4) + 6*sqrt(6) - 14)^2) < (1.00000000000000e-10)
+ 3/5*sqrt(((2*sqrt(6) - 3)*(sqrt(6) - 2) + 7*sqrt(6) - 18)^2 + ((sqrt(6) - 2)*(sqrt(6) - 4) + 6*sqrt(6) - 14)^2) < (1.00000000000000e-10)
sage: abs(abs(delta)).n() < 1e-10
True
diff --git a/src/sage/modules/matrix_morphism.py b/src/sage/modules/matrix_morphism.py
index 17a1d6e290..03892ceec0 100644
--- a/src/sage/modules/matrix_morphism.py
+++ b/src/sage/modules/matrix_morphism.py
@@ -214,9 +214,9 @@ class MatrixMorphism_abstract(sage.categories.morphism.Morphism):
sage: f((1, 0))
Traceback (most recent call last):
...
- TypeError: Unable to coerce entries (=[1.00000000000000*I, 0.000000000000000]) to coefficients in Real Field with 53 bits of precision
+ TypeError: Unable to coerce entries (=[1.00000000000000*I, 0]) to coefficients in Real Field with 53 bits of precision
sage: f((1, 0), coerce=False)
- (1.00000000000000*I, 0.000000000000000)
+ (1.00000000000000*I, 0)
"""
if self.domain().is_ambient():
diff --git a/src/sage/plot/plot.py b/src/sage/plot/plot.py
index 77cdeb8c46..e501e74036 100644
--- a/src/sage/plot/plot.py
+++ b/src/sage/plot/plot.py
@@ -2061,7 +2061,7 @@ def _plot(funcs, xrange, parametric=False,
plot properly (:trac:`13246`)::
sage: parametric_plot((x, arcsec(x)), (x, -2, 2))
- Graphics object consisting of 1 graphics primitive
+ Graphics object consisting of 2 graphics primitives
"""
from sage.plot.colors import Color
diff --git a/src/sage/repl/display/formatter.py b/src/sage/repl/display/formatter.py
index 8ce2e839d7..948207c95e 100644
--- a/src/sage/repl/display/formatter.py
+++ b/src/sage/repl/display/formatter.py
@@ -25,11 +25,11 @@ generally, all sage expression as an ASCII art object::
sage: shell = get_test_shell()
sage: shell.run_cell('%display ascii_art')
sage: shell.run_cell('integral(x^2/pi^x, x)')
- / 2 2 \ -x*log(pi)
- -\x *log (pi) + 2*x*log(pi) + 2/*e
- ---------------------------------------------
- 3
- log (pi)
+ -x / 2 2 \
+ -pi *\x *log (pi) + 2*x*log(pi) + 2/
+ --------------------------------------
+ 3
+ log (pi)
sage: shell.run_cell("i = var('i')")
sage: shell.run_cell('sum(i*x^i, i, 0, 10)')
10 9 8 7 6 5 4 3 2
diff --git a/src/sage/rings/asymptotic/asymptotics_multivariate_generating_functions.py b/src/sage/rings/asymptotic/asymptotics_multivariate_generating_functions.py
index d8ebbf4f76..8c60f65e99 100644
--- a/src/sage/rings/asymptotic/asymptotics_multivariate_generating_functions.py
+++ b/src/sage/rings/asymptotic/asymptotics_multivariate_generating_functions.py
