gh-38770: Add "needs" tags for giac and libgiac
    
Part of #38668. If it's going to
be possible to disable giac, we need to guard all of the tests that use
it with either `# needs giac` or `# needs sage.libs.giac`.

I think I've gotten them all. A crude way to test:

1. `git rm -r src/sage/libs/giac` and rebuild to disable sage.libs.giac
2. build sage, and then delete the giac executable to disable the
pexpect interface

If you do these one at a time, it should ensure that the correct tags
are used. (Typically, if giac is missing, neither sage.libs.giac nor the
giac executable will be present, making it very easy to mix up the
tags.)

For bonus points you can undelete `src/sage/libs/giac` after building
but before testing to make sure the "needs" tags in those files are
accurate.

### Dependencies:

* #38756
* #38686 (not strictly required,
but it adds a few "needs sage.libs.giac" tags of its own)
    
URL: #38770
Reported by: Michael Orlitzky
Reviewer(s): Tobias Diez

Author: Release Manager

src/doc/en/prep/Calculus.rst

@@ -316,8 +316,9 @@ help it look nicer in the browser?
     - 1/10*(sqrt(5) - 3)*log(2*x^2 + x*(sqrt(5) - 1) + 2)/(sqrt(5) - 1)
     + 1/5*log(x + 1)
 
-Some integrals are a little tricky, of course. Sage tries hard to integrate using Maxima, Giac and Sympy::
+Some integrals are a little tricky, of course. Sage tries hard to integrate using Maxima, Sympy, and (optionally, if installed) Giac. The following can only be integrated by Giac::
 
+    sage: # needs sage.libs.giac
     sage: integral(1/(1+x^10),x)
     ...1/20*(sqrt(5) + 1)*arctan((4*x + sqrt(-2*sqrt(5) + 10))/(sqrt(5) + 1))
     + 1/20*(sqrt(5) + 1)*arctan((4*x - sqrt(-2*sqrt(5) + 10))/(sqrt(5) + 1))

src/sage/calculus/calculus.py

@@ -385,7 +385,7 @@
     2*pi
 
 Ensure that :issue:`25626` is fixed. As the form of the answer is dependent of
-the giac version, we simplify it (see :issue:`34037`). ::
+the giac version, we simplify it (see :issue:`34037`)::
 
     sage: t = SR.var('t')
     sage: integrate(exp(t)/(t + 1)^2, t, algorithm='giac').full_simplify()
@@ -568,6 +568,7 @@ def symbolic_sum(expression, v, a, b, algorithm='maxima', hold=False):
 
     An example of this summation with Giac::
 
+        sage: # needs giac
         sage: symbolic_sum(1/(1+k^2), k, -oo, oo, algorithm='giac').factor()
         pi*(e^(2*pi) + 1)/((e^pi + 1)*(e^pi - 1))
 
@@ -843,7 +844,7 @@ def symbolic_product(expression, v, a, b, algorithm='maxima', hold=False):
 
       - ``'maxima'`` -- use Maxima (the default)
 
-      - ``'giac'`` -- use Giac
+      - ``'giac'`` -- use Giac (optional)
 
       - ``'sympy'`` -- use SymPy
 
@@ -1296,7 +1297,7 @@ def limit(ex, dir=None, taylor=False, algorithm='maxima', **argv):
 
     With the standard package Giac::
 
-        sage: from sage.libs.giac.giac import libgiac     # random
+        sage: # needs sage.libs.giac
         sage: (exp(-x)/(2+sin(x))).limit(x=oo, algorithm='giac')
         0
         sage: limit(e^(-1/x), x=0, dir='right', algorithm='giac')
@@ -1564,7 +1565,7 @@ def laplace(ex, t, s, algorithm='maxima'):
 
       - ``'sympy'`` -- use SymPy
 
-      - ``'giac'`` -- use Giac
+      - ``'giac'`` -- use Giac (optional)
 
     .. NOTE::
 
@@ -1668,7 +1669,7 @@ def laplace(ex, t, s, algorithm='maxima'):
         (0, True)
         sage: F        # random - sympy <1.9 includes undefined heaviside(0) in answer
         1
-        sage: laplace(dirac_delta(t), t, s, algorithm='giac')
+        sage: laplace(dirac_delta(t), t, s, algorithm='giac')  # needs giac
         1
 
     Heaviside step function can be handled with different interfaces.
@@ -1677,8 +1678,9 @@ def laplace(ex, t, s, algorithm='maxima'):
         sage: laplace(heaviside(t-1), t, s)
         e^(-s)/s
 
-    Try with giac::
+    Try with giac, if it is installed::
 
+        sage: # needs giac
         sage: laplace(heaviside(t-1), t, s, algorithm='giac')
         e^(-s)/s
 
