[OS X TeX] Binomial Expansion

[Claus Gerhardt]

No round brackets necessary, e.g., one could write

\Expand{(x+1)(x^3+6)^5+9+x^2}

Claus

On Nov 23, 2006, at 19:28, Claus Gerhardt wrote:

> Here is a variant
>
> \newcommand{\Expand}[1]{\polyprint{#1}}
>
> Example
>
> \Expand{(x+1)(x^3+6)^5}
>
> Claus
>
>
> On Nov 23, 2006, at 19:11, Claus Gerhardt wrote:
>
>> Alain,
>>
>> Here is my  little birthday present:
>>
>> \newcommand{\expand}[2]{\polyprint{#1#2}}
>>
>> Notice that the polynomials have to be delimited by round brackets  
>> like
>>
>> \expand{(x+1)}{(x+8)^3}
>>
>> This will gives you the fully expanded polynomial. A reverse long  
>> division scheme is a bit more difficult, and frankly, I can't see  
>> its necessity.
>>
>> Claus
>>
>>
>> On Nov 23, 2006, at 18:11, Alain Schremmer wrote:
>>
>>> Claus Gerhardt wrote:
>>>
>>>> Happy Birthday Alain!
>>>
>>> Thank you!
>>>
>>>> I had a look at the polynom.sty manual. It is only 6 pages and  
>>>> well  written. You should give it a try.
>>>
>>> I did about a year ago and I have been using \polylongdiv ever  
>>> since. That was not the point of my post. What I wanted to do  
>>> over the Christmas break was to learn a little bit about  
>>> programming in LaTeX. The idea was to write, in the spirit of  
>>> polylongdiv, a command
>>>
>>>    \Expand{a}{b}{some degree}
>>>
>>> that would expand and typeset (a+b)^n. I am still going, The TeX  
>>> Book in hand, to try.
>>>
>>>> If \Expand{a}{b}{some degree} should represent polynomial  
>>>> division, then
>>>>
>>>> \polylongdiv[stage=3] {(X-1)(X-1)(X^2+1)^4} {(X-1)(X+1)(X+1)}
>>>>
>>>> might be what you want.
>>>
>>> Not really since I can expand (a+b)^n in my head and polylongdiv  
>>> gives me the output but no source to copy-paste.
>>>
>>> Nevertheless, \polylongdiv{(x+a)^{n}}{1}(with an actual value for  
>>> n) is indeed very neat and I will try to cut some more from  
>>> polynom.sty to get rid of the division (I already got rid of  
>>> Horner but that was a bit of trial and error.)
>>>
>>> What I wanted was to learn a bit about LaTeX along the theme of  
>>> writing the command.
>>>
>>> But, indeed, I hadn't realized that polylongdiv could multiply  
>>> which of course was dumb since it has to multiply in order to  
>>> divide (not quite as in "we had to destroy the city in order to  
>>> save it" of everlasting fame.)
>>>
>>> Of course, what I would kill for is a polylongdiv in ascending  
>>> order. But, as I wrote, Heinz didn't respond to my two requests  
>>> so I think she or he has better things to do.
>>>
>>> Very grateful regards
>>> --schremmer
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>>
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>
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