Subject: Making the result of INTEGRATE into a function
From: Robert Dodier
Date: Thu, 11 Aug 2005 12:27:22 -0600
hi dan,
> ''(F(X)) means evaluate the expression F(X) an extra
> time. ''F(X) means return the verb form of F applied
> to [X].
well, when a noun operator N appears in an expression,
e.g. N(x,y,z), its arguments are evaluated but N (ev(x), ev(y), ev(z))
is not evaluated. in contrast if a verb operator V appears,
you get ev (V (ev(x), ev(y), ev(z))).
by default most operators are verbs, i.e., they are applied when
mentioned in an expression. if an operator V is a verb by default,
then ' V (x, y, z) makes it act like a noun. if an operator N is a
noun by default, then '' N (x, y, z) makes it act like a verb.
e.g., integrate is a verb by default:
integrate (x, x) => x^2/2
quote mark nounifies it:
' integrate (x, x) => (integral sign)
sin is a noun by default:
sin (1) => sin (1)
quote quote verbifies it:
'' sin (1) => 0.8414
> F(x,y) := ''integrate(integrate(f(x,y),x),y);
>
> F(x,y) := integrate(integrate(f(x,y),x),y);
you are correct, these two are indeed identical.
there's more that can be said but i'll leave it at that for the moment --
all the best & hope this helps,
robert dodier