[numbers] Negation vs substraction

My brain is melting while trying to reduce^H^H^H^H^H^H remove redundancy from my script...

Can "-" be used as the negation operator, if I'm completely sure that that operation can be transformed into another one, which only uses "-" as the substractor?

I mean, if my script was stupid enough to ignore the following solution:
(a+b)*(c-d)
but could output the following instead:
(-a-b)*(d-c)
could it be allright??

Posted: Friday, October 17 2003 03:36 AM
Quote

Is this valid?

-1-2-3+4+5+6
4+5+6-1-2-3

or

4+5+6+(-1-2-3)

The first and third one are not correct, because you cannot use unary minus (-1). If they were 4-1-2-3+5+6 and 4+5+6-(1+2+3), you'd have:

f1(a,b,c,d,e,f)=d-a-b-c+e+f
f2(a,b,c,d,e,f)=d+e+f-a-b-c
f3(a,b,c,d,e,f)=d+e+f-(a+b+c)

f1()-f2()=0 for all a,b,c,d,e,f
f1()-f3()=0 for all a,b,c,d,e,f

So, they're all duplicates and you may output only one of them.

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answer posted by xs0