Use the faster libgiac interface for "giac" integration

src/sage/calculus/calculus.py

@@ -387,6 +387,7 @@
 Ensure that :issue:`25626` is fixed. As the form of the answer is dependent of
 the giac version, we simplify it (see :issue:`34037`). ::
 
+    sage: # needs sage.libs.giac
     sage: t = SR.var('t')
     sage: integrate(exp(t)/(t + 1)^2, t, algorithm='giac').full_simplify()
     ((t + 1)*Ei(t + 1) - e^(t + 1))/(t*e + e)

src/sage/functions/piecewise.py

@@ -827,6 +827,7 @@ def integral(self, parameters, variable, x=None, a=None, b=None, definite=False,
 
             Check that the algorithm keyword can be used::
 
+                sage: # needs sage.libs.giac
                 sage: ex = piecewise([([0, 1], 1), ((1, oo), 1/x**2)])
                 sage: integral(ex, x, 0, 100, algorithm='giac')
                 199/100

src/sage/symbolic/integration/external.py

@@ -214,53 +214,13 @@ def fricas_integrator(expression, v, a=None, b=None, noPole=True):
     return result
 
 
-def giac_integrator(expression, v, a=None, b=None):
-    r"""
-    Integration using Giac.
-
-    EXAMPLES::
-
-        sage: from sage.symbolic.integration.external import giac_integrator
-        sage: giac_integrator(sin(x), x)
-        -cos(x)
-        sage: giac_integrator(1/(x^2+6), x, -oo, oo)
-        1/6*sqrt(6)*pi
-
-    TESTS::
-
-        sage: giac_integrator(e^(-x^2)*log(x), x)
-        integrate(e^(-x^2)*log(x), x)
-
-    Check that :issue:`30133` is fixed::
-
-        sage: ee = SR.var('e')
-        sage: giac_integrator(ee^x, x)
-        e^x/log(e)
-        sage: y = SR.var('π')
-        sage: giac_integrator(cos(y), y)
-        sin(π)
-
-    Check that :issue:`29966` is fixed::
-
-        sage: giac_integrator(sqrt(x + sqrt(x)), x)
-        1/12*(2*sqrt(x)*(4*sqrt(x) + 1) - 3)*sqrt(x + sqrt(x))...
-    """
-    ex = expression._giac_()
-    if a is None:
-        result = ex.integrate(v._giac_())
-    else:
-        result = ex.integrate(v._giac_(), a._giac_(), b._giac_())
-    if 'integrate' in format(result) or 'integration' in format(result):
-        return expression.integrate(v, a, b, hold=True)
-    return result._sage_()
-
-
 def libgiac_integrator(expression, v, a=None, b=None):
     r"""
     Integration using libgiac.
 
     EXAMPLES::
 
+        sage: # needs sage.libs.giac
         sage: import sage.libs.giac
         ...
         sage: from sage.symbolic.integration.external import libgiac_integrator
@@ -272,12 +232,14 @@ def libgiac_integrator(expression, v, a=None, b=None):
 
     TESTS::
 
+        sage: # needs sage.libs.giac
         sage: libgiac_integrator(e^(-x^2)*log(x), x)
         integrate(e^(-x^2)*log(x), x)
 
     The following integral fails with the Giac Pexpect interface, but works
     with libgiac (:issue:`31873`)::
 
+        sage: # needs sage.libs.giac
         sage: a, x = var('a,x')
         sage: f = sec(2*a*x)
         sage: F = libgiac_integrator(f, x)

src/sage/symbolic/integration/integral.py

@@ -28,7 +28,7 @@
 available_integrators['sympy'] = external.sympy_integrator
 available_integrators['mathematica_free'] = external.mma_free_integrator
 available_integrators['fricas'] = external.fricas_integrator
-available_integrators['giac'] = external.giac_integrator
+available_integrators['giac'] = external.libgiac_integrator
 available_integrators['libgiac'] = external.libgiac_integrator
 
 ######################################################
@@ -59,6 +59,7 @@ def __init__(self):
 
         Check for :issue:`28913`::
 
+            sage: # needs sage.libs.giac
             sage: Ex = (1-2*x^(1/3))^(3/4)/x
             sage: integrate(Ex, x, algorithm='giac')  # long time
             4*(-2*x^(1/3) + 1)^(3/4) + 6*arctan((-2*x^(1/3) + 1)^(1/4)) - 3*log((-2*x^(1/3) + 1)^(1/4) + 1) + 3*log(abs((-2*x^(1/3) + 1)^(1/4) - 1))
@@ -200,6 +201,7 @@ def __init__(self):
 
         Check for :issue:`32354`::
 
+            sage: # needs sage.libs.giac
             sage: ex = 1/max_symbolic(x, 1)**2
             sage: integral(ex, x, 0, 2, algorithm='giac')
             3/2
@@ -467,9 +469,9 @@ def integrate(expression, v=None, a=None, b=None, algorithm=None, hold=False):
 
       - ``'fricas'`` -- use FriCAS (the optional fricas spkg has to be installed)
 
-      - ``'giac'`` -- use Giac
+      - ``'giac'`` -- use libgiac
 
-      - ``'libgiac'`` -- use libgiac
+      - ``'libgiac'`` -- use libgiac (alias for ``'giac'``)
 
     To prevent automatic evaluation, use the ``hold`` argument.
 
@@ -690,6 +692,7 @@ def integrate(expression, v=None, a=None, b=None, algorithm=None, hold=False):
 
     Using Giac to integrate the absolute value of a trigonometric expression::
 
+        sage: # needs sage.libs.giac
         sage: integrate(abs(cos(x)), x, 0, 2*pi, algorithm='giac')
         4
         sage: result = integrate(abs(cos(x)), x, 0, 2*pi)