R help - Dec 2009 - Adding and Multiplying two Unevaluated Expressions

HI,

As I'm trying to compute Taylor series, I'm having problems in adding
and multiplying unevaluated expressions. I searched for a solution but found
none.

my Taylor function works fine for evaluating functions as you can see here:


rTaylorVal=function(exp,x0,dx,n) {

ls=list(x=x0)

newexp=eval(exp,ls)

exp0=exp

for (i in 1:n){
exp0=D(exp0,"x")
newexp=newexp+eval(exp0,ls)/factorial(i)*dx^i
}

return(newexp)

}

Where exp is an expression like exp=expression(x^2*sin(x)), x0 is the
startvalue, dx the difference between startvalue and searched value and n is the
length of the series.

So I tried to remove dx as a value, to get a Taylor series expression, but it
doesn't work as simple multiplication (*) and accumulation (+) is not good
for expressions.

That's my point so far, now my question:

Is it actually possible to add and/or multiply expressions, and how?

Thank you so far.

Benjamin M?ller
Geographer (B.Sc.)


-- 
GRATIS f?r alle GMX-Mitglieder: Die maxdome Movie-FLAT!

Benjamin M?ller wrote:
> HI,
> 
> As I'm trying to compute Taylor series, I'm having problems in
adding and multiplying unevaluated expressions. I searched for a solution but
found none.
> 
> my Taylor function works fine for evaluating functions as you can see here:
> 
> 
> rTaylorVal=function(exp,x0,dx,n) {
> 
> ls=list(x=x0)
> 
> newexp=eval(exp,ls)
> 
> exp0=exp
> 
> for (i in 1:n){
> exp0=D(exp0,"x")
> newexp=newexp+eval(exp0,ls)/factorial(i)*dx^i
> }
> 
> return(newexp)
> 
> }
> 
> Where exp is an expression like exp=expression(x^2*sin(x)), x0 is the
startvalue, dx the difference between startvalue and searched value and n is the
length of the series.
> 
> So I tried to remove dx as a value, to get a Taylor series expression, but
it doesn't work as simple multiplication (*) and accumulation (+) is not
good for expressions.
> 
> That's my point so far, now my question:
> 
> Is it actually possible to add and/or multiply expressions, and how?

Well, although R as a numerical language is not designed for these kind 
of things, you can do it, e.g. using a function

opExpr <- function(expr1, expr2, op = "+"){
     expr <- expression(a + b)
     expr[[1]][[1]] <- as.name(op)
     expr[[1]][[2]] <- expr1[[1]]
     expr[[1]][[3]] <- expr2[[1]]
     expr
}

that can construct such expressions as in:

opExpr(expression(x * sin(x)), expression(x^2 * sin(x)))
opExpr(expression(x * sin(x)), expression(x^2 * sin(x)), "*")

Best wishes,
Uwe Ligges


> Thank you so far.
> 
> Benjamin M?ller
> Geographer (B.Sc.)
> 
>