Calculate the product of two polynomial in R

Question

I want to create a function "f" which calculates the product of two polynomials

a0 +a1X + ···+anX^n and b0+b1X+···+bmX^m

For example, since (1 + x)(3 + 2x^2) = 3 + 3x + 2x^2 + 2x^3,we expect the following resuslt:

f(c(1,1),c(3,0,2))
  [1] 3 3 2 2

I have some idea here:

X^0: a0b0
X^1: a0b1+a1b0
X^2: a0b2+a1b1+a2b0
.
.

So, I have the function like this

A =(a0,a1,....,an),B=(b0,b1,...,bn)
f= function(A,B){
          n=length(A)
          m=length(B)
     for(k in 0:(n+m-2))
       for(j in 0:k)
             {
               C[k+1]=sum(A[j+1]*B[k-j+1])
}
     }

But it doesn't work when I type f(A,B) Did anyone has better idea?

use the package `polynom` .. it is already able to do the job. — J_F, Oct 11 '16 at 14:45
You're referring to an object called `C` in your function but there's no object called `C`. — Hack-R, Oct 11 '16 at 14:48
It seems right, but how do I create object C ? >C = matrix(col=n+m-1,row=1) it's not work — 梁楷葳, Oct 11 '16 at 14:53
@梁楷葳 Something like that, yes. Except it's `matrix(ncol=n+m-1,nrow=1)`. Once you've fixed that part of the problem I think there must be an additional problem we still need to fix though. — Hack-R, Oct 11 '16 at 14:53
The other problem is the way you've indexed the original objects. For instance `A` is of length 2 but sometimes you're trying to access the 4th element. — Hack-R, Oct 11 '16 at 15:00

Roland · Answer 1 · 2016-10-11T14:59:29.013

3

library(polynom)
p1 <- polynomial(c(1,1))
p2 <- polynomial(c(3,0,2))

p1 * p2
#3 + 3*x + 2*x^2 + 2*x^3 

coefficients(p1 * p2)
#[1] 3 3 2 2

Here is how the multiplication is implemented in the package:

m <- outer(c(1,1), c(3,0,2))
as.vector(tapply(m, row(m) + col(m), sum))
#[1] 3 3 2 2

See the source code of

polynom:::`Ops.polynomial`

edited Oct 11 '16 at 14:59

answered Oct 11 '16 at 14:48

Roland

127,288
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thank you, but we are not allow to use 'polynom' yet – 梁楷葳 Oct 11 '16 at 14:49
SO is not a homework service. This is a valid answer to your question. You are under no obligation to accept it, but I prefer to provide this answer for others. – Roland Oct 11 '16 at 14:50
@梁楷葳 If you want to ask a homework question on SO they ask that you show some effort (which you did), label it as being for homework, and cite SO in your assignment. So basically you just need to label it as being for homework. – Hack-R Oct 11 '16 at 14:51
Yes, I have no issue with your question. But you are asking for better ideas and this is better. Outside of homework, if you had valid reasons not to use a package, you could just extract the code from package polynom. – Roland Oct 11 '16 at 14:56
@梁楷葳 Yes, you did. I was just saying that you also need to label it as homework. This gives people context so that they provide relevant answers, etc. – Hack-R Oct 11 '16 at 14:58
Thanks for your answer – 梁楷葳 Oct 11 '16 at 15:10

Calculate the product of two polynomial in R

1 Answers1