In "sqrt2", instead of factoring expression manually, we can use existing
"froot":
--- a/src/algebra/solvefor.spad
+++ b/src/algebra/solvefor.spad
@@ -64,14 +64,10 @@
-- we will return both roots later.
sqrt2(s : F) : F ==
if F is Expression RR then
- smpsqfr := squareFree numer s
- a : F := coerce("*"/[f.factor^(f.exponent quo 2) for f in
factorList smpsqfr])
- b : F := coerce("*"/[f.factor^(f.exponent rem 2) for f in
factorList smpsqfr])
- u : RR := retract(coerce(unit smpsqfr)@F)
- sqfru := squareFree u
- ua := "*"/[f.factor^(f.exponent quo 2) for f in factorList
sqfru]
- ub := "*"/[f.factor^(f.exponent rem 2) for f in factorList
sqfru]
- ua*a*sqrt(ub*b)
+ K ==> Kernel F
+ PP ==> SparseMultivariatePolynomial(RR, K)
+ res := froot(s, 2)$PolynomialRoots(IndexedExponents K, K,
RR, PP, F)
+ res.coef * (res.radicand)^(1/res.exponent)
else
s^(1/2)
--
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