The Sigma Function on the WP34

[Eddie W. Shore]

How is the Sigma function used?

I am trying to find the sum:

10

Sigma  .5^x * .2   (= .399805)

x=0

If understand the manual correctly, I am supposed to enter the counter in the x stack as ccc.fffiii:

So I would enter 0.01001?  (final = 10, increment = 0, c = 0)

I am not getting the answer I expected.  Please help.

Here is what I have: 

LBL FF

.

5

x<>y

y^x

.2

x

RTN

.01001 g [3] f [ENTER] FF ??  (I'm not getting what I am expecting, I get .2000)

Thanks in advance.

[Paul Dale]

The source for sum is in the subversion repository.

The big problem I think you're encountering is that the loop is a DSE loop not an ISG one. So, try entering 10 SUM'FF

The finish value defaults to 0 and the increment/decrement defaults to 1.

- Pauli

[Paul Dale]

Small correction.

You need to start the sum from 11 and subtract 1 at the start of the function. The sum stops before the zero term is evaluated.

Thus,

    LBL A

    DEC x

    .

    5

    x<>y

    y^x

    5

    /

    RTN

Then 11 g Sigma A gives 0.3998046875

- Pauli

[Dieter]

Quote:

---

The big problem I think you're encountering is that the loop is a DSE loop not an ISG one. So, try entering 10 SUM'FF

---

Not just him. ;-) That's one of the things that made me read the manual twice before I finally realized that the sum and product loops are working backwards.

Pauli, I think this is a quite unintuitive feature. I'm a big fan of POLA user interfaces (policy of least astonishment - things should work the way the average user expects). That's why I think the sum and product functions should count upwards. Simply think of the way you write down a sum: it's from 1 to n, not from n down to 1. And this way there is also no problem with an index starting at zero. ;-)

Dieter

[Paul Dale]

Originally I had both product and sum counting up then the documentation had them counting down so I switched.

There are arguments both ways on this:

• Counting up limits you to a final value to 999, counting down doesn't.

• Counting up lets you get a zero index easily, counting down doesn't.

• Counting up requires more keystrokes (e.g. sum 1 to 5 requires 1.005 SUM as opposed to 5 SUM).

• For summations whose terms diminish as the index increases (i.e. many), counting down is generally more accurate.
  

The change to make the count go the other way is trivial -- the DSE becomes an ISG in the main loop. I guess we could implement alternate commands to count the other way or switch to counting up again. I'm indecisive on this one, like I said advantages both ways.

- Pauli

Edited: 25 Apr 2011, 9:41 p.m.

[exschr]

how about a flag to decide (switch) if counting up or down is used?

(but I bet you are tight on flag usage though)

Anyway, very nice work done, I'm looking forward to buy a 30b and starting to flash the business out of it ;-)

Thanks a lot for more fun!

[Paul Dale]

We wouldn't use a flag for this, we'd define two commands for each.

- Pauli

[Namir]

How about using the sign of the summation range as a way to tell if you are summing up or down. Let's say a negative value means you are counting down, and vice versa?

Namir