R help - Dec 2004 - how can I get the coefficients of x^0, x^1, x^2, . , x^6 from expansion of (1+x+x^2)^3

Hi, 

 

I would like to get the coefficients of x^0, x^1, x^2,  . , x^6 from
expansion of (1+x+x^2)^3.

The result should be 1, 3, 6, 7, 6, 3, 1; 

 

How can I calculate in R? 

 

You help will be greatly appreciated.

 

Peter 

 

 


	[[alternative HTML version deleted]]

Use the 'polynom' library:
> p <- as.polynomial(c(1,1,1))
> p
1 + x + x^2
> p^3
1 + 3*x + 6*x^2 + 7*x^3 + 6*x^4 + 3*x^5 + x^6
 > unclass(p^3)
[1] 1 3 6 7 6 3 1
>
__________________________________________________________
James Holtman        "What is the problem you are trying to solve?"
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                      "Peter Yang"
                      <peterwyang at gmail.com        To:       <r-help at
stat.math.ethz.ch>
                      >                            cc:
                      Sent by:                     Subject:  [R] how can I get
the coefficients of x^0, x^1, x^2, . ,    x^6 from
                      r-help-bounces at stat.m         expansion of (1+x+x^2)^3
                      ath.ethz.ch


                      12/03/2004 14:56






Hi,



I would like to get the coefficients of x^0, x^1, x^2,  . , x^6 from
expansion of (1+x+x^2)^3.

The result should be 1, 3, 6, 7, 6, 3, 1;



How can I calculate in R?



You help will be greatly appreciated.



Peter






             [[alternative HTML version deleted]]

______________________________________________
R-help at stat.math.ethz.ch mailing list
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PLEASE do read the posting guide!
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Have you considered library(polynom)?  If you don't already have 
it but have R, install.packages("polynom") should get it. 

      hope this helps.  spencer graves

Peter Yang wrote:
>Hi, 
>
> 
>
>I would like to get the coefficients of x^0, x^1, x^2,  . , x^6 from
>expansion of (1+x+x^2)^3.
>
>The result should be 1, 3, 6, 7, 6, 3, 1; 
>
> 
>
>How can I calculate in R? 
>
> 
>
>You help will be greatly appreciated.
>
> 
>
>Peter 
>
> 
>
> 
>
>
>	[[alternative HTML version deleted]]
>
>______________________________________________
>R-help at stat.math.ethz.ch mailing list
>https://stat.ethz.ch/mailman/listinfo/r-help
>PLEASE do read the posting guide!
http://www.R-project.org/posting-guide.html
>  
>
-- 
Spencer Graves, PhD, Senior Development Engineer
O:  (408)938-4420;  mobile:  (408)655-4567

From:   Peter Yang <peterwyang at gmail.com>
>I would like to get the coefficients of x^0, x^1, x^2, . , x^6 from
>expansion of (1+x+x^2)^3.

# modification of DD in example(D) to support 0th derivative
DD <- function(expr,name, order = 0) {
   if(order == 0) 
	expr
   else DD(D(expr, name), name, order - 1)
}

# take symbolic derivatives, evaluate at 0 and divide by factorial n
sapply(0:6, function(i) eval(DD(e,"x",i),list(x=0)))/factorial(0:6)

From: Peter Yang <peterwyang at gmail.com>
>I would like to get the coefficients of x^0, x^1, x^2, . , x^6 from
>expansion of (1+x+x^2)^3.

# modification of DD in example(D) to support 0th derivative
DD <- function(expr,name, order = 0) {
if(order == 0) 
     expr
else DD(D(expr, name), name, order - 1)
}

# take symbolic derivatives, evaluate at 0 and divide by factorial n
sapply(0:6, function(i) eval(DD(e,"x",i),list(x=0)))/factorial(0:6)


By the way, e in the above is your expression, in this case:

 e <- expression((1+x+x^2)^3)

Alternatively, how about the following: 

library(polynom)
coefficients(polynomial(c(1,1,1))^3)
[1] 1 3 6 7 6 3 1

      hope this helps.  spencer graves

Gabor Grothendieck wrote:
> 
>
>From: Peter Yang <peterwyang at gmail.com>
>
>  
>
>>I would like to get the coefficients of x^0, x^1, x^2, . , x^6 from
>>expansion of (1+x+x^2)^3.
>>    
>>
>
>
># modification of DD in example(D) to support 0th derivative
>DD <- function(expr,name, order = 0) {
>if(order == 0) 
>     expr
>else DD(D(expr, name), name, order - 1)
>}
>
># take symbolic derivatives, evaluate at 0 and divide by factorial n
>sapply(0:6, function(i)
eval(DD(e,"x",i),list(x=0)))/factorial(0:6)
>
>
>By the way, e in the above is your expression, in this case:
>
> e <- expression((1+x+x^2)^3)
>
>______________________________________________
>R-help at stat.math.ethz.ch mailing list
>https://stat.ethz.ch/mailman/listinfo/r-help
>PLEASE do read the posting guide!
http://www.R-project.org/posting-guide.html
>  
>
-- 
Spencer Graves, PhD, Senior Development Engineer
O:  (408)938-4420;  mobile:  (408)655-4567