@Adam Ledger 

as in i dont feel as if im in bad company with the appreciation of its convenience as you put it. i have a number of counter examples to it being of no theoretical interest too, starting with how it relates to a form of integral functions and the hankel tranforms of which evaluate to integral hypergeometric functions but yea thats one for starters.

@vv ok thanks yep ill check the help page ive only started using the conformal plots.

@Carl Love 

and regarding the delta its mathematically convenient but of no value?

couldnt have chosen another one how about gamma or zeta those two dont seem to be pulling their weight lately :-P

@vv thanks well i like the title ill add it to the list. to be honest there is so much reading i get done inside the help interface with maple using the function advisor, yes i did notice maple now have a conversion feature to wolfram sorry whoops mathematica.

@Carl Love ok thanks ill add that one to my purchase list. asymptotic time complexity ok got it. But sorry ok i over use the delta but isnt it essentially equivalent to a if then statement?

ok and also can you just list the criteria aside from the time complexity that you use to conclude expressions are of no computational or theoretical value, im not quite clear there.

@Carl Love im going to try compare it to this one which is obviously yet another way about things that i mentioned earlier

@Carl Love 

yep hence my horror im very bad with explaining myself sometimes.

sorry i got mixed up 0 is arbitarily in the set as a consequence of the evaluation of the piece-wise delta for all of the non primes and is removed with the minus operator on the {0} singleton. but yep basic principle would just be an elaboration on the basic criteria of a number being prime in terms of the number of divisors being exactly 2, so 3 was placed in the piece-wise delta as it is counted with multiplicity.

i cant believe i forgot about that one cheers

@Carl Love 

There is that legendre method for the prime counting function also ive just seen that seems feasibly crazy for me to try and make a patch for

@Carl Love 

ah. yep so much of what i write is going to be my use of syntax as opposed to the actually efficiency of the procedure. i do actually read the maple help files in case you were wondering im just caught between mathematician and programmer, therefore making my maple interface and i a bit like conjoined twins that cant see each other due to the angle of attachment. ok wow what an analogy im a sicko thats for sure.

@Carl Love 

right ok thats a massive difference isnt it. how can i get maple to show me the whole procedure for the "isprime" and "select" functions?  like yes that is much more efficient but those two words alone dont tell me why! i think there is a way to view it, unless its a part of the kernel in which case they dont let anyone see how its done lol.

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/prime_subset_up_to_N.mw .

Download prime_subset_up_to_N.mw

@vv wow ok and i thought i knew everything there was to know about floor functions interesting ill have to have a play around with this one cheers

yes thanks for that. yes thats the basic trick behind the expression inside the delta along with the number 3. I of course intuitively expected it to be less efficient than the standard trial division but the point of me sharing this really is to get an idea exactly how less efficient it is.

One idea i had was to write a proc that returns the ratio of the time required for computation of the two methods, how would i declare this in a procedure?

im just guessing there must be code to return the time value shown in the bottom right hand corner of the interface, so i was thinking this was so i have a generic means of comparing the computational efficiency of any two procedures ive written hence answering my own question there.