Trac 16908: fix doctests

src/doc/de/tutorial/tour_algebra.rst

@@ -212,7 +212,7 @@ Lösung: Berechnen Sie die Laplace-Transformierte der ersten Gleichung
 
     sage: de1 = maxima("2*diff(x(t),t, 2) + 6*x(t) - 2*y(t)")
     sage: lde1 = de1.laplace("t","s"); lde1
-    2*(-?%at('diff(x(t),t,1),t=0)+s^2*'laplace(x(t),t,s)-x(0)*s)-2*'laplace(y(t),t,s)+6*'laplace(x(t),t,s)
+    2*(-%at('diff(x(t),t,1),t=0)+s^2*'laplace(x(t),t,s)-x(0)*s)-2*'laplace(y(t),t,s)+6*'laplace(x(t),t,s)
 
 Das ist schwierig zu lesen, es besagt jedoch, dass
 
@@ -228,7 +228,7 @@ Laplace-Transformierte der zweiten Gleichung:
 
     sage: de2 = maxima("diff(y(t),t, 2) + 2*y(t) - 2*x(t)")
     sage: lde2 = de2.laplace("t","s"); lde2
-    -?%at('diff(y(t),t,1),t=0)+s^2*'laplace(y(t),t,s)+2*'laplace(y(t),t,s)-2*'laplace(x(t),t,s)-y(0)*s
+    -%at('diff(y(t),t,1),t=0)+s^2*'laplace(y(t),t,s)+2*'laplace(y(t),t,s)-2*'laplace(x(t),t,s)-y(0)*s
 
 Dies besagt
 

src/doc/en/constructions/calculus.rst

@@ -116,7 +116,7 @@ The Maclaurin and power series of
     sage: [bernoulli(2*i) for i in range(1,7)]
     [1/6, -1/30, 1/42, -1/30, 5/66, -691/2730]
     sage: maxima(f).powerseries(x,0)    # TODO: write this without maxima
-    'sum((-1)^i2*2^(2*i2-1)*bern(2*i2)*_SAGE_VAR_x^(2*i2)/(i2*factorial(2*i2)),i2,1,inf)
+    'sum((-1)^i3*2^(2*i3-1)*bern(2*i3)*_SAGE_VAR_x^(2*i3)/(i3*factorial(2*i3)),i3,1,inf)
 
 .. index::
    pair: calculus; integration

src/doc/en/tutorial/tour_algebra.rst

@@ -206,7 +206,7 @@ the notation :math:`x=x_{1}`, :math:`y=x_{2}`):
 
     sage: de1 = maxima("2*diff(x(t),t, 2) + 6*x(t) - 2*y(t)")
     sage: lde1 = de1.laplace("t","s"); lde1
-    2*(-?%at('diff(x(t),t,1),t=0)+s^2*'laplace(x(t),t,s)-x(0)*s)-2*'laplace(y(t),t,s)+6*'laplace(x(t),t,s)
+    2*(-%at('diff(x(t),t,1),t=0)+s^2*'laplace(x(t),t,s)-x(0)*s)-2*'laplace(y(t),t,s)+6*'laplace(x(t),t,s)
 
 This is hard to read, but it says that
 
@@ -221,7 +221,7 @@ Laplace transform of the second equation:
 
     sage: de2 = maxima("diff(y(t),t, 2) + 2*y(t) - 2*x(t)")
     sage: lde2 = de2.laplace("t","s"); lde2
-    -?%at('diff(y(t),t,1),t=0)+s^2*'laplace(y(t),t,s)+2*'laplace(y(t),t,s)-2*'laplace(x(t),t,s)-y(0)*s
+    -%at('diff(y(t),t,1),t=0)+s^2*'laplace(y(t),t,s)+2*'laplace(y(t),t,s)-2*'laplace(x(t),t,s)-y(0)*s
 
 This says
 

src/doc/fr/tutorial/tour_algebra.rst

@@ -183,7 +183,7 @@ Solution : Considérons la transformée de Laplace de la première équation
 
     sage: de1 = maxima("2*diff(x(t),t, 2) + 6*x(t) - 2*y(t)")
     sage: lde1 = de1.laplace("t","s"); lde1
-    2*(-?%at('diff(x(t),t,1),t=0)+s^2*'laplace(x(t),t,s)-x(0)*s)-2*'laplace(y(t),t,s)+6*'laplace(x(t),t,s)
+    2*(-%at('diff(x(t),t,1),t=0)+s^2*'laplace(x(t),t,s)-x(0)*s)-2*'laplace(y(t),t,s)+6*'laplace(x(t),t,s)
 
