Hi Waldek,
Since the method used by "possibleOrder" is random in nature,
so it doesn't harm to try a few times right?
With following patch it gives another try when encountering "division
by zero". And now the failure rate drops to lower than 10%. Of course
we can try more times.
- Qian
diff --git a/src/algebra/pfo.spad b/src/algebra/pfo.spad
index 22deba96..ba961c56 100644
--- a/src/algebra/pfo.spad
+++ b/src/algebra/pfo.spad
@@ -376,7 +376,12 @@ PointsOfFiniteOrder(R0, F, UP, UPUP, R) : Exports
== Implementation where
kbad3Num(h, m) == lcm [kbadBadNum(c, m) for c in coefficients h]
torsionIfCan d ==
- zero?(n := possibleOrder(d := reduce d)) => "failed"
+ d := reduce d
+ nu : Union(N, "failed") := trappedSpadEval(possibleOrder(d))$Lisp
+ if nu case "failed" then nu := trappedSpadEval(possibleOrder(d))$Lisp
+ if nu case "failed" then error "tried twice"
+ n := nu::N
+ zero?(n) => "failed"
(g := generator reduce(n::Z * d)) case "failed" => "failed"
[n, g@R]
On 1/24/24 22:05, 'Nasser M. Abbasi' via FriCAS - computer algebra
system wrote:
FYI,
When first used, Fricas gives division by zero on some integrals. When
called again, the error goes away. This still happens in V 1.3.10. So all
these count as failed since not possible to try again same integral as each
call uses new instance of Fricas process each time.
fricas
FRICAS="/usr/local/lib/fricas/target/x86_64-linux-gnu"
spad-lib="/usr/local/lib/fricas/target/x86_64-linux-gnu/lib/libspad.so"
FriCAS Computer Algebra System
Version: FriCAS 1.3.10 built with sbcl 2.3.11
Timestamp: Wed Jan 10 09:37:52 PM CST 2024
(1) -> setSimplifyDenomsFlag(true)
(2) -> integrate(1/(2^(2/3)-x)/(x^3-1)^(1/2),x)
>> Error detected within library code:
catdef: division by zero
(2) -> integrate(1/(2^(2/3)-x)/(x^3-1)^(1/2),x)
(2)
+-+
\|3
etc...
Same for (with minus sign)
1) -> setSimplifyDenomsFlag(true)
(1) false
(2) -> integrate(1/(2^(2/3)-x)/(-x^3-1)^(1/2),x)
>> Error detected within library code:
catdef: division by zero
I noticed some of these go away when not using
setSimplifyDenomsFlag(true). From new session:
1) -> integrate(1/(2^(2/3)-x)/(-x^3-1)^(1/2),x)
x
++ 1
(1) | ------------------------ d%B
++ +---------+
3+-+2 | 3
(\|2 - %B)\|- %B - 1
No division by zero.
--Nasser
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