function( 'name' [ , arguments ] )

The symbolic function name in SageMath determined from keyword arguments for evaluation and manipulation.

Symbolic functions are needed to avoid TypeError messages when providing input to SageMath functions that only take symbolic expressions as arguments, as for example piecewise.

Keyword arguments:

narg=integer number of arguments
eval_func=method for automatic evaluation
evalf_func=method for numeric evaluation
evalf_params_first=True|False
conjugate_func=method for complex conjugation
real_part_func=method for taking real parts
imag_part_func=method for taking imaginary parts
derivative_func=method for (partial) differentiation
tderivative_func=method for differentiation
power_func=method for taking powers
series_func=method for series expansion
print_func=method for custom printing
print_latex_func=method for custom LaTeX printing
latex_name=name for printing in LaTeX mode
conversions=dictionary of names of function in other systems

Examples:

Note that arguments self and **kwds are critical for avoiding errors here:

def numeric(self, x, **kwds):
  var('u')
  return numerical_integral(u,0,x)[0] 

symbolic = function('symbolic', nargs=1, evalf_func=numeric)

f = piecewise([[(0,1),symbolic(x)]])
plot( f, 0, 1, figsize=[4.5,2], color=(0,.5,1) )

Related functions:   piecewise

Function category: basic functions sagemath-docs