Summation notation

[DarkWater]

Just curious to know if anyone has ever coded a summation notation function in PHP. =P  Has anyone?

 

If not, I'll write one and post it up here, I was just curious.

[Brian W]

Not that I can find... I'd much appreciate if you did one for us. Thanks 

[Mchl]

Summation notation?

 

You mean function like

 

function sigma($nStart,$nEnd,$nExpression) {

for ($i = $nStart;$i<=$nEnd;$i++) {
  //work on nExpression 
}

}

 

?

[Brian W]

I'll have to go back to that project and test it later... but thanks in advance because I have a feeling it will work.

[Mchl]

Well yeah... What I wrote is just oversimplified example. I have a feeling there might much more to it than just simple for() loop.

 

For example, what would be the format of $nExpression ?

 

Would it be like

 

$nExpression = "(1+(1/%N%))";

 

and then replace "%N%" with $i, parse and iterate?

[DarkWater]

See, that's the problem.  It would use eval() like 4327908432190 times, lol.  That was an exaggeration.  Like, there are certain rules with summation notation to "simplify" things, like if you had:

 

 

You could really simplify it to:

 

 

And stuff like that makes it hard to get this to work. xD

 

[Brian W]

Within my project, I need it to find the summation of 1-$given which is normally like 1-9 or 1-55... never any thing more complex.

[DarkWater]

Wait, so you end up getting a negative number? =P  Anyway, you can easily hardcode that one.  I'm talking about truly dynamic summations.

[Brian W]

excuse me, I should have put 1 through $given. This should be something like

$given = 100
1+2+3..+98+99+$given (which is = 5050)

[DarkWater]

That's simple.

 

<?php
$total = array_sum(range(1, $given));
?>

[Brian W]

THANK YOU!!! I didn't know about the range function. Cool

I'm a newb still  :'(

-Solved for me-

[DarkWater]

Aha, no problem.   Now, if someone could figure this one out...that would be great.  I don't think PHP would be the best option for this though, to be honest.   Just wanted to see if it could be done in any coherent manner.

[GingerRobot]

It really depends on the scope of the problems you're trying to solve. Obviously the advantage of a computer is that it is often acceptable to repeat the calculation many times, negating the need to find a way of simplifying the expression. On the other hand, it shouldn't be too hard to come up with something to simplify an expression given a relatively small size of potential expressions to solve.

[DarkWater]

Lol, I don't actually NEED it for anything, I just thought it would be kinda cool.

[Brian W]

I am just developing a text based game for the learning experience during my free time. But I gave up on that piece of math and just created a table with all the number input>>outputs. made things so much more simple. This was only an option because they can't use a number higher than 100.

[Ken2k7]

There's an easier way.

 

This formula works:

$start = 1;
$end = 100;

echo ($start + $end) * ($end / 2);

[Mchl]

This will work for specific series. We're looking for general solution here