@@ -151,8 +151,8 @@ A multiple point example (Example 6.5 of [RaWi2012]_)::
[(x + 2*y - 1, 1), (2*x + y - 1, 1)])
sage: F1 = decomp[1]
sage: F1.asymptotics(p, alpha, 2)
- (-3*((2*a^2 - 5*a*b + 2*b^2)*r^2 + (a + b)*r + 3)*((1/3)^(-a)*(1/3)^(-b))^r,
- (1/3)^(-a)*(1/3)^(-b), -3*(2*a^2 - 5*a*b + 2*b^2)*r^2 - 3*(a + b)*r - 9)
+ (-3*((2*a^2 - 5*a*b + 2*b^2)*r^2 + (a + b)*r + 3)*(1/((1/3)^a*(1/3)^b))^r,
+ 1/((1/3)^a*(1/3)^b), -3*(2*a^2 - 5*a*b + 2*b^2)*r^2 - 3*(a + b)*r - 9)
sage: alpha = [4, 3]
sage: decomp = F.asymptotic_decomposition(alpha)
sage: F1 = decomp[1]
@@ -2159,7 +2159,7 @@ class FractionWithFactoredDenominator(RingElement):
sage: p = {x: 1/3, y: 1/3}
sage: alpha = (var('a'), var('b'))
sage: F.asymptotics_multiple(p, alpha, 2, var('r')) # long time
- (3*((1/3)^(-a)*(1/3)^(-b))^r*e^(2/3), (1/3)^(-a)*(1/3)^(-b), 3*e^(2/3))
+ (3*(1/((1/3)^a*(1/3)^b))^r*e^(2/3), 1/((1/3)^a*(1/3)^b), 3*e^(2/3))
"""
from itertools import product
from sage.calculus.functions import jacobian
diff --git a/src/sage/stats/basic_stats.py b/src/sage/stats/basic_stats.py
index 16a268a02c..5fd244e93b 100644
--- a/src/sage/stats/basic_stats.py
+++ b/src/sage/stats/basic_stats.py
@@ -183,7 +183,7 @@ def std(v, bias=False):
sage: std([])
NaN
sage: std([I, sqrt(2), 3/5])
- sqrt(1/450*(10*sqrt(2) - 5*I - 3)^2 + 1/450*(5*sqrt(2) - 10*I + 3)^2 + 1/450*(5*sqrt(2) + 5*I - 6)^2)
+ 1/15*sqrt(1/2)*sqrt((10*sqrt(2) - 5*I - 3)^2 + (5*sqrt(2) - 10*I + 3)^2 + (5*sqrt(2) + 5*I - 6)^2)
sage: std([RIF(1.0103, 1.0103), RIF(2)])
0.6998235813403261?
sage: import numpy
diff --git a/src/sage/symbolic/expression.pyx b/src/sage/symbolic/expression.pyx
index ab4c05de3a..60f0dc549a 100644
--- a/src/sage/symbolic/expression.pyx
+++ b/src/sage/symbolic/expression.pyx
@@ -622,7 +622,7 @@ cdef class Expression(CommutativeRingElement):
sage: x^(-5)
x^(-5)
sage: x^(-y)
- x^(-y)
+ 1/(x^y)
sage: 2*x^(-1)
2/x
sage: i*x
@@ -3621,14 +3621,14 @@ cdef class Expression(CommutativeRingElement):
sage: repl_dict = {b_0: b_0, b_3: b_1, b_2: b_3, b_1: b_2}
sage: P = precomp.substitute(repl_dict)
sage: P.expand()
- -2^(-b_0)*2^(-b_2)*2^b_3 - 2^b_0*2^(-b_2)*2^b_3 -
- 2^(-b_0)*2^b_2*2^b_3 + 2^b_0*2^b_2*2^b_3 - 2*2^(-b_0)*2^(-b_2)
- - 2*2^b_0*2^(-b_2) - 2*2^(-b_0)*2^b_2 + 2*2^b_0*2^b_2 +
- 2^(-b_0)*2^b_3 + 2^b_0*2^b_3 + 2^(-b_2)*2^b_3 + 2^b_2*2^b_3 +
- 2*2^(-b_0) + 2*2^b_0 + 2*2^(-b_2) + 2*2^b_2 - 9*2^b_3 -
- 2^(-b_0)*2^(-b_2)/2^b_3 - 2^b_0*2^(-b_2)/2^b_3 -
- 2^(-b_0)*2^b_2/2^b_3 + 2^b_0*2^b_2/2^b_3 + 2^(-b_0)/2^b_3 +
- 2^b_0/2^b_3 + 2^(-b_2)/2^b_3 + 2^b_2/2^b_3 - 9/2^b_3 - 18
