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Algebra

Expand polynomial

Alan Smith
Posted 10 years ago

Hi - apologies in advance because this must be simple, but I have tried a long list of commands without getting closer ... I want to expand a polynomial, grouped in powers of the variable. EG: given w=1+bx+cx^2+dx^3 Then I'd like to do something like Collect[w^2] and get 1 + 2bx + (2c+c^2)x^2 + 2(d+bc)x^3 + .... everything I have tried just gives me (1+bx+cx^2+dx^3)^2 Thanks
POSTED BY: Alan Smith
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Alan Smith
Alan Smith
Posted 10 years ago

That's great, thanks again Bill.
POSTED BY: Alan Smith
Bill Simpson
Bill Simpson
Posted 10 years ago

There is a ClearAll documented in the help system, but that only does it for specific names you give it.

You can try the menu bar

Evaluation->Quit Kernel->Local->Quit

and that should deal with most things.
POSTED BY: Bill Simpson
Alan Smith
Alan Smith
Posted 10 years ago

Perfect! Many thanks Bill (I had tried Collect, must have done something wrong, maybe something earlier not cleared ....). By the way - am I the only one who wishes there was a 'ClearAll' command that cleared everything from the current workspace (document)? I know I can specify types to be cleared, but would prefer to have a 'complete reset' available - unless there is one I don't know of?
POSTED BY: Alan Smith
Bill Simpson
Bill Simpson
Posted 10 years ago

.

In[1]:= w = 1 + b*x + c*x^2 + d*x^3;
Collect[1 + w + w^2 + w^3, x]

Out[2]= 4 + 6 b x + (4 b^2 + 6 c) x^2 + (b^3 + 8 b c + 6 d) x^3 + (3 b^2 c + 4 c^2 + 8 b d) x^4 +
    (3 b c^2 + 3 b^2 d + 8 c d) x^5 + (c^3 + 6 b c d + 4 d^2) x^6 + (3 c^2 d + 3 b d^2) x^7 + 3 c d^2 x^8 + d^3 x^9
POSTED BY: Bill Simpson
Alan Smith
Alan Smith
Posted 10 years ago

That was just an example, I don't actually know the polynomial that might emerge, which is why I wanted to see if mathematica could do it. So to summarise, I have a general poly, like w= 1 +bx + cx^2 + dx^3 ... once I know what the right commands are, I will want to experiment with this. Then I want to make a series - 1 + w + w^2 + w^3 +... but again I might want to extend it further.

So I will input w= 1 +bx + cx^2 + dx^3, then I want the commands that will take 1 + w + w^2 + w^3 and output that result, grouped in powers of x - so I would expect (only as an example) something like 1 + (...)x + (....)x^2 + (.....)x^3 + ...still keeping it general, with the b,c etc coefficiants. Thanks
POSTED BY: Alan Smith

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POSTED BY: Simon Cadrin

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POSTED BY: Simon Cadrin
Alan Smith
Alan Smith
Posted 10 years ago

Thanks, but I want the output polynomial grouped by powers of x, so something like 1 +bx + (a^2+b...)x^2 + (......)x^3 + and so on?
POSTED BY: Alan Smith
Alan Smith
Alan Smith
Posted 10 years ago

Hi, the expanded form you show is what I am looking for, but I want it in terms of the unknown coefficients a, b, c etc. - and in terms of a power of w, because once I can get w^2 I will try to get the series 1 + w + w^2 + w^3 + maybe higher terms. Thanks
POSTED BY: Alan Smith

enter image description here
POSTED BY: Simon Cadrin

enter image description here
POSTED BY: Simon Cadrin
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