/usr/share/axiom-20170501/src/algebra/QUATCT2.spad is in axiom-source 20170501-3.
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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 26 27 28 29 | )abbrev package QUATCT2 QuaternionCategoryFunctions2
++ Author: Robert S. Sutor
++ Date Created: 23 May 1990
++ Date Last Updated: 23 May 1990
++ Description:
++ \spadtype{QuaternionCategoryFunctions2} implements functions between
++ two quaternion domains. The function \spadfun{map} is used by
++ the system interpreter to coerce between quaternion types.
QuaternionCategoryFunctions2(QR,R,QS,S) : SIG == CODE where
R : CommutativeRing
S : CommutativeRing
QR : QuaternionCategory R
QS : QuaternionCategory S
SIG ==> with
map : (R -> S, QR) -> QS
++ map(f,u) maps f onto the component parts of the quaternion u.
++ to convert an expression in Quaterion(R) to Quaternion(S)
++
++X f(a:FRAC(INT)):COMPLEX(FRAC(INT)) == a::COMPLEX(FRAC(INT))
++X q:=quatern(2/11,-8,3/4,1)
++X map(f,q)
CODE ==> add
map(fn : R -> S, u : QR): QS ==
quatern(fn real u, fn imagI u, fn imagJ u, fn imagK u)$QS
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