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
That's great, thanks again Bill.
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
and that should deal with most things.
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?
In:= w = 1 + b*x + c*x^2 + d*x^3;
Collect[1 + w + w^2 + w^3, x]
Out= 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
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
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?
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.