R : Copyright 2005, The R Foundation for Statistical Computing
Version 2.1.1  (2005-06-20), ISBN 3-900051-07-0

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> ### * <HEADER>
> ###
> attach(NULL, name = "CheckExEnv")
> assign(".CheckExEnv", as.environment(2), pos = length(search())) # base
> ## add some hooks to label plot pages for base and grid graphics
> setHook("plot.new", ".newplot.hook")
> setHook("persp", ".newplot.hook")
> setHook("grid.newpage", ".gridplot.hook")
> 
> assign("cleanEx",
+        function(env = .GlobalEnv) {
+ 	   rm(list = ls(envir = env, all.names = TRUE), envir = env)
+            RNGkind("default", "default")
+ 	   set.seed(1)
+    	   options(warn = 1)
+ 	   delayedAssign("T", stop("T used instead of TRUE"),
+ 		  assign.env = .CheckExEnv)
+ 	   delayedAssign("F", stop("F used instead of FALSE"),
+ 		  assign.env = .CheckExEnv)
+ 	   sch <- search()
+ 	   newitems <- sch[! sch %in% .oldSearch]
+ 	   for(item in rev(newitems))
+                eval(substitute(detach(item), list(item=item)))
+ 	   missitems <- .oldSearch[! .oldSearch %in% sch]
+ 	   if(length(missitems))
+ 	       warning("items ", paste(missitems, collapse=", "),
+ 		       " have been removed from the search path")
+        },
+        env = .CheckExEnv)
> assign("..nameEx", "__{must remake R-ex/*.R}__", env = .CheckExEnv) # for now
> assign("ptime", proc.time(), env = .CheckExEnv)
> grDevices::postscript("polynom-Examples.ps")
> assign("par.postscript", graphics::par(no.readonly = TRUE), env = .CheckExEnv)
> options(contrasts = c(unordered = "contr.treatment", ordered = "contr.poly"))
> options(warn = 1)    
> library('polynom')
> 
> assign(".oldSearch", search(), env = .CheckExEnv)
> assign(".oldNS", loadedNamespaces(), env = .CheckExEnv)
> cleanEx(); ..nameEx <- "Math.polynomial"
> 
> ### * Math.polynomial
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Math.polynomial
> ### Title: Math Group Methods for Polynomials
> ### Aliases: Math.polynomial
> ### Keywords: symbolmath
> 
> ### ** Examples
> 
> op <- options(digits=18)
> p <- poly.from.values(1:4, (2:5)^2)
> ## 1 + 2.00000000000001*x + x^2
> p <- round(p)
> ## 1 + 2*x + x^2
> options(op)
> 
> 
> 
> cleanEx(); ..nameEx <- "Ops.polynomial"
> 
> ### * Ops.polynomial
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Ops.polynomial
> ### Title: Arithmetic Ops Group Methods for Polynomials
> ### Aliases: Ops.polynomial
> ### Keywords: symbolmath
> 
> ### ** Examples
> 
> p <- polynomial(c(1, 2, 1))
> ## 1 + 2*x + x^2
> r <- poly.calc(-1 : 1)
> ## -1*x + x^3
> (r - 2 * p)^2
4 + 20*x + 33*x^2 + 16*x^3 - 6*x^4 - 4*x^5 + x^6 
> ## 4 + 20*x + 33*x^2 + 16*x^3 - 6*x^4 - 4*x^5 + x^6
> 
> 
> 
> cleanEx(); ..nameEx <- "as.function.polynomial"
> 
> ### * as.function.polynomial
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: as.function.polynomial
> ### Title: Coerce a Polynomial to a Function
> ### Aliases: as.function.polynomial
> ### Keywords: symbolmath
> 
> ### ** Examples
> 
> pr <- (poly.calc(-1:1) - 2 * polynomial(c(1, 2, 1)))^2
> pr
4 + 20*x + 33*x^2 + 16*x^3 - 6*x^4 - 4*x^5 + x^6 
> ## 4 + 20*x + 33*x^2 + 16*x^3 - 6*x^4 - 4*x^5 + x^6
> prf <- as.function(pr)
> prf
function (x) 
4 + x * (20 + x * (33 + x * (16 + x * (-6 + x * (-4 + x * (1))))))
<environment: 0x19d7364>
> ## function (x) 
> ## 4 + x * (20 + x * (33 + x * (16 + x * (-6 + x * (-4 + x * (1))))))
