Hi , I am working on some math stuff and I need to check some points ,

so are theses formulas correct ?

 

ISZ(x) : is it 0 ?

 

isz (x) = cos ( pi * ( (2*ceil( abs(x) ) + 1)) / 2 ) / cos(1)

 

Ins : Real number x

 

Out : 1 if x=0 , 0 if x <> 0

 

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SGN(x) : Sign

 

sgn(x) = abs(x) / ( x + isz(x) )

 

Ins : Real number x

 

Out : 1 if x>0 , 0 if x = 0 , -1 if x < 0

more here

Dirbax

 

thanks

Well yes.

 

But... why?

I am trying to create a new math branch DIMD

But things like the sign function and the dirac delta function... already exist.

Yes but I still should mention them since I am making the basis of DIMD, an other point is trying to avoid semantic presentation of functions such as

this and go for smooth calculations

For one abs() isn't smooth, at all, neither is ceiling().

 

And why don't you want the way a function is presented to be semantic? It's not like you're saving on computability, trig functions are clearly more expensive than a check for properties that are written into the way a number is stored.

For one abs() isn't smooth, at all, neither is ceiling().

True , I am still working on it in order to minimise the number of functions such as ceil and abs which use semantic definition .

Again, what's wrong with a semantic definition? If makes things possible to read, as well as computationally cheaper, what could possibly be wrong with it?

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Merged post follows:

Consecutive posts merged

And it just occurred to me, if you're trying to define discontinuous functions as compositions of continuous ones, it can't be done.