>> the question is to find some formulas, which look as they would 
>> require
>> the value 'E', but do not really need it.

> You're going to have to explain why.  Unless you can explain a good 
> reason,
> this looks too silly to spend time on.

So (I suggest) don't :-)
He, like you, as you oft times note, doesn't *have* to do anything 
and, as you also note, needs not have anyone tell him that he does.
But I'll hazard a guess which may well be wrong but which indicates 
that reasonable reasons may exist.

Guess / example:    A system is required to obfuscate the means by 
which a process achieves its aims. By providing an algorithm with one 
or more parameters which appear on 'reasonable inspection' to form a 
part in the process, but which in fact have no effect on the computed 
result, the user seeks to mislead would be system breakers. Further, 
'data' which is provided to the system may in fact not affect the 
computation per se but be part of a security or checking subsystem 
which seeks to determine whether the system is being utilised 
improperly.

Whatever.

eg

E = [(A^2-B^2)/(C^2+ 2.C.D + D^2)] x [(C+D)/(A-B)] x [ (C+D)/(A+B)] x 
F

E will always equal F :-)

A, B, C, & D are all irrelevant to the result (except that certain 
combinations are not allowed in order to prevent the result going to 
infinity. eg A<>B, A <> -B, C <>D, C <> -D.)

The eg ratio of the parameters A...D to each other or their sums or 
some other features may be set in some manner so that, while they do 
not alter the fact that E = F , do indicate to a knowledgeable 
inspector whether they have been set by someone who 'knows the rules'.

____________

Very vaguely similar real world example:        The last digit in your 
VISA etc card number is a checksum which is derived in a complex but 
computationally simple manner (so you can easily enough calculate it 
mentally) from all the other digits, with the aim of determining 
whether the card number can in fact be a valid one. It's intended use 
is probably not so much to check correct data entry but to identify 
simple minded fraud. A randomly generated number has one chance in 10 
of being legitimate by this test.



        RM


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