The function Ops.freealg() passes binary arithmetic operators
(“+”, “-”, “*”,
“^”, and “==”) to the appropriate
specialist function.
The caret, as in a^n, denotes arithmetic exponentiation, as in
x^3==x*x*x. As an experimental feature, this is (sort of)
vectorised: if n is a vector, then a^n returns the sum
of a raised to the power of each element of n. For example,
a^c(n1,n2,n3) is a^n1 + a^n2 + a^n3. Internally,
n is tabulated in the interests of efficiency, so
a^c(0,2,5,5,5,) = 1 + a^2 + 3a^5 is evaluated with only a
single fifth power. Similar functionality is implemented in the
mvp package.
The only comparison operators are equality and inequality; x==y
is defined as is.zero(x-y).
Functions lowlevel_foo() are low-level functions that interface
directly with the C routines in the src/ directory and
are not intended for the end-user.
Function inv() is defined only for freealg objects with a
single term. If x has a single term we have
inv(x)*x=x*inv(x)=1. There is no corresponding division in the
package because a/b may be either a*inv(b) or
inv(b)*a.