disable abs_integrate buggy module of maxima

Author: fchapoton

src/sage/calculus/desolvers.py

@@ -542,7 +542,7 @@ def desolve(de, dvar, ics=None, ivar=None, show_method=False, contrib_ode=False,
         sage: forget()
         sage: y = function('y')(x)
         sage: desolve(diff(y, x) == sqrt(abs(y)), dvar=y, ivar=x)
-        sqrt(-y(x))*(sgn(y(x)) - 1) + (sgn(y(x)) + 1)*sqrt(y(x)) == _C + x
+        integrate(1/sqrt(abs(y(x))), y(x)) == _C + x
 
     AUTHORS:
 

src/sage/functions/piecewise.py

@@ -793,7 +793,7 @@ def integral(self, parameters, variable, x=None, a=None, b=None, definite=False)
                 sage: f.integral(definite=True)
                 2
                 sage: f.integral()
-                piecewise(x|-->-1/2*((sgn(x) - 1)*e^(2*x) - 2*e^x*sgn(x) + sgn(x) + 1)*e^(-x) - 1 on (-oo, +oo); x)
+                piecewise(x|-->-integrate(e^(-abs(x)), x, x, +Infinity) on (-oo, +oo); x)
 
             ::
 

src/sage/interfaces/maxima_lib.py

@@ -170,7 +170,7 @@
 
 init_code = ['besselexpand : true', 'display2d : false', 'domain : complex', 'keepfloat : true',
             'load(to_poly_solve)', 'load(simplify_sum)',
-            'load(abs_integrate)', 'load(diag)']
+            'load(diag)']
 
 
 # Turn off the prompt labels, since computing them *very
@@ -725,7 +725,7 @@ def sr_integral(self,*args):
 
         ::
 
-            sage: integrate(sgn(x) - sgn(1-x), x)
+            sage: integrate(sgn(x) - sgn(1-x), x)  # known bug
             abs(x - 1) + abs(x)
 
         This is a known bug in Sage symbolic limits code, see
@@ -736,12 +736,12 @@ def sr_integral(self,*args):
 
         ::
 
-            sage: integrate(1/(1 + abs(x)), x)
+            sage: integrate(1/(1 + abs(x)), x)  # known bug
             1/2*(log(x + 1) + log(-x + 1))*sgn(x) + 1/2*log(x + 1) - 1/2*log(-x + 1)
 
         ::
 
-            sage: integrate(cos(x + abs(x)), x)
+            sage: integrate(cos(x + abs(x)), x)  # known bug
             -1/2*x*sgn(x) + 1/4*(sgn(x) + 1)*sin(2*x) + 1/2*x
 
         The last example relies on the following simplification::
@@ -752,7 +752,7 @@ def sr_integral(self,*args):
         An example from sage-support thread e641001f8b8d1129::
 
             sage: f = e^(-x^2/2)/sqrt(2*pi) * sgn(x-1)
-            sage: integrate(f, x, -Infinity, Infinity)
+            sage: integrate(f, x, -Infinity, Infinity)  # known bug
             -erf(1/2*sqrt(2))
 
         From :trac:`8624`::
@@ -762,12 +762,12 @@ def sr_integral(self,*args):
 
         ::
 
-            sage: integrate(sqrt(x + sqrt(x)), x).canonicalize_radical()
+            sage: integrate(sqrt(x + sqrt(x)), x).canonicalize_radical()  # known bug
             1/12*((8*x - 3)*x^(1/4) + 2*x^(3/4))*sqrt(sqrt(x) + 1) + 1/8*log(sqrt(sqrt(x) + 1) + x^(1/4)) - 1/8*log(sqrt(sqrt(x) + 1) - x^(1/4))
 
         And :trac:`11594`::
 
-            sage: integrate(abs(x^2 - 1), x, -2, 2)
+            sage: integrate(abs(x^2 - 1), x, -2, 2)  # known bug
             4
 
         This definite integral returned zero (incorrectly) in at least
@@ -777,24 +777,6 @@ def sr_integral(self,*args):
             sage: integrate(f, (x, -infinity, infinity))
             1/3*pi^2
 
-        Sometimes one needs different simplification settings, such as
-        ``radexpand``, to compute an integral (see :trac:`10955`)::
-
-            sage: f = sqrt(x + 1/x^2)
-            sage: maxima = sage.calculus.calculus.maxima
-            sage: maxima('radexpand')
-            true
-            sage: integrate(f, x)
-            integrate(sqrt(x + 1/x^2), x)
-            sage: maxima('radexpand: all')
-            all
-            sage: g = integrate(f, x); g
-            2/3*sqrt(x^3 + 1) - 1/3*log(sqrt(x^3 + 1) + 1) + 1/3*log(sqrt(x^3 + 1) - 1)
-            sage: (f - g.diff(x)).canonicalize_radical()
-            0
-            sage: maxima('radexpand: true')
-            true
-
         The following integral was computed incorrectly in versions of
         Maxima before 5.27 (see :trac:`12947`)::
 

src/sage/symbolic/integration/integral.py

@@ -804,6 +804,17 @@ def integrate(expression, v=None, a=None, b=None, algorithm=None, hold=False):
         275.510983763312
         sage: a.imag_part()    # abs tol 1e-13
         0.0
+
+    This used to be solved by the ``abs_integrate`` Maxima package
+    but can be solved now without it::
+
+        sage: integrate(abs(x), x)
+        1/2*x*abs(x)
+        sage: integral(abs(cos(x))*sin(x),(x,pi/2,pi))
+        1/2
+        sage: f = (x^2)*exp(x) / (1+exp(x))^2
+        sage: integrate(f, (x, -infinity, infinity))
+        1/3*pi^2
     """
     expression, v, a, b = _normalize_integral_input(expression, v, a, b)
     if algorithm is not None: