Math Is Fun Forum / Generating Functions

anonimnystefy · 2012-04-30 23:45:25

Procedural form?

bobbym · 2012-04-30 23:48:35

Loops and such.

anonimnystefy · 2012-04-30 23:50:12

There is no other way.At least not that I know of.But Maxima allows while loops.

bobbym · 2012-04-30 23:51:23

While loops are procedural. Why are you not using math commands to do math?

anonimnystefy · 2012-04-30 23:58:25

What would you to sum those terms then?

bobbym · 2012-05-01 00:03:45

Sum[x^k,k,1,6] yields

anonimnystefy · 2012-05-01 00:08:53

Code:

CombGF(list) := block([i, a, m, s],
i = 1,
m = 1,
while i <= length(list) do
[
a = get(list,i),
s=sum(x^k/k!,k,1,i),
m = m * s,
delete(a,list,1),
i = i + 1
],
print(m)
);

Last edited by anonimnystefy (2012-05-01 00:11:39)

bobbym · 2012-05-01 00:16:17

You do not need the while loop and you are jumping ahead. Let's get the OGF's down first.

To have the probability gf for 2 die:

Sum[x^k/6,k,1,6]^2 yields

anonimnystefy · 2012-05-01 00:18:58

I want the function to do everything for me.I just have to input 6,6 instead of just 6 to get probability for 2 dice.

bobbym · 2012-05-01 00:25:02

I want the function to do everything for me.I just have to input 6,6 instead of just 6 to get probability for 2 dice.

That is overkill. You make functions that do the minimum and use other commands on them. You do not try to make functions to do everything.

You make a function that inputs the parameters you need and then you use the series inside the function.

Here is pseudocode:

gf(a,b,d)

Begin:

Sum[x^k/d,k,a,b]

End:

Now when you call gf(1,6,6) you get:

Congratulations you just threw a die!

To throw 2 you just go

gf(1,6,6)^2

Simple, no need to make a function throw n die when you just have to square or cube or raise to the 10th power...

I want you to work on creating a function gf that inputs the 3 parameters as I have indicated.

anonimnystefy · 2012-05-01 01:51:13

This code both compiles and runs,but doesn't give a good output:

Code:

CombGF(list) := block([i, a, m, s],
i : 1,
m : 1,
while i <= length(list) do
[
a : first(list),
print(a),
s : sum(x^k, k, 0, a),
m : m * s,
list:rest(list),
i : i + 1
],
print(m)
);

and the output for:

list:[1,1,2,3];
CombGF(list);

is:

[1,1,2,3]
1
1
(x+1)^2

Last edited by anonimnystefy (2012-05-01 01:51:46)

anonimnystefy · 2012-05-01 02:08:14

Done it! Could you do a little test on the code:

Exp GF:

Code:

CombEGF(list) := block([i, a, m, s],
i : 1,
m : 1,
l : length(list),
while i <= l do
[
a : first(list),
s : sum(x^k/k!, k, 0, a),
m : m * s,
list : rest(list),
i : i + 1
],
m
);
©anonimnystefy 2012

Ordinary GF:

Code:

CombOGF(list) := block([i, a, m, s],
i : 1,
m : 1,
l : length(list),
while i <= l do
[
a : first(list),
s : sum(x^k, k, 0, a),
m : m * s,
list : rest(list),
i : i + 1
],
m
);
©anonimnystefy 2012

The coefficient of OGF:

Code:

OGFcoeff(list,n) := ratcoeff(CombOGF(list),x^n);
©anonimnystefy 2012

The coefficient of EGF:

Code:

EGFcoeff(list,n) := ratcoeff(CombEGF(list),x^n)*n!;
©anonimnystefy 2012

Notice that I multiply by n! in the EGFcoeff function to get the final result immediately.

Last edited by anonimnystefy (2012-05-01 02:50:58)

bobbym · 2012-05-01 03:19:51

Hi;

Please look at my hidden text message in post 110.

anonimnystefy · 2012-05-01 03:24:18

I did even more than that.The function CombOGF can create those generating functions.

bobbym · 2012-05-01 03:40:32

You missed alot of what I am trying to say by sticking to the procedural
approach. It is not uncommon for people being introduced into new
fields to try to keep what they already know.