@@ -1691,6 +1693,7 @@ def laplace(ex, t, s, algorithm='maxima'):
 
     Testing Giac::
 
+        sage: # needs giac
         sage: var('t, s')
         (t, s)
         sage: laplace(5*cos(3*t-2)*heaviside(t-2), t, s, algorithm='giac')
@@ -1699,13 +1702,14 @@ def laplace(ex, t, s, algorithm='maxima'):
     Check unevaluated expression from Giac (it is locale-dependent, see
     :issue:`22833`)::
 
-        sage: var('n')
-        n
+        sage: # needs giac
+        sage: n = SR.var('n')
         sage: laplace(t^n, t, s, algorithm='giac')
         laplace(t^n, t, s)
 
     Testing SymPy::
 
+        sage: n = SR.var('n')
         sage: F, a, cond = laplace(t^n, t, s, algorithm='sympy')
         sage: a, cond
         (0, re(n) > -1)
@@ -1806,7 +1810,7 @@ def inverse_laplace(ex, s, t, algorithm='maxima'):
 
       - ``'sympy'`` -- use SymPy
 
-      - ``'giac'`` -- use Giac
+      - ``'giac'`` -- use Giac (optional)
 
     .. SEEALSO::
 
@@ -1843,11 +1847,13 @@ def inverse_laplace(ex, s, t, algorithm='maxima'):
 
     The same instance with Giac::
 
+        sage: # needs giac
         sage: inverse_laplace(1/s^2*exp(-s), s, t, algorithm='giac')
         (t - 1)*heaviside(t - 1)
 
     Transform a rational expression::
 
+        sage: # needs giac
         sage: inverse_laplace((2*s^2*exp(-2*s) - exp(-s))/(s^3+1), s, t,
         ....:                 algorithm='giac')
         -1/3*(sqrt(3)*e^(1/2*t - 1/2)*sin(1/2*sqrt(3)*(t - 1))
@@ -1864,7 +1870,7 @@ def inverse_laplace(ex, s, t, algorithm='maxima'):
         dirac_delta(t)
         sage: inverse_laplace(1, s, t, algorithm='sympy')
         dirac_delta(t)
-        sage: inverse_laplace(1, s, t, algorithm='giac')
+        sage: inverse_laplace(1, s, t, algorithm='giac')  # needs giac
         dirac_delta(t)
 
     TESTS:
@@ -1878,6 +1884,7 @@ def inverse_laplace(ex, s, t, algorithm='maxima'):
 
     Testing Giac::
 
+        sage: # needs giac
         sage: inverse_laplace(exp(-s)/s, s, t, algorithm='giac')
         heaviside(t - 1)
 
@@ -1888,12 +1895,14 @@ def inverse_laplace(ex, s, t, algorithm='maxima'):
 
     Testing unevaluated expression from Giac::
 
-        sage: n = var('n')
+        sage: # needs giac
+        sage: n = SR.var('n')
         sage: inverse_laplace(1/s^n, s, t, algorithm='giac')
         ilt(1/(s^n), t, s)
 
     Try with Maxima::
 
+        sage: n = SR.var('n')
         sage: inverse_laplace(1/s^n, s, t, algorithm='maxima')
         ilt(1/(s^n), s, t)
 
@@ -1909,6 +1918,7 @@ def inverse_laplace(ex, s, t, algorithm='maxima'):
 
     Testing the same with Giac::
 
+        sage: # needs giac
         sage: inverse_laplace(cos(s), s, t, algorithm='giac')
         ilt(cos(s), t, s)
     """
@@ -2472,13 +2482,18 @@ def _find_var(name, interface=None):
 
     EXAMPLES::
 
-        sage: y = var('y')
+        sage: y = SR.var('y')
         sage: sage.calculus.calculus._find_var('y')
         y
         sage: sage.calculus.calculus._find_var('I')
         I
         sage: sage.calculus.calculus._find_var(repr(maxima(y)), interface='maxima')
         y
+
+    ::
+
+        sage: # needs giac
+        sage: y = SR.var('y')
         sage: sage.calculus.calculus._find_var(repr(giac(y)), interface='giac')
         y
     """
@@ -2585,6 +2600,7 @@ def symbolic_expression_from_string(s, syms=None, accept_sequence=False, *, pars
 
     The Giac interface uses a different parser (:issue:`30133`)::
 
