Re: Determining the inverse function operation from a function definition

Ron Foster wrote:
>
> Hi.
> I am working on a small project to evaluate and execute unit conversion
> expressions. I started wondering whether it was possible to determine what
> the reverse conversion rules might blook like.
>
> For example, one might want to define the classic Celsius to Fahrenheit
> convesrion expression along the lines of:
>
> F( c ) = ( 9 / 5 ) * c + 32.
>
> It seems as though there's enough information there to deduce the inverse
> Fahrenheit to Celsius conversion:
>
> C( f ) = ( f - 32 ) / ( 5 / 9 )


You did a bit too much, using my school math the result should read:
    C( f ) = ( f - 32 ) / ( 9 / 5 )


There should't exist too many linear conversion formulas, so a table
with the constants and the two conversion functions should be feasable.
Perhaps all you need is y=a*x+b and y=a/x+b, with the according inverse
functions. Things will become a bit more complicated with
exponentiation, sine, or other non-linear functions.


In the general case you can build an expression tree and implement a
transformation procedure for the reverse expression. Using an
appropriate language with built-in list manipulation will simplify
things a lot. I remember one of my first LISP exercises, a conversion
from/to RPN...


IMO you better ask your questions in a math group. Even if your problem
is related to "symbol manipulation" or "transformation", it's not a
matter of compilers nor grammars.


DoDi

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