Substitution

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

Usage

subs(S, ..., drop = TRUE)
subsy(S, ..., drop = 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

drop

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

Value

Functions subs(), subsy() and subsmvp() return a multivariate polynomial unless drop 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).

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.

Author

Robin K. S. Hankin

See also

drop

Examples

p <- rmvp(6,2,2,letters[1:3])
p
#> mvp object algebraically equal to
#> 2 a b + a c + 3 b^2 + 5 c
subs(p,a=1)
#> mvp object algebraically equal to
#> 2 b + 3 b^2 + 6 c
subs(p,a=1,b=2)
#> mvp object algebraically equal to
#> 16 + 6 c

subs(p,a="1+b x^3",b="1-y")
#> mvp object algebraically equal to
#> 5 + 6 c + c x^3 - c x^3 y + 2 x^3 - 4 x^3 y + 2 x^3 y^2 - 8 y + 3 y^2
subs(p,a=1,b=2,c=3,drop=FALSE)
#> mvp object algebraically equal to
#> 34

do.call(subs,c(list(as.mvp("z")),rep(c(z="C+z^2"),5)))
#> mvp object algebraically equal to
#> C + 2 C z^16 + 4 C z^24 + 8 C z^28 + 16 C z^30 + C^2 + 4 C^2 z^8 + 8 C^2 z^12 +
#> 16 C^2 z^14 + 6 C^2 z^16 + 24 C^2 z^20 + 48 C^2 z^22 + 28 C^2 z^24 + 112 C^2
#> z^26 + 120 C^2 z^28 + 2 C^3 + 8 C^3 z^4 + 16 C^3 z^6 + 16 C^3 z^8 + 48 C^3 z^10
#> + 80 C^3 z^12 + 48 C^3 z^14 + 60 C^3 z^16 + 240 C^3 z^18 + 320 C^3 z^20 + 336
#> C^3 z^22 + 728 C^3 z^24 + 560 C^3 z^26 + 5 C^4 + 16 C^4 z^2 + 40 C^4 z^4 + 64
#> C^4 z^6 + 156 C^4 z^8 + 256 C^4 z^10 + 248 C^4 z^12 + 480 C^4 z^14 + 1150 C^4
#> z^16 + 1440 C^4 z^18 + 1848 C^4 z^20 + 2912 C^4 z^22 + 1820 C^4 z^24 + 14 C^5 +
#> 48 C^5 z^2 + 120 C^5 z^4 + 304 C^5 z^6 + 560 C^5 z^8 + 816 C^5 z^10 + 1736 C^5
#> z^12 + 3440 C^5 z^14 + 4500 C^5 z^16 + 6160 C^5 z^18 + 8008 C^5 z^20 + 4368 C^5
#> z^22 + 26 C^6 + 112 C^6 z^2 + 360 C^6 z^4 + 832 C^6 z^6 + 1648 C^6 z^8 + 3696
#> C^6 z^10 + 7000 C^6 z^12 + 9888 C^6 z^14 + 13860 C^6 z^16 + 16016 C^6 z^18 +
#> 8008 C^6 z^20 + 44 C^7 + 240 C^7 z^2 + 784 C^7 z^4 + 2048 C^7 z^6 + 5040 C^7
#> z^8 + 9968 C^7 z^10 + 15456 C^7 z^12 + 22176 C^7 z^14 + 24024 C^7 z^16 + 11440
#> C^7 z^18 + 69 C^8 + 416 C^8 z^2 + 1536 C^8 z^4 + 4480 C^8 z^6 + 9940 C^8 z^8 +
#> 17280 C^8 z^10 + 25872 C^8 z^12 + 27456 C^8 z^14 + 12870 C^8 z^16 + 94 C^9 +
#> 640 C^9 z^2 + 2520 C^9 z^4 + 6800 C^9 z^6 + 13740 C^9 z^8 + 22176 C^9 z^10 +
#> 24024 C^9 z^12 + 11440 C^9 z^14 + 114 C^10 + 816 C^10 z^2 + 3040 C^10 z^4 +
#> 7600 C^10 z^6 + 13860 C^10 z^8 + 16016 C^10 z^10 + 8008 C^10 z^12 + 116 C^11 +
#> 800 C^11 z^2 + 2784 C^11 z^4 + 6160 C^11 z^6 + 8008 C^11 z^8 + 4368 C^11 z^10 +
#> 94 C^12 + 608 C^12 z^2 + 1848 C^12 z^4 + 2912 C^12 z^6 + 1820 C^12 z^8 + 60
#> C^13 + 336 C^13 z^2 + 728 C^13 z^4 + 560 C^13 z^6 + 28 C^14 + 112 C^14 z^2 +
#> 120 C^14 z^4 + 8 C^15 + 16 C^15 z^2 + C^16 + z^32

subvec(p,a=1,b=2,c=1:5)   # supply a named list of vectors
#> [1] 22 28 34 40 46

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
#>  Huey Dewie Louie 
#>  1042  1909  3122 

varchange(as.mvp("1+x+xy + x*y"),x="newx") # variable xy unchanged
#> mvp object algebraically equal to
#> 1 + newx + newx y + xy

kahle(5,3,1:3) |> subs(a="a + delta")
#> mvp object algebraically equal to
#> 2 a b delta e^3 + 3 a b^2 c delta^2 + a d^3 e^2 + a^2 b e^3 + 3 a^2 b^2 c delta
#> + a^3 b^2 c + b delta^2 e^3 + b^2 c delta^3 + b^3 c^2 d + c^3 d^2 e + d^3 delta
#> e^2

varchange(p,a="]")  # nonstandard variable names OK
#> mvp object algebraically equal to
#> 2 ] b + ] c + 3 b^2 + 5 c

varchange_formal(p,"\\]","a")
#> mvp object algebraically equal to
#> 2 a b + a c + 3 b^2 + 5 c