> ## <environment: 0x402440f0>
> prf(-3:3)
[1] 1024   64    0    4   64  144   64
> ##  1024 64  0 4 64 144 64
> predict(pr, -3:3)
[1] 1024   64    0    4   64  144   64
> ##  1024 64  0 4 64 144 64
> 
> 
> 
> cleanEx(); ..nameEx <- "change.origin"
> 
> ### * change.origin
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: change.origin
> ### Title: Change Origin for a Polynomial
> ### Aliases: change.origin
> ### Keywords: symbolmath
> 
> ### ** Examples
> 
> pr <- poly.calc(1:5)
> pr
-120 + 274*x - 225*x^2 + 85*x^3 - 15*x^4 + x^5 
> ## -120 + 274*x - 225*x^2 + 85*x^3 - 15*x^4 + x^5
> change.origin(pr, 3)
4*x - 5*x^3 + x^5 
> ## 4*x - 5*x^3 + x^5
> 
> 
> 
> cleanEx(); ..nameEx <- "deriv.polynomial"
> 
> ### * deriv.polynomial
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: deriv.polynomial
> ### Title: Differentiate a Polynomial
> ### Aliases: deriv.polynomial
> ### Keywords: symbolmath
> 
> ### ** Examples
> 
> pr <- poly.calc(1:5)
> pr
-120 + 274*x - 225*x^2 + 85*x^3 - 15*x^4 + x^5 
> ## -120 + 274*x - 225*x^2 + 85*x^3 - 15*x^4 + x^5
> deriv(pr)
274 - 450*x + 255*x^2 - 60*x^3 + 5*x^4 
> ##  274 - 450*x + 255*x^2 - 60*x^3 + 5*x^4
> 
> 
> 
> cleanEx(); ..nameEx <- "integral.polynomial"
> 
> ### * integral.polynomial
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: integral.polynomial
> ### Title: Integrate a Polynomial
> ### Aliases: integral integral.polynomial
> ### Keywords: symbolmath
> 
> ### ** Examples
> 
> p <- poly.calc(1:5)
> p
-120 + 274*x - 225*x^2 + 85*x^3 - 15*x^4 + x^5 
> ## -120 + 274*x - 225*x^2 + 85*x^3 - 15*x^4 + x^5
> deriv(p)
274 - 450*x + 255*x^2 - 60*x^3 + 5*x^4 
> ## 274 - 450*x + 255*x^2 - 60*x^3 + 5*x^4
> integral(deriv(p)) - 120
-120 + 274*x - 225*x^2 + 85*x^3 - 15*x^4 + x^5 
> ## -120 + 274*x - 225*x^2 + 85*x^3 - 15*x^4 + x^5
> 
> 
> 
> cleanEx(); ..nameEx <- "lines.polynomial"
> 
> ### * lines.polynomial
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: lines.polynomial
> ### Title: Lines Method for Polynomials
> ### Aliases: lines.polynomial
> ### Keywords: symbolmath
> 
> ### ** Examples
> 
> plot  (poly.calc(-1:5))
> lines (poly.calc( 2:4), lty = 2)
> points(poly.calc(-2:6), pch = 4)
> 
> 
> 
> cleanEx(); ..nameEx <- "plot.polynomial"
> 
> ### * plot.polynomial
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: plot.polynomial
> ### Title: Plot Method for Polynomials
> ### Aliases: plot.polynomial
> ### Keywords: symbolmath
> 
> ### ** Examples
> 
> plot(p <- poly.calc(-1:5))
> 
> 
> 
> cleanEx(); ..nameEx <- "points.polynomial"
> 
> ### * points.polynomial
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: points.polynomial
> ### Title: Points Method for Polynomials
> ### Aliases: points.polynomial
> ### Keywords: symbolmath
> 
> ### ** Examples
> 
> plot(poly.calc(-1:5))
> lines(poly.calc(2:4), lty=2)
> points(poly.calc(-2:6), pch=4)
> 
> 
> 
> cleanEx(); ..nameEx <- "poly.calc"
> 
> ### * poly.calc
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: poly.calc
> ### Title: Calculate Polynomials from Zeros or Values
> ### Aliases: poly.calc poly.from.zeros poly.from.roots poly.from.values
> ### Keywords: symbolmath
> 
> ### ** Examples
> 
> poly.calc(rep(1,3))
-1 + 3*x - 3*x^2 + x^3 
> ## -1 + 3*x - 3*x^2 + x^3 
> poly.calc(0:4, (0:4)^2 + 1)
1 + x^2 
> ## 1 + x^2 
> poly.calc(0:4, cbind(0:4, (0:4)^2 + 1), lab = letters[1:2])
List of polynomials:
$a
x 

