On Fri, 9 Jul 2010, Grigory Sarnitskiy wrote:
Imagine I want to have a function that returns the derivative of real-valued
function of one real variable, something like
Deriv : ((Float) -> Float) -> ((Float) -> Float)
As Martin wrote, axiom only handles derivatives of expressions.
In Leibniz' times every function was an expression, nowadays this is not
true anymore.
In Axiom an object of type Float->Float is a function in the sense of
programming, i.e., it takes an object of type float and returns an object
of type float.
You can always turn an expression into a function in this sense:
(1) -> y:=sin x + 1
(1) sin(x) + 1
Type: Expression(Integer)
(2) -> function(y,f,x)
(2) f
Type: Symbol
(3) -> f(u)
Compiling function f with type Variable(u) -> Expression(Integer)
(3) sin(u) + 1
Type: Expression(Integer)
(4) -> f(1.0)
Compiling function f with type Float -> Float
(4) 1.8414709848 078965067
Type: Float
regards,
Franz
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