misc

DESCRIPTION

@@ -4,7 +4,7 @@ Version: 0.0.0.9000
 Authors@R: 
     person("Stéphane", "Laurent", , "laurent_step@outlook.fr", role = c("aut", "cre"))
 Description: Introduces the 'symbolicQspray' objects. Such an object
-    defines a multivariate polynomial whose coefficients are fractions of
+    represents a multivariate polynomial whose coefficients are fractions of
     multivariate polynomials with rational coefficients. The package
     allows arithmetic on such polynomials. It is based on the 'qspray' and 
     'ratioOfQsprays' packages. Some functions for 'qspray' polynomials have
@@ -33,8 +33,6 @@ LinkingTo:
     Rcpp,
     RcppArmadillo,
     RcppCGAL
-Remotes: 
-    stla/ratioOfQsprays
 Config/testthat/edition: 3
 Encoding: UTF-8
 RoxygenNote: 7.3.1

NAMESPACE

@@ -38,6 +38,7 @@ importFrom(gmp,c_bigq)
 importFrom(methods,new)
 importFrom(methods,setAs)
 importFrom(methods,setClass)
+importFrom(methods,setGeneric)
 importFrom(methods,setMethod)
 importFrom(methods,show)
 importFrom(qspray,"showQsprayOption<-")
@@ -69,6 +70,5 @@ importFrom(ratioOfQsprays,rRatioOfQsprays)
 importFrom(ratioOfQsprays,ratioOfQsprays_from_list)
 importFrom(ratioOfQsprays,showRatioOfQspraysX1X2X3)
 importFrom(ratioOfQsprays,showRatioOfQspraysXYZ)
-importFrom(utils,capture.output)
 importFrom(utils,head)
 useDynLib(symbolicQspray, .registration=TRUE)

R/show.R

@@ -1,5 +1,5 @@
 #' @title Print a 'symbolicQspray' object
-#' @description Print a \code{symbolicQspray} object given a function to print
+#' @description Prints a \code{symbolicQspray} object given a function to print
 #'   a \code{ratioOfQsprays} object.
 #'
 #' @param showRatioOfQsprays a function which prints a \code{ratioOfQsprays}
@@ -83,7 +83,7 @@ showSymbolicQspray <- function(
 }
 
 #' @title Print a 'symbolicQspray' object
-#' @description Print a \code{symbolicQspray} object.
+#' @description Prints a \code{symbolicQspray} object.
 #'
 #' @param a a string, usually a letter, to denote the non-indexed variables
 #'   of the \code{ratioOfQsprays} coefficients

R/symbolicQspray.R

@@ -2,9 +2,8 @@
 #' @importFrom Rcpp evalCpp
 #' @importFrom qspray orderedQspray
 #' @importFrom ratioOfQsprays as.ratioOfQsprays
-#' @importFrom methods setMethod setClass new show setAs
+#' @importFrom methods setMethod setClass new show setAs setGeneric
 #' @importFrom gmp as.bigq
-#' @importFrom utils capture.output
 #' @include symbolicQspray.R
 NULL
 
@@ -22,7 +21,7 @@ setMethod(
 )
 
 
-setAs( # for usage in qspray::MSPcombination
+setAs( # for usage in qspray::MSPcombination and unit tests of 'jack'
   "qspray", "symbolicQspray", function(from) {
     new(
       "symbolicQspray",

R/symmetricPolynomials.R

@@ -37,6 +37,7 @@ setMethod(
 )
 
 #' @rdname compactSymmetricQspray
+#' @export
 setMethod(
   "compactSymmetricQspray", c("symbolicQspray", "missing"),
   function(qspray, check) {

README.Rmd

@@ -20,8 +20,8 @@ knitr::opts_chunk$set(echo = TRUE, collapse = TRUE, message = FALSE)
 ___
 
 These notes about the **symbolicQspray** package assume that the reader is a 
-bit familiar with the [**qspray** package](https://github.com/stla/qspray) 
-and the [**ratioOfQsprays** package](https://github.com/stla/ratioOfQsprays).
+bit familiar with the [**qspray** package][qspray] and with the 
+[**ratioOfQsprays** package][ratioOfQsprays].
 
