polymult <- function(a,b)
{
##########################################################################
#
# polymult
# Copyright (C) 2017 Tucker McElroy
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <https://www.gnu.org/licenses/>.
#
############################################################################
################# Documentation #####################################
#
# Purpose: compute the product of two polynomials
# Inputs:
# a: vector of polynomial coefficients, where a[1] is the zeroth coefficient,
# a[2] is the first coefficient, etc.
# b: vector of polynomial coefficients, where b[1] is the zeroth coefficient,
# b[2] is the first coefficient, etc.
# Outputs:
# c: vector of polynomial coefficients for c(z) = a(z)*b(z),
# where c[1] is the zeroth coefficient, c[2] is the first coefficient, etc.
#
##########################################################################################
bb <- c(b,rep(0,length(a)-1))
B <- toeplitz(bb)
B[lower.tri(B)] <- 0
aa <- rev(c(a,rep(0,length(b)-1)))
prod <- B %*% matrix(aa,length(aa),1)
return(rev(prod[,1]))
}
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