+ 2^b_0*2^b_2*2^b_3 + 2*2^b_0*2^b_2 + 2^b_0*2^b_3 + 2^b_2*2^b_3 +
+ 2*2^b_0 + 2*2^b_2 - 9*2^b_3 + 2^b_0*2^b_2/2^b_3 -
+ 2^b_0*2^b_3/2^b_2 - 2^b_2*2^b_3/2^b_0 - 2*2^b_0/2^b_2 -
+ 2*2^b_2/2^b_0 + 2^b_0/2^b_3 + 2^b_2/2^b_3 + 2^b_3/2^b_0 +
+ 2^b_3/2^b_2 + 2/2^b_0 + 2/2^b_2 - 2^b_0/(2^b_2*2^b_3) -
+ 2^b_2/(2^b_0*2^b_3) - 9/2^b_3 - 2^b_3/(2^b_0*2^b_2) -
+ 2/(2^b_0*2^b_2) + 1/(2^b_0*2^b_3) + 1/(2^b_2*2^b_3) -
+ 1/(2^b_0*2^b_2*2^b_3) - 18
sage: _0,b_1,b_2=var('b_0,b_1,b_2')
sage: f = 1/27*b_2^2/(2^b_2)^2 + 1/27*b_1^2/(2^b_1)^2 + \
@@ -3809,7 +3809,7 @@ cdef class Expression(CommutativeRingElement):
sage: x = SR.symbol('x', domain='real')
sage: (x^3)^(1/3)
- (x^3)^(1/3)
+ x
sage: (x^4)^(1/4)
abs(x)
sage: (x^8)^(1/4)
@@ -3872,7 +3872,7 @@ cdef class Expression(CommutativeRingElement):
sage: 2^(x/log(2))
e^x
sage: 2^(-x^2/2/log(2))
- e^(-1/2*x^2)
+ 1/e^(1/2*x^2)
sage: x^(x/log(x))
x^(x/log(x))
sage: assume(x > 0)
@@ -4816,18 +4816,24 @@ cdef class Expression(CommutativeRingElement):
sage: ((x+y)^(x+y)).match(w0^w0)
{$0: x + y}
sage: t = ((a+b)*(a+c)).match((a+w0)*(a+w1))
- sage: t[w0], t[w1]
- (c, b)
+ sage: set([t[w0], t[w1]]) == set([b, c])
+ True
sage: ((a+b)*(a+c)).match((w0+b)*(w0+c))
{$0: a}
sage: t = ((a+b)*(a+c)).match((w0+w1)*(w0+w2))
- sage: t[w0], t[w1], t[w2]
- (a, c, b)
- sage: print(((a+b)*(a+c)).match((w0+w1)*(w1+w2)))
- None
+ sage: t[w0]
+ a
+ sage: set([t[w1], t[w2]]) == set([b, c])
+ True
+ sage: t = ((a+b)*(a+c)).match((w0+w1)*(w1+w2))
+ sage: t[w1]
+ a
+ sage: set([t[w0], t[w2]]) == set([b, c])
+ True
sage: t = (a*(x+y)+a*z+b).match(a*w0+w1)
- sage: t[w0], t[w1]
- (x + y, a*z + b)
+ sage: s = set([t[w0], t[w1]])
+ sage: s == set([x+y, a*z+b]) or s == set([z, a*(x+y)+b])
+ True
sage: print((a+b+c+d+f+g).match(c))
None
sage: (a+b+c+d+f+g).has(c)
@@ -4836,7 +4842,7 @@ cdef class Expression(CommutativeRingElement):
{$0: a + b + d + f + g}
sage: (a+b+c+d+f+g).match(c+g+w0)
{$0: a + b + d + f}
- sage: (a+b).match(a+b+w0)
+ sage: (a+b).match(a+b+w0) # known bug
{$0: 0}
sage: print((a*b^2).match(a^w0*b^w1))
None
@@ -5009,7 +5015,7 @@ cdef class Expression(CommutativeRingElement):
a^3 + b^3 + (x + y)^3
sage: t.subs(w0 == w0^2)
- (x^2 + y^2)^18 + a^16 + b^16
+ a^8 + b^8 + (x^2 + y^2)^6
sage: t.subs(a == b, b == c)
(x + y)^3 + b^2 + c^2
@@ -8392,9 +8398,13 @@ cdef class Expression(CommutativeRingElement):
sage: SR(I).arctan2(1)
arctan2(I, 1)
sage: SR(CDF(0,1)).arctan2(1)
- NaN + +infinity*I
- sage: SR(1).arctan2(CDF(0,1)) # known bug
- 0.7853981633974484 - 19.012501686914433*I
+ Traceback (most recent call last):
+ ...
