Ralf Hemmecke wrote:
>
> Does someone know whether FriCAS already has a implementation of an
> infinite product?
Infinite products currently are implementes as 'exp' of
infinite sums of logs. Infinite sum is done via addiag.
We could add infinite product similar to addiag, see
attached diff.
> I'd like to use/implement qPochhammer
> http://en.wikipedia.org/wiki/Q-Pochhammer_symbol
> as UnivariateLaurentSeries(K, q, 0).
That is finite product...
--
Waldek Hebisch
[email protected]
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--- ../ax-build140/src/algebra/STTAYLOR.spad 2014-11-28 11:08:17.000000000
-0500
+++ STTAYLOR.spad 2014-11-30 15:27:25.000000000 -0500
@@ -95,6 +95,12 @@
++ addiag(x) performs diagonal addition of a stream of streams. if x =
++ \spad{[[a<0, 0>, a<0, 1>, ..], [a<1, 0>, a<1, 1>, ..], [a<2, 0>, a<2,
1>, ..], ..]}
++ and \spad{addiag(x) = [b<0, b<1>, ...], then b<k> = sum(i+j=k, a<i,
j>)}.
+ prodiag : ST ST A -> ST A
+ ++ prodiag(x) performs "diagonal" infinite product of a stream
+ ++ of streams. When \spad{x(i)} is interpreted as stream of
+ ++ coefficients of series \spad{f_i(z), i=1,...}, then
+ ++ \spad{prodiag(x) = (g(z) - 1)/z} where
+ ++ \spad{g(z) = (1 + z*f_1(z))*(1 + z^2*f_2(x))*...}
lambert : ST A -> ST A
++ lambert(st) computes \spad{f(x) + f(x^2) + f(x^3) + ...}
++ if st is a stream representing \spad{f(x)}.
@@ -336,6 +342,16 @@
error "revert: should start 0, x, ... with invertible x"
error "revert: should start 0, x, ..."
+ prodiag1(ststa : ST ST A, n : Integer) : ST(A) == delay
+ empty? ststa => zro()
+ f1 := frst ststa
+ r1 := rst ststa
+ p1 := prodiag1(r1, n + 1)
+ empty? f1 => concat(0, p1)
+ concat(frst(f1), rst(f1) + p1 + concat(rpSt(n, 0), f1)*p1)
+
+ prodiag(ststa : ST ST A) == prodiag1(ststa, 1)
+
--% lambert functions
addiag(ststa : ST ST A) == delay
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