# hyper complex numbers

gary thompson garyt at bmb.leeds.ac.uk
Tue Oct 17 10:00:28 CDT 2006

```what is the best and most efficiednt way to deal with hyper complex numbers
in numpy/scipy

e.g.

for a 1d array we have a complex number containing real and imaginary
pairs... conceptually we have

((r,i),(r,i)...(r,i))

however, for a hypercomplex number in 2d we have quartets of numbers e.g.
((rr,ir,ir,ii),rr,ir,ir,ii)....),
((rr,ir,ir,ii),rr,ir,ir,ii)....),
.
.
.
((rr,ir,ir,ii),rr,ir,ir,ii)....),

or planes of complex numbers

r.
((r,i),(r,i)...(r,i)),
((r,i),(r,i)...(r,i)),
.
.
.
((r,i),(r,i)...(r,i))

i.
((r,i),(r,i)...(r,i)),
((r,i),(r,i)...(r,i)),
.
.
.
((r,i),(r,i)...(r,i))

that is the best way to deal with these in scipy/numpy especially with
respect to 2D fourier transforms and data processing

regards
gary
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