Simpifying Output of Deriv and Extract the Coefficients in R - r

Question

I have two calculations for partial derivatives of an equation in R.
p_deriv_m <- Deriv(eqn, 'm')
#"-(2 * (6 - (b + m)) + 4 * (5 - (2 * m + b)) + 6 * (7 - (3 * m + b)) + 8 * (10 - (4 * m + b)))"
p_deriv_b <- Deriv(eqn, 'b')
#"-(2 * (10 - (4 * m + b)) + 2 * (5 - (2 * m + b)) + 2 * (6 - (b + m)) + 2 * (7 - (3 * m + b)))"
I would like to...
(1) Simplify these equations into something like of the form (making up the coefficients here) p_deriv_m = 8 + 9b - 10m and p_deriv_b = 10 + 15b + 8m
(2) Extract the Coefficients from these partial derivative equations so I can solve for m, b when the partial derivatives both equal 0. Using the examples I made up in (1) above...
9b - 10m = -8
15b + 8m = -10
Pop those numbers into a matrix and solve like this solution here - Solving simultaneous equations with R outputting and m and b.
If anyone knows how I can do (1) and/or (2), help would be greatly appreciated.
Rest of my code for reference:
library(Ryacas)
library(Deriv)
x_p <- c(1,2,3,4)
y_p <- c(6,5,7,10)
# Turn m and b into symbols
b <- Ryacas::Sym("b")
m <- Ryacas::Sym("m")
# Create a function
rss <- function(b,m,x_points, y_points)
(y_points[1] - (b + x_points[1]*m))^2 +
(y_points[2] - (b + x_points[2]*m))^2 +
(y_points[3] - (b + x_points[3]*m))^2 +
(y_points[4] - (b + x_points[4]*m))^2
# Create the equation
eqn <- rss(b,m,x_p,y_p)
p_deriv_m <- Deriv(eqn, 'm')
p_deriv_b <- Deriv(eqn, 'b')
ANSWER: Ended up doing it manually
sls_manual.R
# Doing a linear regression manually - want to find m and b
# Such that rss is minimized
library(Ryacas)
library(Deriv)
source('get_coeff.r')
# Sample Points - keeping the number of points small for now for
# the purposes of this example
x_p <- c(1,2,3,4)
y_p <- c(6,5,7,10)
b <- Ryacas::Sym("b")
m <- Ryacas::Sym("m")
# Create a function
rss <- function(b,m,x_points, y_points)
(y_points[1] - (b + x_points[1]*m))^2 +
(y_points[2] - (b + x_points[2]*m))^2 +
(y_points[3] - (b + x_points[3]*m))^2 +
(y_points[4] - (b + x_points[4]*m))^2
# Create the equation
eqn <- rss(b,m,x_p,y_p)
p_deriv_m <- Deriv(eqn, 'm')
p_deriv_b <- Deriv(eqn, 'b')
simplified_m_deriv <- yacas(Expand(p_deriv_m))
simplified_b_deriv<- yacas(Expand(p_deriv_b))
row_1_coeff <- get_coefficients(simplified_m_deriv)
row_2_coeff <- get_coefficients(simplified_b_deriv)
r_1_coeff <- c(row_1_coeff[[1]][1], row_1_coeff[[2]][1], row_1_coeff[[3]][1])
r_2_coeff <- c(row_2_coeff[[1]][1], row_2_coeff[[2]][1], row_2_coeff[[3]][1])
A <- matrix(data=c(r_1_coeff[1], r_1_coeff[2]
,r_2_coeff[1], r_2_coeff[2])
,nrow=2, ncol=2, byrow=TRUE)
b <- matrix(data=c((-1*r_1_coeff[3]),(-1*r_2_coeff[3]))
,nrow=2, ncol=1, byrow=TRUE)
result <- solve(A,b)
m_coeff = result[1]
b_coeff = result[2]
# Last step is to verify that this does the same thing as lm:w
# fit <- lm(y_p ~ x_p)
# fit
get_coeff.R
get_coefficients <- function(exp) {
# Take out the whitespace
g <- gsub(" ", "", as.character(exp))
# Sub the minuses for a +-
g2 <- gsub("-", "+-", g)
g3 <- gsub("[()]", "", g2)
# break at the plusses
g4 <- strsplit(g3, "[//+]")
b_coeff = 0
m_coeff = 0
other_coeff = 0
i = 1
while(i <= 3)
{
piece <- as.character(g4[[1]][i])
contains_b = grepl("b",piece)
contains_m = grepl("m",piece)
contains_both = contains_b & contains_m
if (contains_b == TRUE){
b_coeff = as.numeric(gsub("[//*b|b//*]", "", piece))
} else if (contains_m == TRUE){
m_coeff = as.numeric(gsub("[//*m|m//*]", "", piece))
} else if (contains_both == FALSE) {
other_coeff = as.numeric(piece)
} else {
}
i = i + 1
}
output <- list(m_coeff,b_coeff, other_coeff)
return(output)
}