17407: more fixes

Author: rwst

src/sage/rings/ideal.py

@@ -965,8 +965,8 @@ def category(self):
         EXAMPLES::
 
             sage: I = ZZ.ideal(7)
-            sage: J = ZZ['x'].ideal(7,x)
-            sage: K = ZZ['x'].ideal(7)
+            sage: J = ZZ[x].ideal(7,x)
+            sage: K = ZZ[x].ideal(7)
             sage: I.category()
             Category of ring ideals in Integer Ring
             sage: J.category()

src/sage/rings/polynomial/polynomial_element.pyx

@@ -6860,7 +6860,7 @@ cdef do_karatsuba_different_size(left, right, Py_ssize_t K_threshold):
 
     Here, we use Fibonacci numbers that need deepest recursion in this method.
 
-        sage: K = ZZ[x]
+        sage: K = ZZ['x']
         sage: f = K.random_element(21)
         sage: g = K.random_element(34)
         sage: f*g - f._mul_karatsuba(g,0)

src/sage/rings/polynomial/polynomial_number_field.pyx

@@ -102,10 +102,10 @@ class Polynomial_absolute_number_field_dense(Polynomial_generic_dense_field):
 
         EXAMPLES::
 
-            sage: f = QQ[I]['x'].random_element()
+            sage: f = QQ[I][x].random_element()
             sage: type(f)
             <class 'sage.rings.polynomial.polynomial_number_field.Polynomial_absolute_number_field_dense'>
-            sage: a = QQ[I]['x'](x)
+            sage: a = QQ[I][x](x)
             sage: a.is_gen()
             True
         """
@@ -150,7 +150,7 @@ class Polynomial_absolute_number_field_dense(Polynomial_generic_dense_field):
             sage: x = var('x')
             sage: N = NumberField(x-3, 'a')
             sage: a = N.gen()
-            sage: R = N[x]
+            sage: R = N['x']
             sage: f = R.random_element()
             sage: g1 = R.random_element()
             sage: g2 = g1*R.random_element() + 1
@@ -234,7 +234,7 @@ class Polynomial_relative_number_field_dense(Polynomial_generic_dense_field):
 
         EXAMPLES::
 
-            sage: f = NumberField([x^2-2, x^2-3], 'a')[x].random_element()
+            sage: f = NumberField([x^2-2, x^2-3], 'a')['x'].random_element()
             sage: type(f)
             <class 'sage.rings.polynomial.polynomial_number_field.Polynomial_relative_number_field_dense'>
         """
@@ -275,7 +275,7 @@ class Polynomial_relative_number_field_dense(Polynomial_generic_dense_field):
         TESTS::
 
             sage: x = var('x')
-            sage: R = NumberField([x^2-2, x^2-3], 'a')[x]
+            sage: R = NumberField([x^2-2, x^2-3], 'a')['x']
             sage: f = R.random_element()
             sage: g1 = R.random_element()
             sage: g2 = R.random_element()*g1+1
@@ -286,7 +286,7 @@ class Polynomial_relative_number_field_dense(Polynomial_generic_dense_field):
 
         Test for degree one extensions::
 
-            sage: R = NumberField([x-2,x+1,x-3],'a')[x]
+            sage: R = NumberField([x-2,x+1,x-3],'a')['x']
             sage: f = R.random_element(2)
             sage: g1 = R.random_element(2)
             sage: g2 = R.random_element(2)*g1+1

src/sage/rings/ring.pyx

@@ -1518,7 +1518,7 @@ cdef class IntegralDomain(CommutativeRing):
 
         EXAMPLES::
 
-            sage: ZZ.is_integral_domain(); QQ.is_integral_domain(); ZZ[x].is_integral_domain()
+            sage: ZZ.is_integral_domain(); QQ.is_integral_domain(); ZZ['x'].is_integral_domain()
             True
             True
             True

src/sage/tests/french_book/mpoly.py

@@ -270,7 +270,7 @@
 
   sage: R.<x,y,t> = QQ[]
   sage: eq = x^2 + (y-t)^2 - 1/2*(t^2+1)
-  sage: fig = add((eq(t=k/5)*QQ['x,y']).plot() for k in (-15..15))
+  sage: fig = add((eq(t=k/5)*QQ[x,y]).plot() for k in (-15..15))
   sage: fig.show(aspect_ratio=1,xmin=-2,xmax=2,ymin=-3,ymax=3)
 
 Sage example in ./mpoly.tex, line 900::

src/sage/tests/french_book/polynomes.py

@@ -48,7 +48,7 @@
 
 Sage example in ./polynomes.tex, line 162::
 
-  sage: x = polygen(QQ); y = polygen(QQ['x'], 'y')
+  sage: x = polygen(QQ); y = polygen(QQ[x], 'y')
   sage: p = x^3 + x*y + y + y^2; p
   y^2 + (x + 1)*y + x^3
   sage: q = QQ['x,y'](p); q