Hello,
We have the following specification for the series function.
http://fricas.github.io/api/UnivariateLaurentSeriesCategory.html#l-univariate-laurent-series-category-series
Well, it looks a bit vague for my taste, but I would say that
http://axiom-wiki.newsynthesis.org/SandBoxBugLaurentSeries
demonstrates a bug in UnivariateLaurentSeries.
For the record also attached to this mail.
Ralf
===============================================================
echo ')read "buglaurent.input"'|fricas -nosman > buglaurent.out
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Z==>Integer; Q==>Fraction Z
z: Symbol := 'z; P==>UnivariatePolynomial(z,Q)
t:P := monomial(1,1)
p:P := (1-t)*(1-t^2)*(1-t^3)
L==>UnivariateLaurentSeries(Q,z,0)
R ==> Record(k: Z, c: Q)
l: List R := reverse [[degree m, leadingCoefficient m]$R for m in monomials p]
series(l)$L
l1: List R := [[n, if n=5 then 0 else n/1]$R for n in 1..7]
series(l1)$L
-- It seems weird that the resulting series is aborted at a non-existing
-- coefficient in the input list.
l2: List R := [[n, n/1]$R for n in 1..7|n~=5]
series(l2)$L
-- There is obviously also a bug here, because the zero coefficient
-- should have been removed.
-- I would, however, accept such a result if the specification of
--
"series":http://fricas.github.io/api/UnivariateLaurentSeriesCategory.html#l-univariate-laurent-series-category-series
-- were made precise as to rely on the input stream not to contain
-- zero coefficients.
S ==> SparseUnivariateLaurentSeries(Q,z,0)
series(l)$S
series(l1)$S
series(l2)$S
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Checking for foreign routines
AXIOM="/home/hemmecke/g/fricas-bisect/install/lib/fricas/target/x86_64-unknown-linux"
spad-lib="/home/hemmecke/g/fricas-bisect/install/lib/fricas/target/x86_64-unknown-linux/lib/libspad.so"
foreign routines found
openServer result -2
FriCAS Computer Algebra System
Version: FriCAS 3b640a58565eaaac9a1d22923fb6db1e23973c67
Timestamp: Sun Nov 9 11:50:05 CET 2014
-----------------------------------------------------------------------------
Issue )copyright to view copyright notices.
Issue )summary for a summary of useful system commands.
Issue )quit to leave FriCAS and return to shell.
-----------------------------------------------------------------------------
(1) -> Z==>Integer; Q==>Fraction Z
Type: Void
z: Symbol := 'z; P==>UnivariatePolynomial(z,Q)
Type: Void
t:P := monomial(1,1)
(3) z
Type: UnivariatePolynomial(z,Fraction(Integer))
p:P := (1-t)*(1-t^2)*(1-t^3)
6 5 4 2
(4) - z + z + z - z - z + 1
Type: UnivariatePolynomial(z,Fraction(Integer))
L==>UnivariateLaurentSeries(Q,z,0)
Type: Void
R ==> Record(k: Z, c: Q)
Type: Void
l: List R := reverse [[degree m, leadingCoefficient m]$R for m in monomials p]
(7)
[[k= 0,c= 1], [k= 1,c= - 1], [k= 2,c= - 1], [k= 4,c= 1], [k= 5,c= 1],
[k= 6,c= - 1]]
Type: List(Record(k: Integer,c: Fraction(Integer)))
series(l)$L
2
(8) 1 - z - z
Type: UnivariateLaurentSeries(Fraction(Integer),z,0)
l1: List R := [[n, if n=5 then 0 else n/1]$R for n in 1..7]
(9)
[[k= 1,c= 1], [k= 2,c= 2], [k= 3,c= 3], [k= 4,c= 4], [k= 5,c= 0],
[k= 6,c= 6], [k= 7,c= 7]]
Type: List(Record(k: Integer,c: Fraction(Integer)))
series(l1)$L
2 3 4 6 7
(10) z + 2z + 3z + 4z + 6z + 7z
Type: UnivariateLaurentSeries(Fraction(Integer),z,0)
-- It seems weird that the resulting series is aborted at a non-existing
-- coefficient in the input list.
l2: List R := [[n, n/1]$R for n in 1..7|n~=5]
(11)
[[k= 1,c= 1],[k= 2,c= 2],[k= 3,c= 3],[k= 4,c= 4],[k= 6,c= 6],[k= 7,c= 7]]
Type: List(Record(k: Integer,c: Fraction(Integer)))
series(l2)$L
2 3 4
(12) z + 2z + 3z + 4z
Type: UnivariateLaurentSeries(Fraction(Integer),z,0)
-- There is obviously also a bug here, because the zero coefficient
-- should have been removed.
-- I would, however, accept such a result if the specification of
--
"series":http://fricas.github.io/api/UnivariateLaurentSeriesCategory.html#l-univariate-laurent-series-category-series
-- were made precise as to rely on the input stream not to contain
-- zero coefficients.
S ==> SparseUnivariateLaurentSeries(Q,z,0)
Type: Void
series(l)$S
2 4 5 6
(14) 1 - z - z + z + z - z
Type: SparseUnivariateLaurentSeries(Fraction(Integer),z,0)
series(l1)$S
2 3 4 5 6 7
(15) z + 2z + 3z + 4z + 0z + 6z + 7z
Type: SparseUnivariateLaurentSeries(Fraction(Integer),z,0)
series(l2)$S
2 3 4 6 7
(16) z + 2z + 3z + 4z + 6z + 7z
Type: SparseUnivariateLaurentSeries(Fraction(Integer),z,0)
(17) ->
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