While this is usually a good idea in the case of programming it can
be disastrous. I wanted you to tear down your Pascal or Basic famework
and learn another one.

anonimnystefy · 2012-05-01 03:42:48

But this solution works.It is applicable in many situations.

Last edited by anonimnystefy (2012-05-01 03:42:59)

bobbym · 2012-05-01 03:47:32

I understand that it is tough to do what I ask. Of the two people I taught neither could accomplish it. Perhaps you remember this:

Yibka: Once you start down the path of procedural programming forever will it
dominate your destiny, consume you it will as it did Bit One's apprentice.

Lukky: Is the procedural paradigm stronger?

Yibka: No, no no! Easier! More seductive...

anonimnystefy · 2012-05-01 03:49:15

I do not remember that.Where is that from?

But,I am willing to try if you have the patience.

bobbym · 2012-05-01 03:53:20

I do not remember that.Where is that from?

I think we have been lied to on every level by our masters. I was assured many times that that was standard knowledge.

But,I am willing to try if you have the patience.

I have the patience but do have I have the lifespan of several millenia?

anonimnystefy · 2012-05-01 03:57:31

Well you have already live hundreds of millenia,so that won't be the problem.Let's get started if you want.

bobbym · 2012-05-01 03:58:50

Show me a full output of your best and most complicated example using your function.

anonimnystefy · 2012-05-01 04:25:40

Hi bobbym

Inout:

Code:

list : [1,2,3,4,5,6,7,8,9,10,11,12,13];
CombOGF(list);

Output;

Code:

[1,2,3,4,5,6,7,8,9,10,11,12,13]
(%o74) (x+1)*(x^2+x+1)*(x^3+x^2+x+1)*(x^4+x^3+x^2+x+1)*(x^5+x^4+x^3+x^2+x+1)*(x^6+x^5+x^4+x^3+x^2+x+1)*
(x^7+x^6+x^5+x^4+x^3+x^2+x+1)*(x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1)*(x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1)*
(x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1)*(x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1)*
(x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1)*
(x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1)

bobbym · 2012-05-01 04:38:33

Okay, how do you throw a die 4 times and get the probability of having the
sum of them equal 20?

Taking a break, be back in a while.

anonimnystefy · 2012-05-01 04:50:17

Hi bobbym

35/1296?

Okay,see you later!

Last edited by anonimnystefy (2012-05-01 04:51:12)

bobbym · 2012-05-01 05:55:41

That is correct! Okay, then use yours.

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#101 2012-04-30 23:45:25

Re: Generating Functions

#102 2012-04-30 23:48:35

Re: Generating Functions

#103 2012-04-30 23:50:12

Re: Generating Functions

#104 2012-04-30 23:51:23

Re: Generating Functions

#105 2012-04-30 23:58:25

Re: Generating Functions

#106 2012-05-01 00:03:45

Re: Generating Functions

#107 2012-05-01 00:08:53

Re: Generating Functions

Code:

#108 2012-05-01 00:16:17

Re: Generating Functions

#109 2012-05-01 00:18:58

Re: Generating Functions

#110 2012-05-01 00:25:02

Re: Generating Functions

#111 2012-05-01 01:51:13

Re: Generating Functions

Code:

#112 2012-05-01 02:08:14

Re: Generating Functions

Code:

Code:

Code:

Code:

#113 2012-05-01 03:19:51

Re: Generating Functions

#114 2012-05-01 03:24:18

Re: Generating Functions

#115 2012-05-01 03:40:32

Re: Generating Functions

#116 2012-05-01 03:42:48

Re: Generating Functions

#117 2012-05-01 03:47:32

Re: Generating Functions

#118 2012-05-01 03:49:15

Re: Generating Functions

#119 2012-05-01 03:53:20

Re: Generating Functions

#120 2012-05-01 03:57:31

Re: Generating Functions

#121 2012-05-01 03:58:50

Re: Generating Functions

#122 2012-05-01 04:25:40

Re: Generating Functions

Code:

Code:

#123 2012-05-01 04:38:33

Re: Generating Functions

#124 2012-05-01 04:50:17

Re: Generating Functions

#125 2012-05-01 05:55:41

Re: Generating Functions

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