okay.... I made a list of all diff() and derivative() and  
differentiate() functions that we should probably be caring about for  
this issue. The list does not include aliases.


functions/elementary.py
     class ElementaryFunction_class(CommutativeRingElement):
         def differentiate(self,verbose=None):

interfaces/maxima.py
     class MaximaElement(ExpectElement):
         def diff(self, var='x', n=1):

calculus/calculus.py
     class SymbolicExpression(RingElement):
         def derivative(self, *args):

     class Symbolic_object(SymbolicExpression):
         #def derivative(self, *args):

calculus/functional.py
     def derivative(f, *args, **kwds):

functions/piecewise.py
     class PiecewisePolynomial:
         def derivative(self):

rings/polynomial/polynomial_modn_dense_ntl.pyx
     cdef class Polynomial_dense_mod_n(Polynomial):
         def diff(self, variable, have_ring=False):

rings/polynomial/multi_polynomial_libsingular.pyx
     cdef class MPolynomial_libsingular 
(sage.rings.polynomial.multi_polynomial.MPolynomial):
         def diff(self, MPolynomial_libsingular variable,  
have_ring=True):

rings/polynomial/polynomial_singular_interface.py
     class Polynomial_singular_repr:
         def diff(self, variable, have_ring=False):

misc/functional.py
     def derivative(x):

rings/laurent_series_ring_element.pyx
     cdef class LaurentSeries(AlgebraElement):
         def derivative(self):

rings/polynomial/polynomial_element.pyx
     cdef class Polynomial(CommutativeAlgebraElement):
         def derivative(self):

rings/polynomial/polynomial_element_generic.py
     class Polynomial_generic_sparse(Polynomial):
         def derivative(self):

rings/polynomial/polynomial_modn_dense_ntl.pyx
     cdef class Polynomial_dense_mod_n(Polynomial):
         def derivative(self):
     cdef class Polynomial_dense_modn_ntl_zz(Polynomial_dense_mod_n):
         def derivative(self):

rings/power_series_poly.pyx
     cdef class PowerSeries_poly(PowerSeries):
         def derivative(self):

rings/power_series_ring_element.pyx
     cdef class PowerSeries(AlgebraElement):
         def derivative(self):

rings/sparse_poly.pyx
     cdef class Polynomial:
         def derivative(self):



There's also stuff in the following files which we probably shouldn't  
worry about:

libs/ntl/ntl_GF2X.pyx
libs/ntl/ntl_lzz_pX.pyx
libs/ntl/ntl_ZZ_pEX.pyx
libs/ntl/ntl_ZZ_pX.pyx
libs/ntl/ntl_ZZX.pyx
schemes/elliptic_curves/monsky_washnitzer.py
lfunctions/dokchitser.py

david


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