unimodular {elliptic}

Unimodular matrices

Description

Systematically generates unimodular matrices; numerical verfication of a function's unimodularness

Usage

unimodular(n)
unimodularity(n,o, FUN, ...)

Arguments

n

Maximum size of entries of matrices

o

Two element vector

FUN

Function whose unimodularity is to be checked

...

Further arguments passed to FUN

Details

Here, a ‘unimodular’ matrix is of size 2\times 2, with integer entries and a determinant of unity.

Value

Function unimodular() returns an array a of dimension c(2,2,u) (where u is a complicated function of n). Thus 3-slices of a (that is, a[,,i]) are unimodular.

Function unimodularity() returns the result of applying FUN() to the unimodular transformations of o. The function returns a vector of length dim(unimodular(n))[3]; if FUN() is unimodular and roundoff is neglected, all elements of the vector should be identical.

Note

In function as.primitive(), a ‘unimodular’ may have determinant minus one.

Author(s)

Robin K. S. Hankin

See Also

as.primitive

Examples

unimodular(3)

o <- c(1,1i)
plot(abs(unimodularity(3,o,FUN=g2.fun,maxiter=100)-g2.fun(o)))