+        sage: # needs giac
         sage: from sage.calculus.calculus import SR_parser_giac
         sage: symbolic_expression_from_string(repr(giac(SR.var('e'))), parser=SR_parser_giac)
         e

src/sage/calculus/functional.py

@@ -53,7 +53,7 @@ def simplify(f, algorithm='maxima', **kwds):
         sage: ex = 1/2*I*x + 1/2*I*sqrt(x^2 - 1) + 1/2/(I*x + I*sqrt(x^2 - 1))
         sage: simplify(ex)
         1/2*I*x + 1/2*I*sqrt(x^2 - 1) + 1/(2*I*x + 2*I*sqrt(x^2 - 1))
-        sage: simplify(ex, algorithm='giac')
+        sage: simplify(ex, algorithm='giac')  # needs giac
         I*sqrt(x^2 - 1)
     """
     try:

src/sage/functions/exp_integral.py

@@ -800,7 +800,7 @@ def __init__(self):
             Si(x)
             sage: sin_integral(x)._fricas_init_()
             'Si(x)'
-            sage: sin_integral(x)._giac_()                                              # needs sage.libs.giac
+            sage: sin_integral(x)._giac_()                                              # needs giac
             Si(sageVARx)
         """
         BuiltinFunction.__init__(self, "sin_integral", nargs=1,
@@ -975,7 +975,7 @@ def __init__(self):
             Ci(x)
             sage: cos_integral(x)._fricas_init_()
             'Ci(x)'
-            sage: cos_integral(x)._giac_()                                              # needs sage.libs.giac
+            sage: cos_integral(x)._giac_()                                              # needs giac
             Ci(sageVARx)
         """
         BuiltinFunction.__init__(self, "cos_integral", nargs=1,

src/sage/functions/generalized.py

@@ -253,7 +253,7 @@ def __init__(self):
             H\left(x\right)
             sage: heaviside(x)._sympy_()                                                # needs sympy
             Heaviside(x)
-            sage: heaviside(x)._giac_()                                                 # needs sage.libs.giac
+            sage: heaviside(x)._giac_()                                                 # needs giac
             Heaviside(sageVARx)
             sage: h(x) = heaviside(x)
             sage: h(pi).numerical_approx()
@@ -413,7 +413,7 @@ class FunctionSignum(BuiltinFunction):
         sign(x)
         sage: sgn(x)._fricas_init_()                                                    # needs sage.symbolic
         '(x+->abs(x)/x)(x)'
-        sage: sgn(x)._giac_()                                                           # needs sage.libs.giac sage.symbolic
+        sage: sgn(x)._giac_()                                                           # needs giac sage.symbolic
         sign(sageVARx)
 
     Test for :issue:`31085`::

src/sage/functions/other.py

@@ -1860,7 +1860,7 @@ def __init__(self):
             sage: isinstance(r.operator(),      # known bug                             # needs sympy
             ....:     sage.functions.other.Function_prod)
             True
-            sage: giac(sprod(m, m, 1, n)).sage()
+            sage: giac(sprod(m, m, 1, n)).sage()  # needs giac
             factorial(n)
         """
         BuiltinFunction.__init__(self, "product", nargs=4,

src/sage/functions/piecewise.py

@@ -1470,16 +1470,18 @@ def _giac_init_(self, parameters, variable):
 
             EXAMPLES::
 
+                sage: # needs giac
                 sage: ex = piecewise([((0, 1), pi), ([1, 2], x)])
-                sage: f = ex._giac_(); f                                                # needs sage.libs.giac
+                sage: f = ex._giac_(); f
                 piecewise(((sageVARx>0) and (1>sageVARx)),pi,((sageVARx>=1) and (2>=sageVARx)),sageVARx)
-                sage: f.diff(x)                                                         # needs sage.libs.giac
+                sage: f.diff(x)
                 piecewise(((sageVARx>0) and (1>sageVARx)),0,((sageVARx>=1) and (2>=sageVARx)),1)
 
-                sage: ex = piecewise([((-100, -2), 1/x), ((1, +oo), cos(x))])           # needs sage.libs.giac
-                sage: g = ex._giac_(); g                                                # needs sage.libs.giac
+                sage: # needs giac
+                sage: ex = piecewise([((-100, -2), 1/x), ((1, +oo), cos(x))])
+                sage: g = ex._giac_(); g
                 piecewise(((sageVARx>-100) and ((-2)>sageVARx)),1/sageVARx,sageVARx>1,cos(sageVARx))
-                sage: g.diff(x)                                                         # needs sage.libs.giac
+                sage: g.diff(x)
                 piecewise(((sageVARx>-100) and ((-2)>sageVARx)),-1/sageVARx^2,sageVARx>1,-sin(sageVARx))
 
             TESTS::

src/sage/interfaces/giac.py

@@ -1,3 +1,4 @@
+# sage.doctest: needs giac
 r"""
 Pexpect Interface to Giac
 

src/sage/interfaces/interface.py

@@ -275,7 +275,7 @@ def __call__(self, x, name=None):
 
         Check conversion of Booleans (:issue:`28705`)::
 
-            sage: giac(True)
+            sage: giac(True)  # needs giac
             true
             sage: maxima(True)
             true
@@ -343,7 +343,7 @@ def _coerce_impl(self, x, use_special=True):
 