$b
1 + x^2 

> ## List of polynomials:
> ## $a:
> ## x
> ##
> ## $b:
> ## 1 + x^2 
> 
> 
> 
> cleanEx(); ..nameEx <- "poly.orth"
> 
> ### * poly.orth
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: poly.orth
> ### Title: Construct Orthogonal Polynomials
> ### Aliases: poly.orth
> ### Keywords: symbolmath
> 
> ### ** Examples
> 
> x <- rep(1:4, 1:4)              # x with repetitions for weighting
> x
 [1] 1 2 2 3 3 3 4 4 4 4
> ## [1] 1 2 2 3 3 3 4 4 4 4
> polx <- poly.orth(x, 3)         # calculate orthogonal polynomials
> polx
List of polynomials:
[[1]]
0.3162278 

[[2]]
-0.9486833 + 0.3162278*x 

[[3]]
2.139203 - 1.863177*x + 0.3450328*x^2 

[[4]]
-5.831564 + 8.80369*x - 3.803194*x^2 + 0.4930066*x^3 

> ## List of polynomials:
> ## [[1]]
> ## 0.3162278 
> ## 
> ## [[2]]
> ## -0.9486833 + 0.3162278*x 
> ## 
> ## [[3]]
> ## 2.139203 - 1.863177*x + 0.3450328*x^2 
> ## 
> ## [[4]]
> ## -5.831564 + 8.80369*x - 3.803194*x^2 + 0.4930066*x^3 
> v <- sapply(polx, predict, x)   # orthonormal basis
> round(crossprod(v), 10)         # check orthonormality
     [,1] [,2] [,3] [,4]
[1,]    1    0    0    0
[2,]    0    1    0    0
[3,]    0    0    1    0
[4,]    0    0    0    1
> 
> 
> 
> cleanEx(); ..nameEx <- "polylist"
> 
> ### * polylist
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: polylist
> ### Title: Lists of Polynomials
> ### Aliases: polylist deriv.polylist integral.polylist plot.polylist
> ###   print.polylist
> ### Keywords: symbolmath
> 
> ### ** Examples
> 
> ## Calculate orthogonal polynomials
> pl <- poly.orth(rep(1:4, 1:4), 3)
> pl
List of polynomials:
[[1]]
0.3162278 

