Unimodular matrices
Systematically generates unimodular matrices; numerical verfication of a function's unimodularness
unimodular(n) unimodularity(n,o, FUN, ...)
n |
Maximum size of entries of matrices |
o |
Two element vector |
FUN |
Function whose unimodularity is to be checked |
... |
Further arguments passed to |
Here, a ‘unimodular’ matrix is of size 2x2, with integer entries and a determinant of unity.
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.
In function as.primitive(), a ‘unimodular’ may have
determinant minus one.
Robin K. S. Hankin
unimodular(3) o <- c(1,1i) plot(abs(unimodularity(3,o,FUN=g2.fun,maxiter=100)-g2.fun(o)))
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