sagemathgh-36152: `sage.rings`: Update `# needs`
    
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URL: sagemath#36152
Reported by: Matthias Köppe
Reviewer(s): Kwankyu Lee, Matthias Köppe

Author: Release Manager

src/sage/rings/abc.pyx

@@ -1,4 +1,4 @@
-# sage.doctest: optional - sage.rings.finite_rings
+# sage.doctest: needs sage.rings.finite_rings
 r"""
 Algebraic closures of finite fields
 

src/sage/rings/algebraic_closure_finite_field.py

@@ -119,7 +119,7 @@ def O(*x, **kwds):
         Traceback (most recent call last):
         ...
         ArithmeticError: O(y) not defined
-        sage: O(x, y)                                                                   # needs sage.symbolic
+        sage: O(x, y)
         Traceback (most recent call last):
         ...
         ArithmeticError: O(x, y) not defined

src/sage/rings/big_oh.py

@@ -1,4 +1,4 @@
-# -*- coding: utf-8 -*-
+# sage.doctest: needs sage.symbolic
 r"""
 C-Finite Sequences
 

src/sage/rings/cfinite_sequence.py

@@ -12,7 +12,7 @@ cdef class CCtoCDF(Map):
             sage: f = CCtoCDF(CC, CDF) # indirect doctest
             sage: f(CC.0)
             1.0*I
-            sage: f(exp(pi*CC.0/4))
+            sage: f(exp(pi*CC.0/4))                                                     # needs sage.symbolic
             0.7071067811865476 + 0.7071067811865475*I
         """
         z = <ComplexDoubleElement>ComplexDoubleElement.__new__(ComplexDoubleElement)

src/sage/rings/complex_arb.pyx

@@ -230,7 +230,7 @@ cdef class ComplexIntervalFieldElement(FieldElement):
             '-2.5000000000000000?*I'
             sage: CIF(1.5).str(base=3)
             '1.1111111111111111111111111111111112?'
-            sage: CIF(1, pi).str(style='brackets')
+            sage: CIF(1, pi).str(style='brackets')                                      # needs sage.symbolic
             '[1.0000000000000000 .. 1.0000000000000000] + [3.1415926535897931 .. 3.1415926535897936]*I'
 
         .. SEEALSO::
@@ -285,16 +285,18 @@ cdef class ComplexIntervalFieldElement(FieldElement):
 
         EXAMPLES::
 
-            sage: sum(plot(CIF(RIF(1/k, 1/k), RIF(-k, k))) for k in [1..10])
+            sage: sum(plot(CIF(RIF(1/k, 1/k), RIF(-k, k))) for k in [1..10])            # needs sage.plot
             Graphics object consisting of 20 graphics primitives
 
         Exact and nearly exact points are still visible::
 
+            sage: # needs sage.plot
             sage: plot(CIF(pi, 1), color='red') + plot(CIF(1, e), color='purple') + plot(CIF(-1, -1))
             Graphics object consisting of 6 graphics primitives
 
         A demonstration that `z \mapsto z^2` acts chaotically on `|z|=1`::
 
+            sage: # needs sage.plot sage.symbolic
             sage: z = CIF(0, 2*pi/1000).exp()
             sage: g = Graphics()
             sage: for i in range(40):
@@ -351,11 +353,11 @@ cdef class ComplexIntervalFieldElement(FieldElement):
             (2.50000000000000, 3.00000000000000)
             (-4.50000000000000, -4.00000000000000)
 
+            sage: # needs sage.symbolic
             sage: z = CIF(RIF(sqrt(2), sqrt(3)), RIF(e, pi))
             sage: a, b, c, d = z.bisection()
             sage: a.intersection(b).intersection(c).intersection(d) == CIF(z.center())
             True
-
             sage: zz = a.union(b).union(c).union(c)
             sage: zz.real().endpoints() == z.real().endpoints()
             True
@@ -399,9 +401,9 @@ cdef class ComplexIntervalFieldElement(FieldElement):
             True
             sage: CIF(-5, 0).sqrt().is_exact()
             False
-            sage: CIF(0, 2*pi).is_exact()
+            sage: CIF(0, 2*pi).is_exact()                                               # needs sage.symbolic
             False
-            sage: CIF(e).is_exact()
+            sage: CIF(e).is_exact()                                                     # needs sage.symbolic
             False
             sage: CIF(1e100).is_exact()
             True
@@ -985,7 +987,7 @@ cdef class ComplexIntervalFieldElement(FieldElement):
         Here a conversion to Maxima happens, which results in a ``TypeError``::
 
             sage: a = CIF(2.3)
-            sage: maxima(a)
+            sage: maxima(a)                                                             # needs sage.symbolic
             Traceback (most recent call last):
             ...
             TypeError
@@ -999,7 +1001,7 @@ cdef class ComplexIntervalFieldElement(FieldElement):
 
         EXAMPLES::
 
