polynom package - DP

> library(polynom)

> lsf.str("package:polynom")
as.polylist : function (x)
as.polynomial : function (p)
change.origin : function (p, o)
GCD : function (...)
integral : function (expr, ...)
is.polylist : function (x)
is.polynomial : function (p)
LCM : function (...)
monic : function (p)
poly.calc : function (x, y, tol = sqrt(.Machine$double.eps), lab = dimnames(y)[[2]])
poly.from.roots : function (...)
poly.from.values : function (x, y, tol = sqrt(.Machine$double.eps), lab = dimnames(y)[[2]])
poly.from.zeros : function (...)
poly.orth : function (x, degree = length(unique(x)) - 1, norm = TRUE)
polylist : function (...)
polynomial : function (coef = c(0, 1))

> ls("package:polynom")
 [1] "as.polylist"      "as.polynomial"    "change.origin"    "GCD"
 [5] "integral"         "is.polylist"      "is.polynomial"    "LCM"
 [9] "monic"            "poly.calc"        "poly.from.roots"  "poly.from.values"
[13] "poly.from.zeros"  "poly.orth"        "polylist"         "polynomial"

> print(polynomial(coef = c(0, 1, 1)))
x + x^2
> print(is.polynomial(p))
[1] TRUE
> print(as.polynomial(c(1.5, 1, 2)))
1.5 + x + 2*x^2
> print(polynomial(c(2, rep(0, 10), 1)))
2 + x^11

> p <- (polynomial(coef = c(1, 2, 3)))
> change.origin(p, 2)
17 + 14*x + 3*x^2

> poly.calc(rep(1, 2))
1 - 2*x + x^2

> x <- rep(1:4, 1:4)
> poly.orth(x, 3)
List of polynomials:
[[1]]
0.316227766016838

[[2]]
-0.948683298050514 + 0.316227766016838*x

[[3]]
2.1392032339613 - 1.86317701022436*x + 0.345032779671177*x^2

[[4]]
-5.83156435762676 + 8.80369015342205*x - 3.80319414627833*x^2 +
0.493006648591635*x^3

> p <- polynomial(c(1, -2, 1))
> solve(p)
[1] 0.999999990762754 1.000000009237246
> summary(p)
 Summary information for:
1 - 2*x + x^2

 Zeros:
[1] 0.999999990762754 1.000000009237246

 Stationary points:
[1] 1

 Points of inflexion:
numeric(0)

> p <- polynomial(c(1, -2, 1))
> summary(p)
 Summary information for:
1 - 2*x + x^2

 Zeros:
[1] 0.999999990762754 1.000000009237246

 Stationary points:
[1] 1

 Points of inflexion:
numeric(0)

> p <- polynomial(c(1, -2, 1))
> deriv(p)
-2 + 2*x
> q <- as.function(deriv(p))
> q(4)
[1] 6

> p <- polynomial(c(1, -2, 1))
> integral(p, c(-1, 1))
[1] 2.666666666666666

> p <- polynomial(c(1, 2, 1))
> r <- poly.calc(-1:1)
> (r - 2 * p)^2
4 + 20*x + 33*x^2 + 16*x^3 - 6*x^4 - 4*x^5 + x^6

> p <- polynomial(c(1, 2, 1))
> r <- poly.calc(-1:1)
> q <- (r - 2 * p)^2
> plot(q)

> p <- polynomial(c(1, 2, 1))
> r <- poly.calc(-1:1)
> q <- (r - 2 * p)^2
> plot(q)
> points(q)

> p <- polynomial(1)
> for (i in 1:20) {
+     p <- p * polynomial(c(-i, 1))
+ }

> p <- polynomial(1)
> for (i in 1:20) {
+     p <- p * polynomial(c(-i, 1))
+ }
> summary(p)
 Summary information for:
2432902008176640000 - 8752948036761600000*x + 13803759753640699904*x^2 -
1.2870931245151e+19*x^3 + 8037811822645052416*x^4 - 3599979517947607040*x^5 +
1206647803780372992*x^6 - 311333643161390720*x^7 + 63030812099294896*x^8 -
10142299865511450*x^9 + 1307535010540395*x^10 - 135585182899530*x^11 +
11310276995381*x^12 - 756111184500*x^13 + 40171771630*x^14 - 1672280820*x^15 +
53327946*x^16 - 1256850*x^17 + 20615*x^18 - 210*x^19 + x^20

 Zeros:
 [1]  0.999999999999987  2.000000000005535  2.999999999606676  4.000000008574716
 [5]  4.999999911873786  6.000000539646076  6.999997339135784  8.000015569938538
 [9]  8.999900445816888 10.000515221434165 10.998054322771356 12.005420875422889
[13] 12.989040850306202 14.016826758649714 14.981135267518638 16.015413140609159
[17] 16.990899249881661 18.003527072668859 18.999164114293951 20.000089311845350

 Stationary points:
 [1]  1.247666465029009  2.298691625660685  3.334687623347544  4.364313270139911
 [5]  5.390407382915106  6.414303028386359  7.436791488429580  8.458244768604928
 [9]  9.479505067670450 10.499524555020098 11.521423739485462 12.541100753096529
[13] 13.563090555616593 14.586779485887487 15.608057317428516 16.636904921746151
[17] 17.664724112457709 18.701469607486430 19.752314231591491

 Points of inflexion:
 [1]  1.508386410379220  2.610038102786591  3.682544025758086  4.742567106749005
 [5]  5.795668489744330  6.844510051283738  7.890555111707171  8.935170954112486
 [9]  9.977936801124695 11.022506284777965 12.063799652301372 13.110369399826602
[13] 14.155216259781531 15.203996573864432 16.257912704788911 17.317170459491777
[17] 18.390049101074904 19.491602510447258

> rev(coef(p))
 [1]                     1                  -210                 20615
 [4]              -1256850              53327946           -1672280820
 [7]           40171771630         -756111184500        11310276995381
[10]      -135585182899530      1307535010540395    -10142299865511450
[13]     63030812099294896   -311333643161390656   1206647803780373248
[16]  -3599979517947607040   8037811822645052416 -12870931245150988288
[19]  13803759753640704000  -8752948036761600000   2432902008176640000