 A `symbolicQspray` object represents a multivariate polynomial whose 
 coefficients are fractions of polynomials with rational coefficients. 
@@ -51,10 +51,9 @@ X3 <- Qlone(3)
 ```
 
 The fractions of polynomials such as the first coefficient `a1/(a2^2+1)` 
-in the above example are 
-[**ratioOfQsprays**](https://github.com/stla/ratioOfQsprays) objects, 
+in the above example are [**ratioOfQsprays**][ratioOfQsprays] objects, 
 and the numerator and the denominator of a `ratioOfQsprays` are 
-[**qspray**](https://github.com/stla/qspray) objects.
+[**qspray**][qspray] objects.
 
 Arithmetic on `symbolicQspray` objects is available:
 
@@ -84,7 +83,7 @@ X <- c(4, 3, "2/5")
 ```
 
 There is a discutable point here. A `symbolicQspray` object represents a 
-polynomial with `ratioOfQsprays` coefficients. So one can consider 
+polynomial with `ratioOfQsprays` coefficients. So one could consider 
 that the polynomial variables `X`, `Y` and `Z` represent some indeterminate
 `ratioOfQsprays` fractions, and that it should be possible to replace them 
 with `ratioOfQsprays` objects. However this is not allowed.
@@ -102,17 +101,14 @@ Now let's turn to our promised discussion. Why is replacing the values of the
 polynomial variables with some `ratioOfQsprays` objects not allowed?
 
 Actually my motivation to do this package was inspired by the 
-**Jack polynomials**. In the context of Jack polynomials, the variables 
+[**Jack polynomials**][jack]. In the context of Jack polynomials, the variables 
 `X`, `Y` and `Z` represent indeterminate *numbers*, and the coefficients 
 are *numbers depending on a parameter* (the Jack parameter), and it turns out 
 that they are fractions of polynomials of this parameter. 
 So I consider that a `symbolicQspray` is *not* a polynomial on the field 
 of fractions of polynomials: I consider it is a polynomial with 
 *rational coefficients depending on some parameters*. 
 
-By the way, I'm wondering whether I should rename `symbolicQspray` to 
-`parametricQspray`. Comments?..
-
 Also note that evaluating the `ratioOfQsprays` object 
 `evalSymbolicQspray(Qspray, X = X)` at `a` would make no sense if we took 
 some `ratioOfQsprays` objects for the values of `X`.
@@ -127,15 +123,16 @@ The package provides some functions to perform elementary queries on a
 numberOfVariables(Qspray)
 numberOfParameters(Qspray)
 numberOfTerms(Qspray)
-getCoefficient(Qspray, c(2, 1))
+getCoefficient(Qspray, c(2, 1)) # coefficient of X^2.Y
 getConstantTerm(Qspray)
 isUnivariate(Qspray)
 isConstant(Qspray)
 ```
 
+
 ## Transforming a `symbolicQspray`
 
-You can derivate a `symbolicQspray` polynomial:
+You can differentiate a `symbolicQspray` polynomial:
 
 ```{r}
 derivSymbolicQspray(Qspray, 2) # derivative w.r.t. Y
@@ -190,9 +187,9 @@ to use **symbolicQspray**.
 
 ## Application: Jacobi polynomials
 
-The [Jacobi polynomials](https://en.wikipedia.org/wiki/Jacobi_polynomials) 
-are univariate polynomials depending on two parameters that we will denote by
-`alpha` and `beta`. They are implemented in this package:
+The [Jacobi polynomials][jacobi] are univariate polynomials depending on two
+parameters that we will denote by `alpha` and `beta`. They are implemented in 
+this package:
 
 ```{r}
 JP <- JacobiPolynomial(2)
@@ -204,7 +201,7 @@ JP
 ```
 
 The implementation constructs these polynomials by using the 
-[recurrence relation](https://en.wikipedia.org/wiki/Jacobi_polynomials#Recurrence_relations).
+[recurrence relation][jacobirecurrence].
 This is a child game, one just has to copy the first two terms and this 
 recurrence relation:
 
@@ -245,12 +242,10 @@ JP <- JacobiPolynomial(7)
 hasPolynomialCoefficientsOnly(JP)
 ```
 
-Up to a factor, the 
-[Gegenbauer polynomials](https://en.wikipedia.org/wiki/Gegenbauer_polynomials)
-with parameter `alpha` coincide with the Jacobi polynomials with parameters 
-`alpha - 1/2` and `alpha - 1/2`. Let's derive them from the Jacobi polynomials,
-as an exercise. The factor can be implemented as follows (see Wikipedia for its 
-formula):
+Up to a factor, the [Gegenbauer polynomials][gegenbauer] with parameter `alpha`
+coincide with the Jacobi polynomials with parameters `alpha - 1/2` and 
+`alpha - 1/2`. Let's derive them from the Jacobi polynomials, as an exercise. 
+The factor can be implemented as follows (see Wikipedia for its formula):
 
 ```{r}
 risingFactorial <- function(theta, n) {
@@ -274,7 +269,8 @@ GegenbauerPolynomial <- function(n) {
 }
 ```
 
-Let's check the recurrence relation given in the Wikipedia article is fulfilled:
+Let's check that the recurrence relation given in the Wikipedia article is
+fulfilled:
 
 ```{r}
 n <- 5
@@ -288,8 +284,23 @@ X <- Qlone(1)
 
