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| author | dos-reis <gdr@axiomatics.org> | 2010-02-14 09:23:15 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2010-02-14 09:23:15 +0000 |
| commit | 28d261c72d6347990c751e43e4fc5604716f301c (patch) | |
| tree | 94a7e8dcf4816cfa0477317aa5e2fdc4e23a46ae /src/algebra | |
| parent | e09e82b4e3e7546a4c12c0d80ca90ee95ea3f05c (diff) | |
| download | open-axiom-28d261c72d6347990c751e43e4fc5604716f301c.tar.gz | |
* algebra/sttaylor.spad.pamphlet
(revert$StreamTaylorSeriesOperations): Tidy.
Diffstat (limited to 'src/algebra')
| -rw-r--r-- | src/algebra/sttaylor.spad.pamphlet | 11 | ||||
| -rw-r--r-- | src/algebra/taylor.spad.pamphlet | 2 |
2 files changed, 7 insertions, 6 deletions
diff --git a/src/algebra/sttaylor.spad.pamphlet b/src/algebra/sttaylor.spad.pamphlet index ba55cf92..756129a8 100644 --- a/src/algebra/sttaylor.spad.pamphlet +++ b/src/algebra/sttaylor.spad.pamphlet @@ -111,7 +111,7 @@ StreamTaylorSeriesOperations(A): Exports == Implementation where ++ revert(a) computes the inverse of a power series \spad{a} ++ with respect to composition. ++ the series should have constant coefficient 0 and first - ++ order coefficient 1. + ++ order coefficient should be invertible. addiag : ST ST A -> ST A ++ 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>,..],..]} @@ -311,10 +311,11 @@ StreamTaylorSeriesOperations(A): Exports == Implementation where revert x == empty? x => error "revert should start 0,1,..." - zero? frst x => - empty? rst x => error "revert: should start 0,1,..." - one? frst rst x => lagrange(recip(rst x) :: (ST A)) - error "revert:should start 0,1,..." + zero? frst x and not empty? rst x => + case recip rst x is + y@ST(A) => lagrange y + otherwise => error "revert: should start 0,a,... with invertible a" + error "revert: argument is not reversible" --% lambert functions diff --git a/src/algebra/taylor.spad.pamphlet b/src/algebra/taylor.spad.pamphlet index 3f4aa0ef..e85c7a85 100644 --- a/src/algebra/taylor.spad.pamphlet +++ b/src/algebra/taylor.spad.pamphlet @@ -211,7 +211,7 @@ UnivariateTaylorSeries(Coef,var,cen): Exports == Implementation where revert: % -> % ++ \spad{revert(f(x))} returns a Taylor series \spad{g(x)} such that ++ \spad{f(g(x)) = g(f(x)) = x}. Series \spad{f(x)} should have constant - ++ coefficient 0 and 1st order coefficient 1. + ++ coefficient 0 and invertible 1st order coefficient. multisect: (I,I,%) -> % ++\spad{multisect(a,b,f(x))} selects the coefficients of ++ \spad{x^((a+b)*n+a)}, and changes this monomial to \spad{x^n}. |