fricas
(1) -> Z==>Integer; Q==>Fraction Z
Type: Void
fricas
z: Symbol := 'z; P==>UnivariatePolynomial(z,Q)
Type: Void
fricas
t:P := monomial(1,1)
fricas
p:P := (1-t)*(1-t^2)*(1-t^3)
\label{eq2}-{{z}^{6}}+{{z}^{5}}+{{z}^{4}}-{{z}^{2}}- z + 1
(2) fricas
L==>UnivariateLaurentSeries(Q,z,0)
Type: Void
fricas
R ==> Record(k: Z, c: Q)
Type: Void
fricas
l: List R := reverse [[degree m, leadingCoefficient m]$R for m in monomials p]
\label{eq3}\begin{array}{@{}l} \displaystyle \left[{\left[{k = 0}, \:{c = 1}\right]}, \:{\left[{k = 1}, \:{c = - 1}\right]}, \:{\left[{k = 2}, \:{c = - 1}\right]}, \: \right. \ \ \displaystyle \left.{\left[{k = 4}, \:{c = 1}\right]}, \:{\left[{k = 5}, \:{c = 1}\right]}, \:{\left[{k = 6}, \:{c = - 1}\right]}\right]
(3) Type: List(Record(k: Integer,c: Fraction(Integer)))
fricas
series(l)$L
\label{eq4}1 - z -{{z}^{2}}+{{z}^{4}}+{{z}^{5}}-{{z}^{6}}
(4) Type: UnivariateLaurentSeries
?(Fraction(Integer),
z,
0)
fricas
l1: List R := [[n, if n=5 then 0 else n/1]$R for n in 1..7]
\label{eq5}\begin{array}{@{}l} \displaystyle \left[{\left[{k = 1}, \:{c = 1}\right]}, \:{\left[{k = 2}, \:{c = 2}\right]}, \:{\left[{k = 3}, \:{c = 3}\right]}, \:{\left[{k = 4}, \:{c = 4}\right]}, \: \right. \ \ \displaystyle \left.{\left[{k = 5}, \:{c = 0}\right]}, \:{\left[{k = 6}, \:{c = 6}\right]}, \:{\left[{k = 7}, \:{c = 7}\right]}\right]
(5) Type: List(Record(k: Integer,c: Fraction(Integer)))
fricas
series(l1)$L
\label{eq6}z +{2 \ {{z}^{2}}}+{3 \ {{z}^{3}}}+{4 \ {{z}^{4}}}+{6 \ {{z}^{6}}}+{7 \ {{z}^{7}}}
(6) Type: UnivariateLaurentSeries
?(Fraction(Integer),
z,
0)
It seems weird that the resulting series is aborted at a non-existing
coefficient in the input list.
fricas
l2: List R := [[n, n/1]$R for n in 1..7|n~=5]
\label{eq7}\begin{array}{@{}l} \displaystyle \left[{\left[{k = 1}, \:{c = 1}\right]}, \:{\left[{k = 2}, \:{c = 2}\right]}, \:{\left[{k = 3}, \:{c = 3}\right]}, \:{\left[{k = 4}, \:{c = 4}\right]}, \: \right. \ \ \displaystyle \left.{\left[{k = 6}, \:{c = 6}\right]}, \:{\left[{k = 7}, \:{c = 7}\right]}\right]
(7) Type: List(Record(k: Integer,c: Fraction(Integer)))
fricas
series(l2)$L
\label{eq8}z +{2 \ {{z}^{2}}}+{3 \ {{z}^{3}}}+{4 \ {{z}^{4}}}+{6 \ {{z}^{6}}}+{7 \ {{z}^{7}}}
(8) 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
were made precise as to rely on the input stream not to contain zero coefficients.
fricas
S ==> SparseUnivariateLaurentSeries(Q,z,0)
Type: Void
fricas
series(l)$S
\label{eq9}1 - z -{{z}^{2}}+{{z}^{4}}+{{z}^{5}}-{{z}^{6}}
(9) Type: SparseUnivariateLaurentSeries
?(Fraction(Integer),
z,
0)
fricas
series(l1)$S
\label{eq10}z +{2 \ {{z}^{2}}}+{3 \ {{z}^{3}}}+{4 \ {{z}^{4}}}+{0 \ {{z}^{5}}}+{6 \ {{z}^{6}}}+{7 \ {{z}^{7}}}
(10) Type: SparseUnivariateLaurentSeries
?(Fraction(Integer),
z,
0)
fricas
series(l2)$S
\label{eq11}z +{2 \ {{z}^{2}}}+{3 \ {{z}^{3}}}+{4 \ {{z}^{4}}}+{6 \ {{z}^{6}}}+{7 \ {{z}^{7}}}
(11) Type: SparseUnivariateLaurentSeries
?(Fraction(Integer),
z,
0)