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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | )abbrev package OCTCT2 OctonionCategoryFunctions2
++ Author: Johannes Grabmeier
++ Date Created: 10 September 1990
++ Date Last Updated: 10 September 1990
++ Description:
++ OctonionCategoryFunctions2 implements functions between
++ two octonion domains defined over different rings.
++ The function map is used to coerce between octonion types.
OctonionCategoryFunctions2(OR,R,OS,S) : SIG == CODE where
R : CommutativeRing
S : CommutativeRing
OR : OctonionCategory R
OS : OctonionCategory S
SIG ==> with
map : (R -> S, OR) -> OS
++ map(f,u) maps f onto the component parts of the octonion u
CODE ==> add
map(fn : R -> S, u : OR): OS ==
octon(fn real u, fn imagi u, fn imagj u, fn imagk u,_
fn imagE u, fn imagI u, fn imagJ u, fn imagK u)$OS
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