@@ -790,8 +790,8 @@ class ComplexBallField(UniqueRepresentation, sage.rings.abc.ComplexBallField):
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sage: ( x^ 4 - 1/3) . roots( multiplicities=False) # indirect doctest
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[[-0.759835685651593 +/- ...e-16 ] + [+/- ...e-16 ]* I,
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[0.759835685651593 +/- ...e-16 ] + [+/- ...e-16 ]* I,
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- [+/- ...e-16 ] + [0.759835685651593 +/- ...e-16 ]* I,
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- [+/- ...e-16 ] + [- 0.759835685651593 +/- ...e-16 ]* I]
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+ [+/- ...e-16 ] + [- 0.759835685651593 +/- ...e-16 ]* I,
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+ [+/- ...e-16 ] + [0.759835685651593 +/- ...e-16 ]* I]
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sage: ( x^ 4 - 1/3) . roots( RBF, multiplicities=False)
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[[-0.759835685651593 +/- ...e-16 ], [0.759835685651593 +/- ...e-16 ]]
@@ -803,8 +803,8 @@ class ComplexBallField(UniqueRepresentation, sage.rings.abc.ComplexBallField):
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sage: ( x^ 4 - 3) . roots( ComplexIntervalField( 100) , multiplicities=False)
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[-1.31607401295249246081921890180? + 0.?e-37*I,
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1.31607401295249246081921890180? + 0.?e-37*I,
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- 0.?e-37 + 1.31607401295249246081921890180?*I,
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- 0.?e-37 - 1.31607401295249246081921890180?*I ]
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+ 0.?e-37 - 1.31607401295249246081921890180?*I,
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+ 0.?e-37 + 1.31607401295249246081921890180?*I ]
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sage: ( x^ 2 - i/3) . roots( ComplexBallField( 2) , multiplicities=False)
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[[+/- 0.409 ] + [+/- 0.409 ]* I, [+/- 0.409 ] + [+/- 0.409 ]* I]
@@ -817,8 +817,8 @@ class ComplexBallField(UniqueRepresentation, sage.rings.abc.ComplexBallField):
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sage: (( x - 1) ^ 2) . roots( multiplicities=False, proof=False)
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doctest:...
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UserWarning: roots may have been lost...
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- [[1.00000000000 +/- ...e-12 ] + [+/- ...e-11 ]* I,
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- [1.0000000000 +/- ...e-12 ] + [+/- ...e-12 ]* I]
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+ [[1.000000000... +/- ... ] + [+/- ... ]* I,
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+ [1.000000000... +/- ... ] + [+/- ... ]* I]
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sage: pol = x^ 7 - 2* ( 1000* x - 1) ^ 2 # Mignotte polynomial
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sage: pol. roots( multiplicities=False)
@@ -843,7 +843,8 @@ class ComplexBallField(UniqueRepresentation, sage.rings.abc.ComplexBallField):
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sage: (( x - 1) ^ 2 + 2^ ( -70) * i/3) . roots( RBF, multiplicities=False)
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Traceback ( most recent call last) :
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...
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- ValueError: unable to determine which roots are real
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+ ValueError: unable to isolate the roots ( try using proof=False or
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+ increasing the precision)
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TESTS::
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@@ -4199,14 +4200,14 @@ cdef class ComplexBall(RingElement):
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EXAMPLES::
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- sage: CBF(1, 1).Ei()
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- [1.76462598556385 +/- ...e -15] + [2.38776985151052 +/- ...e -15]*I
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+ sage: CBF(1, 1).Ei() # abs tol 6e-15
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+ [1.76462598556385 +/- 6.03e -15] + [2.38776985151052 +/- 4.23e -15]*I
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sage: CBF(0).Ei()
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- nan
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+ nan...
