The definition of the function recip$NormalizationPackage elicites
a `semantic error' from the compiler because the local variable
`hesrg' is defined in the two branches of an if-statement with two
differen types. That looks like a bug to me. Opinion?
recip(p:P,ts:TS): Record(num:P, den:P) ==
-- ASSUME p is invertible w.r.t. ts
-- ASSUME mvar(p) is algebraic w.r.t. ts
v := mvar(p)
ts_v := select(ts,v)::P
if mdeg(p) < mdeg(ts_v)
then
hesrg: Record (gcd : P, coef2 : P) :=
halfExtendedSubResultantGcd2(ts_v,p)$P
d: P := hesrg.gcd; n: P := hesrg.coef2
else
hesrg: Record (gcd : P, coef1 : P) :=
halfExtendedSubResultantGcd1(p,ts_v)$P
d: P := hesrg.gcd; n: P := hesrg.coef1
g := gcd(n,d)
(n, d) := ((n exquo g)::P, (d exquo g)::P)
remn, remd: Record(rnum:R,polnum:P,den:R)
remn := remainder(n,ts); remd := remainder(d,ts)
cn := remn.rnum; pn := remn.polnum; dn := remn.den
cd := remd.rnum; pd := remd.polnum; dp := remd.den
k: K := (cn / cd) * (dp / dn)
pn := removeZero(pn,ts)
pd := removeZero(pd,ts)
[numer(k) * pn, denom(k) * pd]$Record(num:P, den:P)
-- Gaby
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