diff options
Diffstat (limited to 'pkgs/applications/science/math/sage/patches/pynac-0.7.22.patch')
| -rw-r--r-- | pkgs/applications/science/math/sage/patches/pynac-0.7.22.patch | 479 |
1 files changed, 479 insertions, 0 deletions
diff --git a/pkgs/applications/science/math/sage/patches/pynac-0.7.22.patch b/pkgs/applications/science/math/sage/patches/pynac-0.7.22.patch new file mode 100644 index 00000000000..22f274d608d --- /dev/null +++ b/pkgs/applications/science/math/sage/patches/pynac-0.7.22.patch @@ -0,0 +1,479 @@ +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') |