add bring_power_down = FALSE to deriv; normalize_coefficients()

DESCRIPTION

@@ -1,7 +1,7 @@
 Package: mpoly
 Type: Package
 Title: Symbolic Computation and More with Multivariate Polynomials
-Version: 1.1.1.901
+Version: 1.1.1.902
 URL: https://github.com/dkahle/mpoly
 BugReports: https://github.com/dkahle/mpoly/issues
 Authors@R: person("David", "Kahle", email = "david@kahle.io", role = c("aut", "cre"), comment = c(ORCID = "0000-0002-9999-1558"))

NAMESPACE

@@ -69,6 +69,7 @@ export(mp)
 export(mpoly)
 export(mpolyList)
 export(multideg)
+export(normalize_coefficients)
 export(partitions)
 export(permutations)
 export(plug)

NEWS.md

@@ -4,6 +4,11 @@
 
 *   `coef()` allows you to extract the coefficients of an mpoly object (#25, 
     thanks @ggrothendieck).
+
+*   `deriv()` now allows you to not bring the power down as a multiplier.
+
+*   `normalize_coefficients()` now allows you normalize term coefficients 
+    according to an input norm, defaulting to the Euclidean norm.
 
 
 

R/components.R

@@ -11,6 +11,9 @@
 #' @param object mpoly object to pass to [coef()]
 #' @param ... In [coef()], additional arguments passed to [print.mpoly()] for
 #'   the names of the resulting vector
+#' @param p an object of class mpoly or mpolyList
+#' @param norm a norm (function) to normalize the coefficients of a polynomial, 
+#'   defaults to the Euclidean norm
 #' @return An object of class mpoly or mpolyList, depending on the context
 #' @name components
 #' @examples
@@ -35,6 +38,18 @@
 #'
 #' homogeneous_components(p)
 #' 
+#' (p <- mp("(x + y)^2"))
+#' normalize_coefficients(p)
+#' norm <- function(v) sqrt(sum(v^2))
+#' norm(coef( normalize_coefficients(p) ))
+#' 
+#' abs_norm <- function(x) sum(abs(x))
+#' normalize_coefficients(p, norm = abs_norm)
+#' 
+#' p <- mp(c("x", "2 y"))
+#' normalize_coefficients(p)
+#' 
+#' 
 
 
 
@@ -174,3 +189,16 @@ coef.mpoly <- function(object, ...) {
 
 
 
+
+
+#' @rdname components
+#' @export
+normalize_coefficients <- function(p, norm = function(x) sqrt(sum(x^2))) {
+  if (is.mpolyList(p)) return( structure(lapply(p, normalize_coefficients), class = "mpolyList") )
+  normalize <- function(x) x / norm(x)
+  c <- normalize(coef(p))
+  for (i in seq_along(p)) p[[i]]["coef"] <- c[i]
+  p
+}
+
+

R/deriv.mpoly.R

@@ -6,18 +6,25 @@
 #' @param expr an object of class mpoly
 #' @param var character - the partial derivative desired
 #' @param ... any additional arguments
+#' @param bring_power_down if `FALSE`, x^n -> x^(n-1), not n x^(n-1)
 #' @return An object of class mpoly or mpolyList.
 #' @export
 #' @examples
-#' m <- mp("x y + y z + z^2")
-#' deriv(m, "x")
-#' deriv(m, "y")
-#' deriv(m, "z")
-#' deriv(m, c("x","y","z"))
-#' deriv(m, "a")
-#' is.mpoly(deriv(m, "x"))
-#' is.mpolyList( deriv(m, c("x","y","z")) )
-deriv.mpoly <- function(expr, var, ...){
+#' p <- mp("x y + y z + z^2")
+#' deriv(p, "x")
+#' deriv(p, "y")
+#' deriv(p, "z")
+#' deriv(p, "t")
+#' deriv(p, c("x","y","z"))
+#' 
+#' is.mpoly(deriv(p, "x"))
+#' is.mpolyList( deriv(p, c("x","y","z")) )
+#' 
+#' p <- mp("x^5")
+#' deriv(p, "x")
+#' deriv(p, "x", bring_power_down = FALSE)
+#' 
+deriv.mpoly <- function(expr, var, ..., bring_power_down = TRUE){
 
   # argument checks	
   if (missing(var)) stop("var must be specified, see ?deriv.mpoly", call. = FALSE)
@@ -46,7 +53,7 @@ deriv.mpoly <- function(expr, var, ...){
   	if(length(v) == 1) return(c(coef = 0))
     p <- length(v)
     if(!(var %in% names(v[1:p]))) return(c(coef = 0))
-    v["coef"] <- unname(v[var]) * v["coef"]
+    if (bring_power_down) v["coef"] <- unname(v[var]) * v["coef"]
     v[var] <- v[var] - 1
     v
   })

tests/testthat/test-components.R

@@ -129,3 +129,51 @@ test_that("coef works", {
 
 
 
+
+
+test_that("normalize_coefficients works", {
+
+  p <- mp("(x + y)^2")
+
+  expect_equal(
+    normalize_coefficients(p),
+    structure(
+      list(
+        c(x = 2, coef = 0.408248290463863), 
+        c(x = 1, y = 1, coef = 0.816496580927726), 
+        c(y = 2, coef = 0.408248290463863)
+      ), 
+      class = "mpoly"
+    )
+  )
+
+  abs_norm <- function(x) sum(abs(x))
+  expect_equal(
+    normalize_coefficients(p, norm = abs_norm),
+    structure(
+      list(
+        c(x = 2, coef = 0.25), 
+        c(x = 1, y = 1, coef = 0.5), 
+        c(y = 2, coef = 0.25)
+      ), 
+      class = "mpoly"
+    )
+  )
+
+  expect_equal(
+    sum(coef(normalize_coefficients(p))^2),
+    1
+  )
+
+  expect_equal(
+    normalize_coefficients(mp(c("x", "5 y"))),
+    mp(c("x", "y"))
+  )
+
+
+
+
+})
+
+
+

tests/testthat/test-deriv.R

@@ -47,6 +47,21 @@ test_that("vector indeterminates", {
 
 
 
+
+
+test_that("bring_down_power works", {
+
+  p <- mp("x^5")
+
+  expect_equal(
+    mp("x^4"),
+    deriv(p, "x", bring_power_down = FALSE)
+  )
+
+})
+
+
+
 test_that("gradient", {
 
   expect_equal(