Hi and thank you for your time,
I realize my question is in fact very similar to the question in this thread: How to get coefficients of polynomial expression
However, I would like to elaborate on this question.
I have written a program which when given a vector filled with the coefficients of a polynomial in ascending degree with respect to the monomials within that polynomial will output a vector filled with the coefficients of the primitive of this polynomial in a similar manner. For example, when I want to know the primitive of the expression y = 54s^2 - 36s + 3, I would input the vector (3, -36, 54) into my program and it would return the vector (0, 3, -18, 18) since the primitive of this y is 18s^3 - 18s^2 + 3s.
The code for this program is as follows:
# Define function degree
degree <- function() {
# First asks for degree
m1 <- readline("Please input the degree of your polynomial.")
# Checks if degree is integer and non-negative
m2 <- as.integer(m1)
if ((m2 == m1)&(m1>0)) {
print(paste("The degree of your polynomial is", m1))
}
if(m2 != m1) {
print("The degree of a polynomial must be an integer.")
degree()
}
if(m1 < 0) {
print("The degree of a polynomial must be non-negative.")
degree()
}
# Last output of degree is defining numeric m
m <- as.numeric(m1)
}
# Define function polynomial
polynomial <- function() {
# First calls on the degree function
m <- degree()
# Then asks for coefficients
a <- readline("Please input the coefficients of your polynomial in order of their
ascending degree separated by a space, such as: a[0] a[1] a[2] ... a[m]")
# Creates vector a filled with these coefficients
a <- strsplit(a, " ")
a <- a[[1]]
a <- as.numeric(a)
# Checks if any non-numeric values were entered for the coefficients
if (is.na(sum(a)) == TRUE) {
print("The program does not allow for non-numeric coefficients.")
polynomial()
}
# Checks if length of vector is equal to degree + 1
if ((length(a) == m+1)) {
print("Your polynomial can be represented by the vector:")
print(a)
}
if ((length(a) != m+1)) {
print("Please input a coefficient for the degree of each separate monomial within
your polynomial.")
polynomial()
}
# Last output of polynomial is defining numeric a
a <- as.numeric(a)
}
# Define function primitive
primitive <- function() {
# Call on function polynomial
a <- polynomial()
# Calculate the primitive
p <- c()
p[1] <- 0
for (i in 1:length(a)){
p[i + 1] <- a[i]/i
}
print(paste("The degree of your primitive is", (length(p) - 1)))
print("The primitive of your polynomial can be represented by the vector")
print(p)
}
Now this is probably not flawless in itself, but it works fine. The issue I have now however is that I want to be able to calculate Picard iterations of differential equations in the form of a polynomial. Now, I'm quite confident that I can write this code myself, so I will only ask what is relevant for me to continue my work.
I essentially want to be able to be able to simplify any expression to a polynomial form (if the expression allows for this, but we assume it does). For example, if my expression is 6(3s - 1)^2, then I want R to simplify this to 54s^2 - 36s + 6 and put it into the vector form (6, -36, 54), so I can run it with my written program primitive. I have tried using the package rSympy to get the following:
sympy("expand(6*(3*s - 1)**2)")
Which gives me the output
[1] "6 - 36*s + 54*s**2"
However I have no idea how to obtain the (numerical) vector (6, -36, 54) from this output.
In the thread which I linked I saw that they used the function 'gregexpr'. I however have no idea what this function does and how it works, I couldn't for the life of me figure out what exactly I'd have to input into this function in order to obtain the vector I need. I dislike writing code which I do not understand. Please help and explain!