         Check that python type ``complex`` can be converted (:issue:`31775`)::
 
-            sage: giac(complex(I))**2  # should not return `j^2`
+            sage: giac(complex(I))**2  # should not return `j^2`  # needs giac
             -1
         """
         if isinstance(x, bool):
@@ -1196,12 +1196,12 @@ def _repr_(self):
             sage: gap(2)
             2
             sage: x = var('x')
-            sage: giac(x)
+            sage: giac(x)  # needs giac
             sageVARx
-            sage: giac(5)
+            sage: giac(5)  # needs giac
             5
             sage: M = matrix(QQ,2,range(4))
-            sage: giac(M)
+            sage: giac(M)  # needs giac
             [[0,1],[2,3]]
             sage: x = var('x')                  # optional - maple
             sage: maple(x)                      # optional - maple
@@ -1341,7 +1341,7 @@ def __bool__(self):
         By default this returns ``True`` for elements that are considered to be
         not ``False`` by the interface (:issue:`28705`)::
 
-            sage: bool(giac('"a"'))
+            sage: bool(giac('"a"'))  # needs giac
             True
         """
         P = self._check_valid()

src/sage/libs/giac/__init__.py

@@ -1,3 +1,4 @@
+# sage.doctest: needs sage.libs.giac
 """
 Wrappers for Giac functions
 

src/sage/libs/giac/giac.pyx

@@ -1,3 +1,4 @@
+# sage.doctest: needs sage.libs.giac
 # distutils: libraries = giac
 # distutils: language = c++
 # distutils: extra_compile_args = -std=c++11

src/sage/matrix/matrix1.pyx

@@ -216,21 +216,21 @@ cdef class Matrix(Matrix0):
         EXAMPLES::
 
             sage: M = matrix(ZZ, 2, range(4))
-            sage: giac(M)                                                               # needs sage.libs.giac
+            sage: giac(M)                                                               # needs giac
             [[0,1],[2,3]]
 
             sage: M = matrix(QQ, 3, [1,2,3, 4/3,5/3,6/4, 7,8,9])
-            sage: giac(M)                                                               # needs sage.libs.giac
+            sage: giac(M)                                                               # needs giac
             [[1,2,3],[4/3,5/3,3/2],[7,8,9]]
 
             sage: P.<x> = ZZ[]
             sage: M = matrix(P, 2, [-9*x^2-2*x+2, x-1, x^2+8*x, -3*x^2+5])
-            sage: giac(M)                                                               # needs sage.libs.giac
+            sage: giac(M)                                                               # needs giac
             [[-9*sageVARx^2-2*sageVARx+2,sageVARx-1],[sageVARx^2+8*sageVARx,-3*sageVARx^2+5]]
 
             sage: y = var('y')                                                          # needs sage.symbolic
             sage: M = matrix(SR, 2, [y+sin(y), y - 4, 1/y, dilog(y)])                   # needs sage.symbolic
-            sage: giac(M).det().sage()                                                  # needs sage.libs.giac sage.symbolic
+            sage: giac(M).det().sage()                                                  # needs giac sage.symbolic
             (y^2*dilog(y) + y*dilog(y)*sin(y) - y + 4)/y
         """
         s = ','.join('[' + ','.join(cf._giac_init_() for cf in row) + ']'

src/sage/modules/free_module_element.pyx

@@ -1007,20 +1007,20 @@ cdef class FreeModuleElement(Vector):   # abstract base class
         EXAMPLES::
 
             sage: v = vector(ZZ, 4, range(4))
-            sage: giac(v) + v                                                           # needs sage.libs.giac
+            sage: giac(v) + v                                                           # needs giac
             [0,2,4,6]
 
         ::
 
             sage: v = vector(QQ, 3, [2/3, 0, 5/4])
-            sage: giac(v)                                                               # needs sage.libs.giac
+            sage: giac(v)                                                               # needs giac
             [2/3,0,5/4]
 
         ::
 
             sage: P.<x> = ZZ[]
             sage: v = vector(P, 3, [x^2 + 2, 2*x + 1, -2*x^2 + 4*x])
-            sage: giac(v)                                                               # needs sage.libs.giac
+            sage: giac(v)                                                               # needs giac
             [sageVARx^2+2,2*sageVARx+1,-2*sageVARx^2+4*sageVARx]
         """
         return self.list()

src/sage/rings/polynomial/multi_polynomial.pyx

@@ -1114,7 +1114,7 @@ cdef class MPolynomial(CommutativePolynomial):
 
         TESTS::
 
-            sage: # needs sage.libs.giac
+            sage: # needs giac
             sage: R.<x,y,z> = GF(101)['e,i'][]
             sage: f = R('e*i') * x + y^2
             sage: f._giac_init_()