doctest fixes

src/doc/en/prep/Calculus.rst

@@ -308,7 +308,7 @@ help it look nicer in the browser?
 ::
 
     sage: integrate(1/(1+x^5),x)
-    1/5*sqrt(5)*(sqrt(5) + 1)*arctan((4*x + sqrt(5) - 1)/sqrt(2*sqrt(5) + 10))/sqrt(2*sqrt(5) + 10) + 1/5*sqrt(5)*(sqrt(5) - 1)*arctan((4*x - sqrt(5) - 1)/sqrt(-2*sqrt(5) + 10))/sqrt(-2*sqrt(5) + 10) - 1/2*(sqrt(5) + 3)*log(2*x^2 - x*(sqrt(5) + 1) + 2)/(5*sqrt(5) + 5) - 1/2*(sqrt(5) - 3)*log(2*x^2 + x*(sqrt(5) - 1) + 2)/(5*sqrt(5) - 5) + 1/5*log(x + 1)
+    1/5*sqrt(5)*(sqrt(5) + 1)*arctan((4*x + sqrt(5) - 1)/sqrt(2*sqrt(5) + 10))/sqrt(2*sqrt(5) + 10) + 1/5*sqrt(5)*(sqrt(5) - 1)*arctan((4*x - sqrt(5) - 1)/sqrt(-2*sqrt(5) + 10))/sqrt(-2*sqrt(5) + 10) - 1/10*(sqrt(5) + 3)*log(2*x^2 - x*(sqrt(5) + 1) + 2)/(sqrt(5) + 1) - 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.  If Sage doesn't know the
 whole antiderivative, it returns as much of it as it (more properly, as

src/sage/schemes/elliptic_curves/ell_generic.py

@@ -385,7 +385,7 @@ def _symbolic_(self, SR):
             0
 
             sage: 2*w
-            (-2*pi + (2*pi - 3*pi^2 + 10)^2/(-40*pi + 4*pi^3 - 4*pi^2 - 79) + 1 : (3*pi - (2*pi - 3*pi^2 + 10)^2/(-40*pi + 4*pi^3 - 4*pi^2 - 79) - 1)*(2*pi - 3*pi^2 + 10)/sqrt(-40*pi + 4*pi^3 - 4*pi^2 - 79) + 1/2*sqrt(-40*pi + 4*pi^3 - 4*pi^2 - 79) - 1/2 : 1)
+            (-2*pi - (2*pi - 3*pi^2 + 10)^2/(40*pi - 4*pi^3 + 4*pi^2 + 79) + 1 : (3*pi + (2*pi - 3*pi^2 + 10)^2/(40*pi - 4*pi^3 + 4*pi^2 + 79) - 1)*(2*pi - 3*pi^2 + 10)/sqrt(-40*pi + 4*pi^3 - 4*pi^2 - 79) + 1/2*sqrt(-40*pi + 4*pi^3 - 4*pi^2 - 79) - 1/2 : 1)
 
             sage: x, y, z = 2*w; temp = ((y^2 + y) - (x^3 - x^2 - 10*x - 20))
 

src/sage/symbolic/expression.pyx

@@ -3579,22 +3579,6 @@ cdef class Expression(CommutativeRingElement):
 
         TESTS::
 
-            sage: (Mod(2,7)*x^2 + Mod(2,7))^7
-            (2*x^2 + 2)^7
-
-        The leading coefficient in the result above is 1 since::
-
-            sage: t = Mod(2,7); gcd(t, t)^7
-            1
-            sage: gcd(t,t).parent()
-            Ring of integers modulo 7
-
-        ::
-
-            sage: k = GF(7)
-            sage: f = expand((k(1)*x^5 + k(1)*x^2 + k(2))^7); f
-            x^35 + x^14 + 2
-
             sage: x^oo
             Traceback (most recent call last):
             ...
@@ -4310,6 +4294,20 @@ cdef class Expression(CommutativeRingElement):
 
             sage: ((x+sqrt(2)*x)^2).expand()
             2*sqrt(2)*x^2 + 3*x^2
+
+        Check that exactness is preserved::
+
+            sage: ((x+1.001)^2).expand()
+            x^2 + 2.00200000000000*x + 1.00200100000000
+            sage: ((x+1.001)^3).expand()
+            x^3 + 3.00300000000000*x^2 + 3.00600300000000*x + 1.00300300100000
+
+        Check that :trac:`21302` is fixed::
+
+            sage: ((x+1)^-2).expand()
+            1/(x^2 + 2*x + 1)
+            sage: (((x-1)/(x+1))^2).expand()
+            x^2/(x^2 + 2*x + 1) - 2*x/(x^2 + 2*x + 1) + 1/(x^2 + 2*x + 1)
         """
         if side is not None:
             if not is_a_relational(self._gobj):
@@ -5808,8 +5806,8 @@ cdef class Expression(CommutativeRingElement):
 
         The behaviour is undefined with noninteger or negative exponents::
 
-            sage: p = (17/3*a)*x^(3/2) + x*y + 1/x + x^x + 5*x^y
-            sage: rset = set([(1, -1), (y, 1), (17/3*a, 3/2), (x^x, 0), (5, y)])
+            sage: p = (17/3*a)*x^(3/2) + x*y + 1/x + 2*x^x + 5*x^y
+            sage: rset = set([(1, -1), (y, 1), (17/3*a, 3/2), (2, x), (5, y)])
             sage: all([(pair[0],pair[1]) in rset for pair in p.coefficients(x)])
             True
             sage: p.coefficients(x, sparse=False)
@@ -5846,6 +5844,12 @@ cdef class Expression(CommutativeRingElement):
             sage: f.coefficients(g)
             [[t, 0], [3, 1], [1, 2]]
 
+        Handle bound variable strictly as part of a constant::
+
+            sage: (sin(1+x)*sin(1+x^2)).coefficients(x)
+            [[sin(x^2 + 1)*sin(x + 1), 0]]
+            sage: (sin(1+x)*sin(1+x^2)*x).coefficients(x)
+            [[sin(x^2 + 1)*sin(x + 1), 1]]
         """
         cdef vector[pair[GEx,GEx]] vec
         cdef pair[GEx,GEx] gexpair

src/sage/tensor/differential_form_element.py

@@ -312,9 +312,9 @@ class DifferentialForm(AlgebraElement):
         sage: form2
         1/log(y)*dz + dx + e^cos(x)*dy
         sage: d(form2)
-        -(1/y)/log(y)^2*dy/\dz + -e^cos(x)*sin(x)*dx/\dy
+        -1/(y*log(y)^2)*dy/\dz + -e^cos(x)*sin(x)*dx/\dy
         sage: form2.diff()
-        -(1/y)/log(y)^2*dy/\dz + -e^cos(x)*sin(x)*dx/\dy
+        -1/(y*log(y)^2)*dy/\dz + -e^cos(x)*sin(x)*dx/\dy
         sage: d(form1) == form1.diff()
         True