 ## Application to Jack polynomials
 
-The **symbolicQspray** package is used by the 
-[**jack** package](https://github.com/stla/jackR) to compute the Jack 
-polynomials with a symbolic Jack parameter. The Jack polynomials exactly fit to 
-the polynomials represented by the `symbolicQspray` objects: their coefficients 
-are fractions of polynomials by definition, of one variable: the Jack parameter.
+The **symbolicQspray** package is used in the [**jack** package][jack] to 
+compute the Jack polynomials with a symbolic Jack parameter. The Jack 
+polynomials exactly fit to the polynomials represented by the `symbolicQspray`
+objects: their coefficients are fractions of polynomials by definition, of one
+variable: the Jack parameter.
+
+
+<!-- -------------------- links -------------------- -->
+
+[qspray]: https://github.com/stla/qspray "the 'qspray' package on Github"
+
+[ratioOfQsprays]: https://github.com/stla/ratioOfQsprays "the 'ratioOfQsprays' package on Github"
+
+[jack]: https://github.com/stla/jackR "the 'jack' package on Github"
+
+[gegenbauer]: https://en.wikipedia.org/wiki/Gegenbauer_polynomials "Gegenbauer polynomials on Wikipedia"
+
+[jacobi]: https://en.wikipedia.org/wiki/Jacobi_polynomials "Jacobi polynomials on Wikipedia"
+
+[jacobirecurrence]: https://en.wikipedia.org/wiki/Jacobi_polynomials#Recurrence_relations "recurrence relation between Jacobi polynomials"

README.md

@@ -1,7 +1,7 @@
 The ‘symbolicQspray’ package
 ================
 Stéphane Laurent
-2024-04-22
+2024-05-01
 
 ***Multivariate polynomials with symbolic parameters.***
 
@@ -14,8 +14,9 @@ Stéphane Laurent
 
 These notes about the **symbolicQspray** package assume that the reader
 is a bit familiar with the [**qspray**
-package](https://github.com/stla/qspray) and the [**ratioOfQsprays**
-package](https://github.com/stla/ratioOfQsprays).
+package](https://github.com/stla/qspray "the 'qspray' package on Github")
+and with the [**ratioOfQsprays**
+package](https://github.com/stla/ratioOfQsprays "the 'ratioOfQsprays' package on Github").
 
 A `symbolicQspray` object represents a multivariate polynomial whose
 coefficients are fractions of polynomials with rational coefficients.
@@ -47,9 +48,10 @@ X3 <- Qlone(3)
 
 The fractions of polynomials such as the first coefficient `a1/(a2^2+1)`
 in the above example are
-[**ratioOfQsprays**](https://github.com/stla/ratioOfQsprays) objects,
-and the numerator and the denominator of a `ratioOfQsprays` are
-[**qspray**](https://github.com/stla/qspray) objects.
+[**ratioOfQsprays**](https://github.com/stla/ratioOfQsprays "the 'ratioOfQsprays' package on Github")
+objects, and the numerator and the denominator of a `ratioOfQsprays` are
+[**qspray**](https://github.com/stla/qspray "the 'qspray' package on Github")
+objects.
 
 Arithmetic on `symbolicQspray` objects is available:
 
@@ -85,11 +87,11 @@ X <- c(4, 3, "2/5")
 ```
 
 There is a discutable point here. A `symbolicQspray` object represents a
-polynomial with `ratioOfQsprays` coefficients. So one can consider that
-the polynomial variables `X`, `Y` and `Z` represent some indeterminate
-`ratioOfQsprays` fractions, and that it should be possible to replace
-them with `ratioOfQsprays` objects. However this is not allowed. We will
-discuss that, just after checking the consistency:
+polynomial with `ratioOfQsprays` coefficients. So one could consider
+that the polynomial variables `X`, `Y` and `Z` represent some
+indeterminate `ratioOfQsprays` fractions, and that it should be possible
+to replace them with `ratioOfQsprays` objects. However this is not
+allowed. We will discuss that, just after checking the consistency:
 
 ``` r
 evalSymbolicQspray(Qspray, a = a, X = X)
@@ -111,17 +113,15 @@ Now let’s turn to our promised discussion. Why is replacing the values
 of the polynomial variables with some `ratioOfQsprays` objects not
 allowed?
 
