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/usr/share/axiom-20170501/input/newton.input is in axiom-test 20170501-3.

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)set break resume
)spool newton.output
)set message test on
)set message auto off
)clear all
 
--S 1 of 5
newtonStep(f) ==
  fun  := complexNumericFunction f
  deriv := complexDerivativeFunction(f,1)
  (b:Complex DoubleFloat):Complex DoubleFloat +->
    b - fun(b)/deriv(b)
--R 
--R                                                                   Type: Void
--E 1

--S 2 of 5
complexFunPack := _
  MakeUnaryCompiledFunction(EXPR INT, Complex DoubleFloat, Complex DoubleFloat)
--R 
--R
--R   (2)
--R  MakeUnaryCompiledFunction(Expression(Integer),Complex(DoubleFloat),Complex(Do
--R  ubleFloat))
--R                                                                 Type: Domain
--E 2

--S 3 of 5
complexNumericFunction x ==
  v := theVariable x
  compiledFunction(x, v)$complexFunPack
--R 
--R                                                                   Type: Void
--E 3

--S 4 of 5
complexDerivativeFunction(x,n) ==
  v := theVariable x
  df := differentiate(x,v,n)
  compiledFunction(df, v)$complexFunPack
--R 
--R                                                                   Type: Void
--E 4

--S 5 of 5
theVariable x ==
  vl := variables x
  nv := # vl
  nv > 1 => error "Expression is not univariate."
  nv = 0 => 'x
  first vl
--R 
--R                                                                   Type: Void
--E 5
)spool 
)lisp (bye)