42- - 4 months ago 30

R Question

In R how would one represent polynomial expressions and do polynomial math with the numeric vector objects? For example:

`x1 <- c(2,1) # 2 + x`

x2 <- c(-1,3) # -1 + 3*x

And want:

`x1 * x2 # to return -2 + 5*x + 3*x^2`

Note:I answered a question this morning and then the poster apparently deleted it (making me wonder if it were homework.) So I am re-posting the question from memory.

Answer

One could multiply the coefficients directly using `outer`

and then aggregate the results

```
x1 <- c(2,1) # 2 + x
x2 <- c(-1,3) # -1 + 3*x
tmp <- outer(x1, x2)
tapply(tmp, row(tmp) + col(tmp) - 1, sum)
# 1 2 3
#-2 5 3
x1 <- c(2, 1) # 2 + x
x2 <- c(-1, 3, 2) # -1 + 3*x + 2*x^2
tmp <- outer(x1, x2)
tapply(tmp, row(tmp) + col(tmp) - 1, sum) # should give -2 + 5*x + 7*x^2 + 2*x^3
# 1 2 3 4
#-2 5 7 2
```

as discussed in the comments the '-1' in the code isn't necessary. When coming up with the solution that helped me because it allowed me to map each location in the output of `outer`

to where it would end up in the final vector. If we did a '-2' instead then it would map to the exponent on x in the resulting polynomial. But we really don't need it so something like the following would work just as well:

```
tmp <- outer(x1, x2)
tapply(tmp, row(tmp) + col(tmp), sum)
```