[[2]]
-0.9486833 + 0.3162278*x 

[[3]]
2.139203 - 1.863177*x + 0.3450328*x^2 

[[4]]
-5.831564 + 8.80369*x - 3.803194*x^2 + 0.4930066*x^3 

> plot(pl)
> deriv(pl)
List of polynomials:
[[1]]
0 

[[2]]
0.3162278 

[[3]]
-1.863177 + 0.6900656*x 

[[4]]
8.80369 - 7.606388*x + 1.47902*x^2 

> integral(pl)
List of polynomials:
[[1]]
0.3162278*x 

[[2]]
-0.9486833*x + 0.1581139*x^2 

[[3]]
2.139203*x - 0.9315885*x^2 + 0.1150109*x^3 

[[4]]
-5.831564*x + 4.401845*x^2 - 1.267731*x^3 + 0.1232517*x^4 

> 
> 
> 
> cleanEx(); ..nameEx <- "polynomial"
> 
> ### * polynomial
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: polynomial
> ### Title: Polynomials
> ### Aliases: polynomial as.polynomial is.polynomial as.character.polynomial
> ###   print.polynomial coef.polynomial
> ### Keywords: symbolmath
> 
> ### ** Examples
> 
> polynomial(1:4)
1 + 2*x + 3*x^2 + 4*x^3 
> p <- as.polynomial(c(1,0,3,0))
> p
1 + 3*x^2 
> print(p, decreasing = TRUE)
3*x^2 + 1 
> stopifnot(coef(p) == c(1,0,3))
> 
> polynomial(c(2,rep(0,10),1))
2 + x^11 
> 
> 
> 
> cleanEx(); ..nameEx <- "solve.polynomial"
> 
> ### * solve.polynomial
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: solve.polynomial
> ### Title: Zeros of a Polynomial
> ### Aliases: solve.polynomial
> ### Keywords: symbolmath
> 
> ### ** Examples
> 
> p <- polynomial(6:1)
> p
6 + 5*x + 4*x^2 + 3*x^3 + 2*x^4 + x^5 
> ## 6 + 5*x + 4*x^2 + 3*x^3 + 2*x^4 + x^5 
> pz <- solve(p)
> pz
[1] -1.4917980+0.000000i -0.8057865-1.222905i -0.8057865+1.222905i
[4]  0.5516855-1.253349i  0.5516855+1.253349i
> ## [1] -1.49180+0.0000i -0.80579-1.2229i -0.80579+1.2229i
> ## [4]  0.55169-1.2533i  0.55169+1.2533i
> ## To retrieve the original polynomial from the zeros:
> poly.calc(pz)
Warning: imaginary parts discarded in coercion
Warning: out-of-range values treated as 0 in coercion to raw
6 + 5*x + 4*x^2 + 3*x^3 + 2*x^4 + x^5 
> ## Warning: imaginary parts discarded in coercion
> ## 6 + 5*x + 4*x^2 + 3*x^3 + 2*x^4 + x^5
> 
> 
> 
> cleanEx(); ..nameEx <- "summary.polynomial"
> 
> ### * summary.polynomial
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: summary.polynomial
> ### Title: Summary of a Polynomial
> ### Aliases: summary.polynomial print.summary.polynomial
> ### Keywords: symbolmath
> 
> ### ** Examples
> 
> p <- polynomial(6:1)
> p
6 + 5*x + 4*x^2 + 3*x^3 + 2*x^4 + x^5 
> ## 6 + 5*x + 4*x^2 + 3*x^3 + 2*x^4 + x^5 
> pz <- summary(p)
> pz

 Summary information for:
6 + 5*x + 4*x^2 + 3*x^3 + 2*x^4 + x^5 

 Zeros:
[1] -1.4917980+0.000000i -0.8057865-1.222905i -0.8057865+1.222905i
[4]  0.5516855-1.253349i  0.5516855+1.253349i

 Stationary points:
[1] -0.85825757-0.5132192i -0.85825757+0.5132192i  0.05825757-0.9983016i
[4]  0.05825757+0.9983016i

 Points of inflexion:
[1] -0.7211424+0.00000i -0.2394288-0.70523i -0.2394288+0.70523i
> ## [1] -1.49180+0.0000i -0.80579-1.2229i -0.80579+1.2229i
> ## [4]  0.55169-1.2533i  0.55169+1.2533i
> ## To retrieve the original polynomial from the zeros:
> poly.calc(pz)
Warning in xi * p : longer object length
	is not a multiple of shorter object length
Warning in xi * p : longer object length
	is not a multiple of shorter object length
Warning: imaginary parts discarded in coercion
Warning: out-of-range values treated as 0 in coercion to raw
0.9233124 + 2.072266*x + 5.862637*x^2 + 4.444231*x^3 + 2.253262*x^4 -  
0.5543656*x^5 + 1.027714*x^6 + x^7 
> ## Warning: imaginary parts discarded in coercion
> ## 6 + 5*x + 4*x^2 + 3*x^3 + 2*x^4 + x^5
> 
> 
> 
> ### * <FOOTER>
> ###
> cat("Time elapsed: ", proc.time() - get("ptime", env = .CheckExEnv),"\n")
Time elapsed:  0.27 0.02 0.29 0 0 
> grDevices::dev.off()
null device 
          1 
> ###
> ### Local variables: ***
> ### mode: outline-minor ***
> ### outline-regexp: "\\(> \\)?### [*]+" ***
> ### End: ***
> quit('no')