Dear Waldek,
Basic question: How can I see what kernels are cached?
Explanation follows.
In some program I recursively traverse the operator/kernel/ratfun tree
of an algebraic number and rebuild another algebraic number. I seemingly
have a bug there, but cannot easily find it.
The lines
dbgPrint("csfX z", z)
dbgPrint("csfXxx", x)
t := z*x
dbgPrint("CSFX t", t)
gave me the following output
[:> , csfX z, sqrt(-1)*nthRoot(-1, 3)*sqrt(3)]
[:> , csfXxx, nthRoot(-sqrt(-1)*sqrt(3)+1, 3)]
[:> , CSFX t, 3*sqrt(-1)*nthRoot(-1, 3)]
The value of t is completely wrong.
In another place I see two algebraic numbers that print in my program as
-- aa:=(sqrt(-1)*nthRoot(-1, 3)*sqrt(3)+nthRoot(-1,
3))*nthRoot(-sqrt(-1)*sqrt(3)+1, 3)-2*nthRoot(2, 3)
-- ab:=sqrt(-1)*nthRoot(-1, 3)*sqrt(3)*nthRoot(-sqrt(-1)*sqrt(3)+1,
3)+nthRoot(-1, 3)*nthRoot(-sqrt(-1)*sqrt(3)+1, 3)-2*nthRoot(2, 3)
with respective towers
-- ta:=[sqrt(-1),_
nthRoot(-1, 3),_
nthRoot(2, 3),_
sqrt(3),_
nthRoot(-sqrt(-1)*sqrt(3)+1, 3)]
-- tb:=[sqrt(-1),_
nthRoot(-1, 3),_
sqrt(3),_
nthRoot(2, 3),_
nthRoot(-sqrt(-1)*sqrt(3)+1, 3),_
nthRoot(-sqrt(-1)*sqrt(3)+1, 3)]
The surprising fact for me is in this double entry in tb.
Entering ab and computing "tower ab" in the same session gives:
%%% (6) -> ab:=sqrt(-1)*nthRoot(-1,
3)*sqrt(3)*nthRoot(-sqrt(-1)*sqrt(3)+1, 3)+nthRoot(-1,
3)*nthRoot(-sqrt(-1)*sqrt(3)+1, 3)-2*nthRoot(2, 3)
+----------------+
+---+3+---+ +-+ 3+---+ 3| +---+ +-+ 3+-+
(6) (\|- 1 \|- 1 \|3 + \|- 1 )\|- \|- 1 \|3 + 1 - 2 \|2
Type: AlgebraicNumber
%%% (7) -> tower ab
+----------------+
+---+ 3+---+ 3+-+ +-+ 3| +---+ +-+
(7) [\|- 1 , \|- 1 , \|2 , \|3 , \|- \|- 1 \|3 + 1 ]
Type: List(Kernel(AlgebraicNumber))
That is, no duplication of the last kernel.
Long story short... it seems that my program creates a kernel and the
cache does not recognize that it is the same. In order to find exactly
where this happens, I would like to know how I can look at the kernel
cache from SPAD.
Thank you.
Ralf
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