Changes http://wiki.axiom-developer.org/285EqualInAlgebraicNumberFails/diff
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??changed:
-This is quite strange. As I understand it, AN is almost IAN (there are only
three over-riding implementations of three functions: zero?, one?, and =) and
yet, apparently, = in AN is not transitive, but trueEqual in IAN is!
-
+This is quite strange. As I understand it, 'AN' is almost 'IAN' (only three
functions have over-riding implementations: 'zero?' , 'one?' , and '=' ) and
yet, '=' in 'AN' is not transitive, but apparently, 'trueEqual' in 'IAN' is:
\begin{axiom}
g:=(f^2)^(1/2)
++added:
+trueEqual(f,-g)
trueEqual(f,g)
--removed:
trueEqual(f,g)
-trueEqual(f,-g)
trueEqual(g,-g)
??changed:
-There is also = in IAN, which is implemented as = in EXPR INT.
+But this is deceptive since 'trueEqual(g, -g)' is not 'trueEqual(g+g,0)'.
(Note we cannot use 'trueEqual(a,b)' or 'trueEqual(a-b,0)' since there is *no*
coercion from 'AN' to 'IAN' . Moreover, 'trueEqual' is not transitive either.
+
+\begin{axiom}
+trueEqual(g+g,0) -- not the same as trueEqual(g, -g)
+trueEqual(-f,g)
+trueEqual(f,-f)
+\end{axiom}
+
+There is also '=' in 'IAN', which is implemented using '=' in 'EXPR INT' .
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