# unimodular

##### Unimodular matrices

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

- Keywords
- array

##### 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.

##### See Also

##### Examples

```
# NOT RUN {
unimodular(3)
o <- c(1,1i)
plot(abs(unimodularity(3,o,FUN=g2.fun,maxiter=100)-g2.fun(o)))
# }
```

*Documentation reproduced from package elliptic, version 1.4-0, License: GPL-2*