 La réponse n'est pas très lisible, mais elle signifie que
 
@@ -198,7 +198,7 @@ la seconde équation :
 
     sage: de2 = maxima("diff(y(t),t, 2) + 2*y(t) - 2*x(t)")
     sage: lde2 = de2.laplace("t","s"); lde2
-    -?%at('diff(y(t),t,1),t=0)+s^2*'laplace(y(t),t,s)+2*'laplace(y(t),t,s)-2*'laplace(x(t),t,s)-y(0)*s
+    -%at('diff(y(t),t,1),t=0)+s^2*'laplace(y(t),t,s)+2*'laplace(y(t),t,s)-2*'laplace(x(t),t,s)-y(0)*s
 
 Ceci signifie
 

src/doc/ru/tutorial/tour_algebra.rst

@@ -200,7 +200,7 @@ Sage может использоваться для решения диффер
 
     sage: de1 = maxima("2*diff(x(t),t, 2) + 6*x(t) - 2*y(t)")
     sage: lde1 = de1.laplace("t","s"); lde1
-    2*(-?%at('diff(x(t),t,1),t=0)+s^2*'laplace(x(t),t,s)-x(0)*s)-2*'laplace(y(t),t,s)+6*'laplace(x(t),t,s)
+    2*(-%at('diff(x(t),t,1),t=0)+s^2*'laplace(x(t),t,s)-x(0)*s)-2*'laplace(y(t),t,s)+6*'laplace(x(t),t,s)
 
 Данный результат тяжело читаем, однако должен быть понят как
 
@@ -212,7 +212,7 @@ Sage может использоваться для решения диффер
 
     sage: de2 = maxima("diff(y(t),t, 2) + 2*y(t) - 2*x(t)")
     sage: lde2 = de2.laplace("t","s"); lde2
-    -?%at('diff(y(t),t,1),t=0)+s^2*'laplace(y(t),t,s)+2*'laplace(y(t),t,s)-2*'laplace(x(t),t,s)-y(0)*s
+    -%at('diff(y(t),t,1),t=0)+s^2*'laplace(y(t),t,s)+2*'laplace(y(t),t,s)-2*'laplace(x(t),t,s)-y(0)*s
 
 Результат:
 

src/sage/calculus/calculus.py

@@ -762,7 +762,7 @@ def nintegral(ex, x, a, b,
     Now numerically integrating, we see why the answer is wrong::
 
         sage: f.nintegrate(x,0,1)
-        (-480.00000000000006, 5.329070518200754e-12, 21, 0)
+        (-480.0000000000001, 5.329070518200754e-12, 21, 0)
 
     It is just because every floating point evaluation of return -480.0
     in floating point.

src/sage/calculus/tests.py

@@ -109,7 +109,7 @@
     sage: integrate(exp(1-x^2),x)
     1/2*sqrt(pi)*erf(x)*e
     sage: integrate(sin(x^2),x)
-    1/8*sqrt(pi)*((I + 1)*sqrt(2)*erf((1/2*I + 1/2)*sqrt(2)*x) + (I - 1)*sqrt(2)*erf((1/2*I - 1/2)*sqrt(2)*x))
+    1/16*sqrt(pi)*((I + 1)*sqrt(2)*erf((1/2*I + 1/2)*sqrt(2)*x) + (I - 1)*sqrt(2)*erf((1/2*I - 1/2)*sqrt(2)*x) - (I - 1)*sqrt(2)*erf(sqrt(-I)*x) + (I + 1)*sqrt(2)*erf((-1)^(1/4)*x))
 
     sage: integrate((1-x^2)^n,x)
     integrate((-x^2 + 1)^n, x)

src/sage/functions/special.py

@@ -303,11 +303,11 @@ def _maxima_init_evaled_(self, *args):
         TESTS:
 
         Check if complex numbers in the arguments are converted to maxima
-        correctly :trac:`7557`::
+        correctly (see :trac:`7557`)::
 
             sage: t = f(1.2+2*I*elliptic_kc(1-.5),.5)
-            sage: t._maxima_init_(maxima)
-            '0.88771548861927...*%i'
+            sage: t._maxima_init_(maxima)  # abs tol 1e-13
+            '0.88771548861928029 - 1.7301614091485560e-15*%i'
             sage: t.n() # abs tol 1e-13
             0.887715488619280 - 1.79195288804672e-15*I
 

src/sage/interfaces/maxima.py

@@ -286,7 +286,7 @@
 ::
 
     sage: maxima("laplace(diff(x(t),t,2),t,s)")
-    -?%at('diff(x(t),t,1),t=0)+s^2*'laplace(x(t),t,s)-x(0)*s
+    -%at('diff(x(t),t,1),t=0)+s^2*'laplace(x(t),t,s)-x(0)*s
 
