[R] Symbolic derivation using D in package stats - how do I properly convert the returned call into a character string?

[Daniel Berg]

Dear all,

I am using the function 'D' in the 'stats' package to perform symbolic 
derivation.
This works very well and it is much faster than e.g. Mathematica (at 
least for my purposes).
First, I would like to thank the development team for this excellent 
function.

However, I run into trouble in some cases, particularly when I am to do 
some operations on long expressions obtained from using D.
The problem seems to occur when I convert a 'call' or an 'expression' to 
a 'character', then some parts of the original 'expression' is lost.
Is there some way of transforming a call or an expression into a 
character string that I do not know of or alternatively, can I merge two 
calls or two expressions by a numerical operation, e.g. c = a / b where 
both a and b are symbolic expressions and I wish for c to be a symbolic 
expression as well?

Take e.g. the following example:
#---------------------------------
# First, I try with d=2, now it works:
d<-2; u<-rep("u1",d); th<-rep("th1",d)
for(i in 1:d) { u[i] <- paste("u",i,sep=""); th[i] <- paste("th",i,sep="") }
dC1 <- expression((((1 - 2 + u1^(-th1)) + u2^(-th1))^(-1/th1)))
dC2 <- expression(u1)
#These expressions were returned from a combination of several 
expressions of mine...
for(j in 1:(d-1)) { dC1<-D(expr=dC1,name=u[j]); dC2<-D(expr=dC2,name=u[j]) }
# I wish to create a new expression equal to dC1 / dC2 and I proceed as 
follows:
F <- paste("(",as.expression(dC1),")/(",as.expression(dC2),")",sep="")
# To see that it works print dC1, dC2 and F and compare.

# It also works for d=3, but for d=4 something strange happens:
d<-4; u<-rep("u1",d); th<-rep("th1",d)
for(i in 1:d) { u[i] <- paste("u",i,sep=""); th[i] <- paste("th",i,sep="") }
dC1 <- expression((((1 - 2 + u1^(-th1)) + (((1 - 2 + u2^(-th2)) + (((1 - 
2 + u3^(-th3)) + u4^(-th3))^(-1/th3))^(-th2))^(-1/th2))^(-th1))^(-1/th1)))
dC2 <- expression((((1 - 2 + u1^(-th1)) + (((1 - 2 + u2^(-th2)) + 
u3^(-th2))^(-1/th2))^(-th1))^(-1/th1)))
for(j in 1:(d-1)) { dC1<-D(expr=dC1,name=u[j]); dC2<-D(expr=dC2,name=u[j]) }
F <- paste("(",as.expression(dC1),")/(",as.expression(dC2),")",sep="")
# Now paste(dC1) throws away parts of the expression. Try
paste(dC1)
# and see the end of second element.
# You will get a 3-dim char vector where there is something missing at 
the end of the second element.
#-----------------------------------

I am running R 2.2.1 on windows.
Any help, suggestions or comments in general will be highly appreciated.

Thank you.

Best wishes,
Daniel Berg

---------------------
danielberg.no