Substitution

Substitute symbols in a freealg object for numbers or other freealg objects

subs(...)
subsu(S1,S2,r)

Arguments

S1,S2

Objects of class freealg

r

Integer specifying symbol to substitute (\(a=1,b=2\) etc)

...

First element is a freealg object, remainder are named arguments corresponding to variables to substitute

Value

Returns a freealg object.

Details

Function subs() substitutes variables for freealg objects (coerced if necessary) using natural R idiom. Observe that this type of substitution is sensitive to order:

> subs("ax",a="1+x",x="1+a")
free algebra element algebraically equal to
 + 2 + 3*a + 1*aa

> subs("ax",x="1+a",a="1+x")
free algebra element algebraically equal to
 + 2 + 3*x + 1*xx

Functions subsu() is a lower-level formal function, not really intended for the end-user. Function subsu() takes S1 and substitutes occurrences of symbol r with S2.

No equivalent to mvp::subvec() is currently implemented.

Author

Robin K. S. Hankin

Note

Function subs() is one place in the package where the use of letters is effectively hard-wired in. Idiom such as

subs("abccc",b="1+3x")

is very nice, but identifies “b” with 2. Note that argument r of subsu() is canonically an integer but a single character is interpreted as a letter. See also the note at freealg.Rd.

Examples

subs("abccc",b="1+3x")
#> free algebra element algebraically equal to
#> + accc + 3axccc
subs("aaaa",a="1+x")  # binomial
#> free algebra element algebraically equal to
#> + 1 + 4x + 6xx + 4xxx + xxxx

subs("abA",b=31)
#> free algebra element algebraically equal to
#> + 31

subs("1+a",a="A")   # can substitute for an inverse
#> free algebra element algebraically equal to
#> + 1 + A
subs("A",a="1+x")   # inverses are not substituted for
#> free algebra element algebraically equal to
#> + A


## Sequential substitution works:

subs("abccc",b="1+3x",x="1+d+2e")
#> free algebra element algebraically equal to
#> + 4accc + 3adccc + 6aeccc
subs(rfalg(),a=rfalg())
#> free algebra element algebraically equal to
#> + 42aaa + 6ac + 12acaa + 48b + 7bc + 24c + 21caaa + 196caaabaaa + 28caaabac +
#> 56caaabacaa + 231caaabb + 112caaabc + 168caaabcbb + 3cac + 6cacaa + 56cacaabaaa
#> + 8cacaabac + 16cacaabacaa + 66cacaabb + 32cacaabc + 48cacaabcbb + 28cacbaaa +
#> 4cacbac + 8cacbacaa + 33cacbb + 16cacbc + 24cacbcbb + 24cb + 36cbb + 224cbbaaa
#> + 32cbbac + 64cbbacaa + 264cbbb + 128cbbc + 192cbbcbb + 12cc + 7ccb + 112ccbaaa
#> + 16ccbac + 32ccbacaa + 150ccbb + 168ccbbbaaa + 24ccbbbac + 48ccbbbacaa +
#> 198ccbbbb + 96ccbbbc + 144ccbbbcbb + 64ccbc + 96ccbcbb