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TESTS:
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- sage: CBF(Ei(I)) # abs tol 1e-16 # needs sage.symbolic
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+ sage: CBF(Ei(I)) # abs tol 2e-15 # needs sage.symbolic
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[0.337403922900968 +/- 3.76e-16] + [2.51687939716208 +/- 2.01e-15]*I
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"""
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cdef ComplexBall result = self ._new()
@@ -4221,14 +4222,14 @@ cdef class ComplexBall(RingElement):
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EXAMPLES::
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- sage: CBF(1, 1).Si()
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- [1.10422265823558 +/- ...e -15] + [0.88245380500792 +/- ...e -15]*I
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+ sage: CBF(1, 1).Si() # abs tol 3e-15
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+ [1.10422265823558 +/- 2.48e -15] + [0.88245380500792 +/- 3.36e -15]*I
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sage: CBF(0).Si()
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0
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TESTS:
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- sage: CBF(Si(I)) # needs sage.symbolic
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+ sage: CBF(Si(I)) # abs tol 3e-15 # needs sage.symbolic
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[1.05725087537573 +/- 2.77e-15]*I
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"""
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cdef ComplexBall result = self ._new()
@@ -4245,14 +4246,14 @@ cdef class ComplexBall(RingElement):
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EXAMPLES::
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- sage: CBF(1, 1).Ci()
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- [0.882172180555936 +/- ...e -16] + [0.287249133519956 +/- ...e -16]*I
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+ sage: CBF(1, 1).Ci() # abs tol 5e-16
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+ [0.882172180555936 +/- 5.89e -16] + [0.287249133519956 +/- 3.37e -16]*I
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sage: CBF(0).Ci()
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nan + nan*I
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TESTS:
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- sage: CBF(Ci(I)) # abs tol 1e-17 # needs sage.symbolic
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+ sage: CBF(Ci(I)) # abs tol 5e-16 # needs sage.symbolic
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[0.837866940980208 +/- 4.72e-16] + [1.570796326794897 +/- 5.54e-16]*I
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"""
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cdef ComplexBall result = self ._new()
@@ -4269,8 +4270,8 @@ cdef class ComplexBall(RingElement):
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EXAMPLES::
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- sage: CBF(1, 1).Shi()
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- [0.88245380500792 +/- ...e -15] + [1.10422265823558 +/- ...e -15]*I
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+ sage: CBF(1, 1).Shi() # abs tol 3e-15
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+ [0.88245380500792 +/- 3.36e -15] + [1.10422265823558 +/- 2.48e -15]*I
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sage: CBF(0).Shi()
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0
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@@ -4293,14 +4294,14 @@ cdef class ComplexBall(RingElement):
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EXAMPLES::
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- sage: CBF(1, 1).Chi()
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- [0.882172180555936 +/- ...e -16] + [1.28354719327494 +/- ...e -15]*I
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+ sage: CBF(1, 1).Chi() # abs tol 1e-15
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+ [0.882172180555936 +/- 5.89e -16] + [1.28354719327494 +/- 1.01e -15]*I
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sage: CBF(0).Chi()
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nan + nan*I
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TESTS:
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- sage: CBF(Chi(I)) # abs tol 1e -16 # needs sage.symbolic
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+ sage: CBF(Chi(I)) # abs tol 5e -16 # needs sage.symbolic
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[0.337403922900968 +/- 3.25e-16] + [1.570796326794897 +/- 5.54e-16]*I
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"""
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cdef ComplexBall result = self ._new()
@@ -4319,8 +4320,8 @@ cdef class ComplexBall(RingElement):
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EXAMPLES::
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- sage: CBF(1, 1).li()
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- [0.61391166922120 +/- ...e -15] + [2.05958421419258 +/- ...e -15]*I
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+ sage: CBF(1, 1).li() # abs tol 6e-15
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+ [0.61391166922120 +/- 6.23e -15] + [2.05958421419258 +/- 5.59e -15]*I
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sage: CBF(0).li()
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sage: CBF(0).li(offset=True)
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