[OS X TeX] Binomial Expansion
Claus Gerhardt
gerhardt at math.uni-heidelberg.de
Thu Nov 23 13:36:30 EST 2006
Try this one
\newcommand{\expa}[2]{#1 #2=\polyprint{#1#2}}
Claus
On Nov 23, 2006, at 19:31, Claus Gerhardt wrote:
> 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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>
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