+ ValueError: power::eval(): division by zero
+ sage: SR(1).arctan2(CDF(0,1))
+ Traceback (most recent call last):
+ ...
+ ValueError: power::eval(): division by zero
sage: arctan2(0,oo)
0
@@ -8656,7 +8666,7 @@ cdef class Expression(CommutativeRingElement):
1/2*I*pi
sage: SR(1/2).arccosh()
arccosh(1/2)
- sage: SR(CDF(1/2)).arccosh() # rel tol 1e-15
+ sage: SR(CDF(1/2)).arccosh() # rel tol 1e-15
1.0471975511965976*I
sage: maxima('acosh(0.5)')
1.04719755119659...*%i
@@ -11687,7 +11697,7 @@ cdef class Expression(CommutativeRingElement):
sage: a.solve(t)
[]
sage: b = a.canonicalize_radical(); b
- -23040.0*(-2.0*e^(1800*t) + 25.0*e^(900*t) - 32.0)*e^(-2400*t)
+ (46080.0*e^(1800*t) - 576000.0*e^(900*t) + 737280.0)*e^(-2400*t)
sage: b.solve(t)
[]
sage: b.solve(t, to_poly_solve=True)
@@ -12163,14 +12173,14 @@ cdef class Expression(CommutativeRingElement):
sage: (n,k,j)=var('n,k,j')
sage: sum(binomial(n,k)*binomial(k-1,j)*(-1)**(k-1-j),k,j+1,n)
- -(-1)^(-j)*sum((-1)^k*binomial(k - 1, j)*binomial(n, k), k, j + 1, n)
+ -(-1)^j*sum((-1)^k*binomial(k - 1, j)*binomial(n, k), k, j + 1, n)
sage: assume(j>-1)
sage: sum(binomial(n,k)*binomial(k-1,j)*(-1)**(k-1-j),k,j+1,n)
1
sage: forget()
sage: assume(n>=j)
sage: sum(binomial(n,k)*binomial(k-1,j)*(-1)**(k-1-j),k,j+1,n)
- -(-1)^(-j)*sum((-1)^k*binomial(k - 1, j)*binomial(n, k), k, j + 1, n)
+ -(-1)^j*sum((-1)^k*binomial(k - 1, j)*binomial(n, k), k, j + 1, n)
sage: forget()
sage: assume(j==-1)
sage: sum(binomial(n,k)*binomial(k-1,j)*(-1)**(k-1-j),k,j+1,n)
@@ -12178,7 +12188,7 @@ cdef class Expression(CommutativeRingElement):
sage: forget()
sage: assume(j<-1)
sage: sum(binomial(n,k)*binomial(k-1,j)*(-1)**(k-1-j),k,j+1,n)
- -(-1)^(-j)*sum((-1)^k*binomial(k - 1, j)*binomial(n, k), k, j + 1, n)
+ -(-1)^j*sum((-1)^k*binomial(k - 1, j)*binomial(n, k), k, j + 1, n)
sage: forget()
Check that :trac:`16176` is fixed::
diff --git a/src/sage/symbolic/relation.py b/src/sage/symbolic/relation.py
index da6f0eef42..4bd65ef572 100644
--- a/src/sage/symbolic/relation.py
+++ b/src/sage/symbolic/relation.py
@@ -895,7 +895,7 @@ def solve(f, *args, **kwds):
sage: (r[0][x], r[0][y])
(2*lambert_w(1/2), 1)
sage: solve(-2*x**3 + 4*x**2 - 2*x + 6 > 0, x, algorithm='sympy')
- [x < (1/6*sqrt(77) + 79/54)^(1/3) + 1/9/(1/6*sqrt(77) + 79/54)^(1/3) + 2/3]
+ [x < 1/3*(1/2)^(1/3)*(9*sqrt(77) + 79)^(1/3) + 2/3*(1/2)^(2/3)/(9*sqrt(77) + 79)^(1/3) + 2/3]
sage: solve(sqrt(2*x^2 - 7) - (3 - x),x,algorithm='sympy')
[x == -8, x == 2]
sage: solve(sqrt(2*x + 9) - sqrt(x + 1) - sqrt(x + 4),x,algorithm='sympy')
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