subs: Substitution

In mvp: Fast Symbolic Multivariate Polynomials

Substitution

Description

Substitute symbols in an mvp object for numbers or other multivariate polynomials

Usage

subs(S, ..., lose = TRUE)
subsy(S, ..., lose = TRUE)
subvec(S, ...)
subsmvp(S,v,X)
varchange(S,...)
varchange_formal(S,old,new)
namechanger(x,old,new)

Arguments

S,X	Multivariate polynomials
...	named arguments corresponding to variables to substitute
lose	Boolean with default TRUE meaning to return a scalar (the constant) in place of a constant mvp object
v	A string corresponding to the variable to substitute
old,new,x	The old and new variable names respectively; x is a character vector

Details

Function subs() substitutes variables for mvp objects, using a natural R idiom. Observe that this type of substitution is sensitive to order:

> p <- as.mvp("a b^2")
> subs(p,a="b",b="x")
mvp object algebraically equal to
x^3
> subs(p,b="x",a="b")  # same arguments, different order
mvp object algebraically equal to
b x^2

Functions subsy() and subsmvp() are lower-level functions, not really intended for the end-user. Function subsy() substitutes variables for numeric values (order matters if a variable is substituted more than once). Function subsmpv() takes a mvp object and substitutes another mvp object for a specific symbol.

Function subvec() substitutes the symbols of S with numerical values. It is vectorised in its ellipsis arguments with recycling rules and names behaviour inherited from cbind(). However, if the first element of ... is a matrix, then this is interpreted by rows, with symbol names given by the matrix column names; further arguments are ignored. Unlike subs(), this function is generally only useful if all symbols are given a value; unassigned symbols take a value of zero.

Function varchange() makes a formal variable substitution. It is useful because it can take non-standard variable names such as “(a-b)” or “?”, and is used in taylor(). Function varchange_formal() does the same task, but takes two character vectors, old and new, which might be more convenient than passing named arguments. Remember that non-standard names might need to be quoted; also you might need to escape some characters, see the examples. Function namechanger() is a low-level helper function that uses regular expression idiom to substitute variable names.

Value

Functions subs(), subsy() and subsmvp() return a multivariate polynomial unless lose is TRUE in which case a length one numeric vector is returned. Function subvec() returns a numeric vector (sic! the output inherits its order from the arguments).

Author(s)

Robin K. S. Hankin

See Also

lose

Examples

p <- rmvp(6,2,2,letters[1:3])
p
subs(p,a=1)
subs(p,a=1,b=2)

subs(p,a="1+b x^3",b="1-y")
subs(p,a=1,b=2,c=3,lose=FALSE)

do.call(subs,c(list(as.mvp("z")),rep(c(z="C+z^2"),5)))

subvec(p,a=1,b=2,c=1:5)   # supply a named list of vectors

M <- matrix(sample(1:3,26*3,replace=TRUE),ncol=26)
colnames(M) <- letters
rownames(M) <- c("Huey", "Dewie", "Louie")
subvec(kahle(r=3,p=1:3),M)  # supply a matrix

varchange(as.mvp("1+x+xy + x*y"),x="newx") # variable xy unchanged

kahle(5,3,1:3) %>% subs(a="a + delta")

varchange(p,a="]")  # nonstandard variable names OK

varchange_formal(p,"\\]","a")

mvp documentation built on March 31, 2023, 5:43 p.m.