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generate a specific combinatorial sum symbolically

LucMeekes
23-Emerald II

generate a specific combinatorial sum symbolically

Collabs,

I need help with generating a specific combinatorial sum for the symbolic processor (Mcad 11).

See attachment.

Thanks for your time

Luc

1 ACCEPTED SOLUTION

Accepted Solutions

I think the attached shows a simple function that does what you want.

stv

View solution in original post

19 REPLIES 19
MikeArmstrong
5-Regular Member
(To:LucMeekes)

Luc

Haven't really spent much time using symbolic's, but think I have solved for Equation 2.

Mike

Oh, Luc ! ... You are liquefying my brain .

I have recognized 3 quicly enough .

But if it can be completed, then numerical is just enough.

What all that does represent ? Has it got something to

do with the "Chemical pseudoinverse" ?

I think Stuart & Richard would be good in there [Mike too].

Jean

LucMeekes
23-Emerald II
(To:jeanGiraud)

Jean,

To (partly) satisfy your curiosity:

the expression is part of the denominator of an expression that describes outputs of a specfic n-channel amplifier.

In there each Ai is a more complicated expression by itself.

Mathcad (11) is capable of solving my entire n-channel amplifier symbolically, sometimes up to n=4, after which I can evaluate solutions numerically, for n=4 and higher (haven't tried to find the limit yet).

I want to describe the (full) solution in a way that enables to understand it's structure. So I need a compact description of that specific sum of n summations.

That requires I need to "simplify" and you know how good CAS systems are at simplifying.... although I learned a few new tricks in Mathcad along the way.

Thanks,

Luc

Luc Meekes wrote:

Jean,

To (partly) satisfy your curiosity:

the expression is part of the denominator of an expression that describes outputs of a specfic n-channel amplifier.

In there each Ai is a more complicated expression by itself.

Mathcad (11) is capable of solving my entire n-channel amplifier symbolically, sometimes up to n=4, after which I can evaluate solutions numerically, for n=4 and higher (haven't tried to find the limit yet).

I want to describe the (full) solution in a way that enables to understand it's structure. So I need a compact description of that specific sum of n summations.

That requires I need to "simplify" and you know how good CAS systems are at simplifying.... although I learned a few new tricks in Mathcad along the way.

Thanks,

Luc

Thanks Luc, for the explanation.

Though I don't understand the logic in such complicated construct, but applied it quick. That would represent a coding of some sort [just a comment to maintain my brain in gear]. Your last part is the permutation, that works symbolically but can't be extracted . We need a brain storm from collabs in there ! Another way to get the permutations is the lexico construct or from tables [Neil Sloane]. But you have to make sure that all the components are really as they reveal up until your expression [4]. If all those components are true, what's left is the symbolic construct of the permutations, for instance the 6 permutations of [a,b,c] = [a,b,c], [a,c,b], [c,a,b], [c,b,a],[b,a,c], [b,c,a] ... most gorgeous would be an "n permute". The rot(v,n) does it but can't be extraced symbolically for a literal module to apply. I'm sure any reader will be interested as already tuned to the challenge. BTW, the centroid member works for any length but it sems you ignore the last term.

Cheers Luc, Jean

>>>>>>>>>>>>>>>>>

The spell check does not in there , Why ? Don't know.

MikeArmstrong
5-Regular Member
(To:jeanGiraud)

jean Giraud wrote:

>>>>>>>>>>>>>>>>>

The spell check does not in there , Why ? Don't know.

The spell check also can't understand two words joined without a gap. It just makes a suggestion of the first word, doesn't offer a space as a suggestion - Unlike WORD.

Mike

MikeArmstrong
5-Regular Member
(To:LucMeekes)

Luc,

Solved equation 3 see attached. As Jean said one of the more experienced users should be able to show a simpler solution than mine. Hey, still works though.

Cheers

Mike

Luke.

No feedback on the sheets I provided!!

No good?

Mike

Mike,

sorry, I hope I didn't offend you.

I've looked at them to see if I could generalize your particular solutions and saw no way (yet).

Regards,

Luc

MikeArmstrong
5-Regular Member
(To:LucMeekes)

Luc Meekes wrote:

sorry, I hope I didn't offend you.

I've looked at them to see if I could generalize your particular solutions and saw no way (yet).

Regards,

Luc

Luc,

Not at all.

Gold star to Alan for solving.

Mike

Hello Luc,

Finished but the last permutation, can't get it work symbolic otherwise than local and manual, i.e: can't be programmed. Will post tomorrow. Make sure the pattern is extensible , it's not obvious even with expansion 4.

Jean

Luc,

You will understand everything. You can really make it as you wish but for the last term, if you want it more developed, it will take a big bit more construct even for a permute as simple as [a,b,c]. .. But it would be possible. Was very interesting, I never thought the "Centroid" could be applied. In fact, it could do the all lot by itself whereas it is variable in length. Just a matter of adapting or revising the concept of the project [speaking to myself].

Jean

I think the attached shows a simple function that does what you want.

stv

MikeArmstrong
5-Regular Member
(To:AlanStevens)

Alan,

Looks like you have crack it.

Can you explain how the fucntion still works when RED?

"Can you explain how the fucntion still works when RED?"

It's only the numerical solver that would need the a's to be pre-defined. The symbolic solver doesn't give a monkeys!

stv

MikeArmstrong
5-Regular Member
(To:AlanStevens)

Of course, cheers Alan.

LucMeekes
23-Emerald II
(To:AlanStevens)

Thanks Alan,

I suspected that it should be doable by a function, although I thought a recursive function would be needed (if you look at my attempt, you'll see why).

You showed that that isn't necessary.

I've checked your solutions against my stuff, and as far as I've gone the solution is correct.

Now my next task is to embed this function in my symbolic calculation sheet, and see if it works there.

Thanks!

Luc

Works fine here.

MCADstvseries.gif

... not really "combinatorial"

independent of shuffling vector (a)

Alan Stevens wrote:

I think the attached shows a simple function that does what you want.

stv

Alan,

It does, though I missed in the first place. As is, it outputs a single value. I may have muffed the grouping in my first attempt.

Thanks, saved

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