# You are given a function (see below) that computes the coefficients of the multiplication of two…

You are given a function (see below) that computes the coefficients of the multiplication of two polynomials. For example: (1 + 2x)(2 – 3x + 4x ^2 ) = 2 + x – 2x ^2 + 8x^ 3 . Suppose the function is called “poly.mult (c1,c2)” where c1 and c2 are the vectors of the coefficients of two polynomials. In the above example, c1 = (1, 2) and c2 = (2, -3, 4). The value of the function is the vector of coefficients of the multiplication. In this example, the value is (2, 1, -2, 8).

Explain the algorithm based on which the following code has been written.

> poly.mult=function(c1,c2)

+{tmp=NULL

+ A=c1%*%t(c2)

+ power=(0:(length(c1)-1))%*%t(rep(1,length(c2)))+

+ rep(1,length(c1))%*%t(0:(length(c2)-1))

+ for(i in 0:(length(c1)+length(c2)-2))

+ {tmp=c(tmp,sum(A[which(power==i,arr.ind=T)]))

+ }

+ tmp }

> c1=c(1,2)

> c2=c(2,-3,4)

> poly.mult(c1,c2)

[1] 2 1 -2 8

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