-Actually my motivation to do this package was inspired by the **Jack
-polynomials**. In the context of Jack polynomials, the variables `X`,
-`Y` and `Z` represent indeterminate *numbers*, and the coefficients are
-*numbers depending on a parameter* (the Jack parameter), and it turns
-out that they are fractions of polynomials of this parameter. So I
-consider that a `symbolicQspray` is *not* a polynomial on the field of
-fractions of polynomials: I consider it is a polynomial with *rational
-coefficients depending on some parameters*.
-
-By the way, I’m wondering whether I should rename `symbolicQspray` to
-`parametricQspray`. Comments?..
+Actually my motivation to do this package was inspired by the [**Jack
+polynomials**](https://github.com/stla/jackR "the 'jack' package on Github").
+In the context of Jack polynomials, the variables `X`, `Y` and `Z`
+represent indeterminate *numbers*, and the coefficients are *numbers
+depending on a parameter* (the Jack parameter), and it turns out that
+they are fractions of polynomials of this parameter. So I consider that
+a `symbolicQspray` is *not* a polynomial on the field of fractions of
+polynomials: I consider it is a polynomial with *rational coefficients
+depending on some parameters*.
 
 Also note that evaluating the `ratioOfQsprays` object
 `evalSymbolicQspray(Qspray, X = X)` at `a` would make no sense if we
@@ -139,7 +139,7 @@ numberOfParameters(Qspray)
 ## [1] 2
 numberOfTerms(Qspray)
 ## [1] 3
-getCoefficient(Qspray, c(2, 1))
+getCoefficient(Qspray, c(2, 1)) # coefficient of X^2.Y
 ## [ a1 ] %//% [ a2^2 + 1 ]
 getConstantTerm(Qspray)
 ## [ a1 ] %//% [ a2 ]
@@ -151,7 +151,7 @@ isConstant(Qspray)
 
 ## Transforming a `symbolicQspray`
 
-You can derivate a `symbolicQspray` polynomial:
+You can differentiate a `symbolicQspray` polynomial:
 
 ``` r
 derivSymbolicQspray(Qspray, 2) # derivative w.r.t. Y
@@ -212,9 +212,9 @@ order to use **symbolicQspray**.
 ## Application: Jacobi polynomials
 
 The [Jacobi
-polynomials](https://en.wikipedia.org/wiki/Jacobi_polynomials) are
-univariate polynomials depending on two parameters that we will denote
-by `alpha` and `beta`. They are implemented in this package:
+polynomials](https://en.wikipedia.org/wiki/Jacobi_polynomials "Jacobi polynomials on Wikipedia")
+are univariate polynomials depending on two parameters that we will
+denote by `alpha` and `beta`. They are implemented in this package:
 
 ``` r
 JP <- JacobiPolynomial(2)
@@ -229,7 +229,7 @@ JP
 ```
 
 The implementation constructs these polynomials by using the [recurrence
-relation](https://en.wikipedia.org/wiki/Jacobi_polynomials#Recurrence_relations).
+relation](https://en.wikipedia.org/wiki/Jacobi_polynomials#Recurrence_relations "recurrence relation between Jacobi polynomials").
 This is a child game, one just has to copy the first two terms and this
 recurrence relation:
 
@@ -272,11 +272,11 @@ hasPolynomialCoefficientsOnly(JP)
 ```
 
 Up to a factor, the [Gegenbauer
-polynomials](https://en.wikipedia.org/wiki/Gegenbauer_polynomials) with
-parameter `alpha` coincide with the Jacobi polynomials with parameters
-`alpha - 1/2` and `alpha - 1/2`. Let’s derive them from the Jacobi
-polynomials, as an exercise. The factor can be implemented as follows
-(see Wikipedia for its formula):
+polynomials](https://en.wikipedia.org/wiki/Gegenbauer_polynomials "Gegenbauer polynomials on Wikipedia")
+with parameter `alpha` coincide with the Jacobi polynomials with
+parameters `alpha - 1/2` and `alpha - 1/2`. Let’s derive them from the
+Jacobi polynomials, as an exercise. The factor can be implemented as
+follows (see Wikipedia for its formula):
 
 ``` r
 risingFactorial <- function(theta, n) {
@@ -300,8 +300,8 @@ GegenbauerPolynomial <- function(n) {
 }
 ```
 
-Let’s check the recurrence relation given in the Wikipedia article is
-fulfilled:
+Let’s check that the recurrence relation given in the Wikipedia article
+is fulfilled:
 
 ``` r
 n <- 5
@@ -315,9 +315,11 @@ X <- Qlone(1)
 
 ## Application to Jack polynomials
 
-The **symbolicQspray** package is used by the [**jack**
-package](https://github.com/stla/jackR) to compute the Jack polynomials
-with a symbolic Jack parameter. The Jack polynomials exactly fit to the
-polynomials represented by the `symbolicQspray` objects: their
-coefficients are fractions of polynomials by definition, of one
-variable: the Jack parameter.
+The **symbolicQspray** package is used in the [**jack**
+package](https://github.com/stla/jackR "the 'jack' package on Github")
+to compute the Jack polynomials with a symbolic Jack parameter. The Jack
+polynomials exactly fit to the polynomials represented by the
+`symbolicQspray` objects: their coefficients are fractions of
+polynomials by definition, of one variable: the Jack parameter.
+
+<!-- -------------------- links -------------------- -->