R help - Oct 2008 - a really simple question on polynomial multiplication

Dear R people:

Is there a way to perform simple polynomial multiplication; that is,
something like
(x - 3) * (x + 3) = x^2 - 9, please?

I looked in poly and polyroot and expression.  There used to be a
package that had this, maybe?

thanks,
Erin


-- 
Erin Hodgess
Associate Professor
Department of Computer and Mathematical Sciences
University of Houston - Downtown
mailto: erinm.hodgess at gmail.com

Dear Erin,
Yes. Take a look at page 13 in [1].

HTH,

Jorge

[1]  http://cran.r-project.org/web/packages/Ryacas/vignettes/Ryacas.pdf



On Wed, Oct 15, 2008 at 5:44 PM, Erin Hodgess
<erinm.hodgess@gmail.com>wrote:
> Dear R people:
>
> Is there a way to perform simple polynomial multiplication; that is,
> something like
> (x - 3) * (x + 3) = x^2 - 9, please?
>
> I looked in poly and polyroot and expression.  There used to be a
> package that had this, maybe?
>
> thanks,
> Erin
>
>
> --
> Erin Hodgess
> Associate Professor
> Department of Computer and Mathematical Sciences
> University of Houston - Downtown
> mailto: erinm.hodgess@gmail.com
>
> ______________________________________________
> R-help@r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
	[[alternative HTML version deleted]]

One way is to use convolution (?convolve):

If A(x) = a_p*x^p + ... + a_1*x + a_0
and B(x) = b_q*x^q + ... + b_1*x + b_0
and if C(x) = A(x)*B(x) = c_(p+q)*x^(p+q) + ... + c_0 
then c = convolve(a,rev(b),type="open")
where c is the vector (c_(p+q),...,c_0), a is (a_p,...,a_0) and b is
(b_q,...,b_0).
In your case:
> a <- c(1,-3)
> b <- c(1,3)
> c <- convolve(a,rev(b),type="open")
> c
[1]  1.00000e+00 -6.49654e-16 -9.00000e+00

Note that the coefficient of x is not exactly 0 due to the use of fft to compute
convolutions.



--- On Thu, 16/10/08, Erin Hodgess <erinm.hodgess at gmail.com> wrote:
> From: Erin Hodgess <erinm.hodgess at gmail.com>
> Subject: [R]  a really simple question on polynomial multiplication
> To: "R Help" <r-help at r-project.org>
> Received: Thursday, 16 October, 2008, 8:44 AM
> Dear R people:
> 
> Is there a way to perform simple polynomial multiplication;
> that is,
> something like
> (x - 3) * (x + 3) = x^2 - 9, please?
> 
> I looked in poly and polyroot and expression.  There used
> to be a
> package that had this, maybe?
> 
> thanks,
> Erin
> 
> 
> -- 
> Erin Hodgess
> Associate Professor
> Department of Computer and Mathematical Sciences
> University of Houston - Downtown
> mailto: erinm.hodgess at gmail.com
> 
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained,
> reproducible code.

On 16/10/2008, at 10:44 AM, Erin Hodgess wrote:
> Dear R people:
>
> Is there a way to perform simple polynomial multiplication; that is,
> something like
> (x - 3) * (x + 3) = x^2 - 9, please?
>
> I looked in poly and polyroot and expression.  There used to be a
> package that had this, maybe?
The PolynomF package from CRAN will do this.  E.g.

install.packages("PolynomF")
library(PolynomF)
a <- polynom(-3,1)
b <- polynom(3,1)
a*b

The default is to print ``-9 + x^2'' rather than ``x^2 - 9''.

You can of course type
print(a*b,decreasing=TRUE)

to get ``x^2 - 9'', but this is a bit kludgy.  It would be nice to have
an options() setting to change the default.  You could program that up
yourself of course.  (And then send the contributed the improvement to
Bill Venables!)

	cheers,

		Rolf

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On 16/10/2008, at 2:27 PM, Moshe Olshansky wrote:
> Hi Rolf,
>
> Thank you for making me aware of the existence of PolynomF package.
>
> By the way, your solution needs a small modification:
> a <- polynom(c(-3,1)) and not polynom(-3,1) and similar for b.
Indeed; I typed the code into the email separately from typing it into
my R window.  (Bad move!)  I did try the code out (honest!) but then
retyped when I sent my email r.t. copying and pasting.  (Copying and
pasting on a Mac --- on which I am forced to work --- is fraught with
frustrations.)

	cheers,

		Rolf

P. S.  PolynomF seems to be slickly designed.  But then, what do you
expect?  Bill Venables wrote it!

		R.

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