-            sage: sage_input(CIF(RIF(e, pi), RIF(sqrt(2), sqrt(3))), verify=True)
+            sage: sage_input(CIF(RIF(e, pi), RIF(sqrt(2), sqrt(3))), verify=True)       # needs sage.symbolic
             # Verified
             CIF(RIF(RR(2.7182818284590451), RR(3.1415926535897936)), RIF(RR(1.4142135623730949), RR(1.7320508075688774)))
             sage: sage_input(ComplexIntervalField(64)(2)^I, preparse=False, verify=True)
@@ -1997,7 +1999,7 @@ cdef class ComplexIntervalFieldElement(FieldElement):
 
             sage: CIF(2, 1).is_NaN()
             False
-            sage: CIF(NaN).is_NaN()
+            sage: CIF(NaN).is_NaN()                                                     # needs sage.symbolic
             True
             sage: (1 / CIF(0, 0)).is_NaN()
             True
@@ -2019,7 +2021,7 @@ cdef class ComplexIntervalFieldElement(FieldElement):
 
         Check that :trac:`17285` is fixed::
 
-            sage: CIF(cos(2/3))
+            sage: CIF(cos(2/3))                                                         # needs sage.symbolic
             0.7858872607769480?
 
         ALGORITHM:
@@ -2061,7 +2063,7 @@ cdef class ComplexIntervalFieldElement(FieldElement):
 
         Check that :trac:`17825` is fixed::
 
-            sage: CIF(sin(2/3))
+            sage: CIF(sin(2/3))                                                         # needs sage.symbolic
             0.618369803069737?
 
         ALGORITHM:

src/sage/rings/complex_conversion.pyx

@@ -304,7 +304,7 @@ def _magma_init_(self, magma):
 
             sage: magma(ComplexIntervalField(100)) # optional - magma # indirect doctest
             Complex field of precision 30
-            sage: floor(RR(log(2**100, 10)))
+            sage: floor(RR(log(2**100, 10)))                                            # needs sage.symbolic
             30
         """
         return "ComplexField(%s : Bits := true)" % self.prec()
@@ -445,7 +445,7 @@ def __call__(self, x=None, im=None, **kwds):
             TypeError: unable to convert '1+I' to real interval
             sage: CIF(2,3)
             2 + 3*I
-            sage: CIF(pi, e)
+            sage: CIF(pi, e)                                                            # needs sage.symbolic
             3.141592653589794? + 2.718281828459046?*I
             sage: ComplexIntervalField(100)(CIF(RIF(2,3)))
             3.?

src/sage/rings/complex_double.pyx

@@ -1195,27 +1195,27 @@ cdef class MPComplexNumber(sage.structure.element.FieldElement):
 
             sage: MPC = MPComplexField()
             sage: a = MPC(2,1)
-            sage: a.__pari__()
+            sage: a.__pari__()                                                          # needs sage.libs.pari
             2.00000000000000 + 1.00000000000000*I
-            sage: pari(a)
+            sage: pari(a)                                                               # needs sage.libs.pari
             2.00000000000000 + 1.00000000000000*I
-            sage: pari(a).type()
+            sage: pari(a).type()                                                        # needs sage.libs.pari
             't_COMPLEX'
-            sage: a = MPC(pi)
-            sage: pari(a)
+            sage: a = MPC(pi)                                                           # needs sage.libs.pari sage.symbolic
+            sage: pari(a)                                                               # needs sage.libs.pari sage.symbolic
             3.14159265358979
-            sage: pari(a).type()
+            sage: pari(a).type()                                                        # needs sage.libs.pari sage.symbolic
             't_REAL'
             sage: a = MPC(-2).sqrt()
-            sage: pari(a)
+            sage: pari(a)                                                               # needs sage.libs.pari
             1.41421356237310*I
 
         The precision is preserved, rounded up to the wordsize::
 
             sage: MPC = MPComplexField(250)
-            sage: MPC(1,2).__pari__().bitprecision()
+            sage: MPC(1,2).__pari__().bitprecision()                                    # needs sage.libs.pari
             256
-            sage: MPC(pi).__pari__().bitprecision()
+            sage: MPC(pi).__pari__().bitprecision()                                     # needs sage.libs.pari
             256
         """
         if mpfr_zero_p(self.value.re):
@@ -1520,7 +1520,7 @@ cdef class MPComplexNumber(sage.structure.element.FieldElement):
             2.23606797749979
             sage: a.__abs__()
             2.23606797749979
-            sage: float(sqrt(2^2 + 1^1))
+            sage: float(sqrt(2^2 + 1^1))                                                # needs sage.symbolic
             2.23606797749979
 
             sage: b = MPC(42,0)
@@ -2192,7 +2192,7 @@ cdef class MPComplexNumber(sage.structure.element.FieldElement):
             sage: a = MPC(1,0)
             sage: a.dilog()
             1.64493406684823
-            sage: float(pi^2/6)
+            sage: float(pi^2/6)                                                         # needs sage.symbolic
             1.6449340668482262
 
         ::