 It is difficult to read some of these without the 2d
 representation::

src/sage/interfaces/maxima_lib.py

@@ -709,16 +709,12 @@ def sr_integral(self,*args):
         ::
 
             sage: integrate(cos(x + abs(x)), x)
-            -1/4*(2*x - sin(2*x))*real_part(sgn(x)) + 1/2*x + 1/4*sin(2*x)
+            -1/2*x*sgn(x) + 1/4*(sgn(x) + 1)*sin(2*x) + 1/2*x
 
-        Note that the last example yielded the same answer in a
-        simpler form in earlier versions of Maxima (<= 5.29.1), namely
-        ``-1/2*x*sgn(x) + 1/4*(sgn(x) + 1)*sin(2*x) + 1/2*x``.  This
-        is because Maxima no longer simplifies ``realpart(signum(x))``
-        to ``signum(x)``::
+        The last example relies on the following simplification::
 
             sage: maxima("realpart(signum(x))")
-            'realpart(signum(x))
+            signum(x)
 
         An example from sage-support thread e641001f8b8d1129::
 
@@ -1067,7 +1063,7 @@ def to_poly_solve(self,vars,options=""):
             sage: from sage.interfaces.maxima_lib import maxima_lib
             sage: sol = maxima_lib(sin(x) == 0).to_poly_solve(x)
             sage: sol.sage()
-            [[x == pi*z54]]
+            [[x == pi*z62]]
         """
         if options.find("use_grobner=true") != -1:
             cmd=EclObject([[max_to_poly_solve], self.ecl(), sr_to_max(vars),

src/sage/symbolic/expression.pyx

@@ -9349,7 +9349,7 @@ cdef class Expression(CommutativeRingElement):
             sage: from sage.calculus.calculus import maxima
             sage: sol = maxima(cos(x)==0).to_poly_solve(x)
             sage: sol.sage()
-            [[x == 1/2*pi + pi*z82]]
+            [[x == 1/2*pi + pi*z90]]
 
         If a returned unsolved expression has a denominator, but the
         original one did not, this may also be true::

src/sage/symbolic/integration/integral.py

@@ -236,8 +236,6 @@ def _print_latex_(self, f, x, a, b):
             sage: f = function('f')
             sage: print_latex(f(x),x,0,1)
             '\\int_{0}^{1} f\\left(x\\right)\\,{d x}'
-            sage: latex(integrate(1/(1+sqrt(x)),x,0,1))
-            \int_{0}^{1} \frac{1}{\sqrt{x} + 1}\,{d x}
         """
         from sage.misc.latex import latex
         if not is_SymbolicVariable(x):
@@ -456,7 +454,7 @@ def integrate(expression, v=None, a=None, b=None, algorithm=None):
                  x y  + Sqrt[--] FresnelS[Sqrt[--] x]
                              2                 Pi
         sage: print f.integral(x)
-        x*y^z + 1/8*sqrt(pi)*((I + 1)*sqrt(2)*erf((1/2*I + 1/2)*sqrt(2)*x) + (I - 1)*sqrt(2)*erf((1/2*I - 1/2)*sqrt(2)*x))
+        x*y^z + 1/16*sqrt(pi)*((I + 1)*sqrt(2)*erf((1/2*I + 1/2)*sqrt(2)*x) + (I - 1)*sqrt(2)*erf((1/2*I - 1/2)*sqrt(2)*x) - (I - 1)*sqrt(2)*erf(sqrt(-I)*x) + (I + 1)*sqrt(2)*erf((-1)^(1/4)*x))
 
     Alternatively, just use algorithm='mathematica_free' to integrate via Mathematica
     over the internet (does NOT require a Mathematica license!)::
@@ -590,12 +588,11 @@ def integrate(expression, v=None, a=None, b=None, algorithm=None):
         ...
         ValueError: invalid input (x, 1, 2, 3) - please use variable, with or without two endpoints
 
-    Note that this used to be the test, but it is
-    actually divergent (though Maxima as yet does
-    not say so)::
+    Note that this used to be the test, but it is actually divergent
+    (though Maxima currently returns the principal value)::
 
         sage: integrate(t*cos(-theta*t),(t,-oo,oo))
-        integrate(t*cos(t*theta), t, -Infinity, +Infinity)
+        0
 
     Check if :trac:`6189` is fixed::
 

src/sage/symbolic/relation.py

@@ -615,7 +615,7 @@ def solve(f, *args, **kwds):
     be implicitly an integer (hence the ``z``)::
 
         sage: solve([cos(x)*sin(x) == 1/2, x+y == 0],x,y)
-        [[x == 1/4*pi + pi*z80, y == -1/4*pi - pi*z80]]
+        [[x == 1/4*pi + pi*z88, y == -1/4*pi - pi*z88]]
 
     Expressions which are not equations are assumed to be set equal
     to zero, as with `x` in the following example::