diff options
Diffstat (limited to 'src/algebra/sttaylor.spad.pamphlet')
-rw-r--r-- | src/algebra/sttaylor.spad.pamphlet | 16 |
1 files changed, 8 insertions, 8 deletions
diff --git a/src/algebra/sttaylor.spad.pamphlet b/src/algebra/sttaylor.spad.pamphlet index 42def454..febd20d1 100644 --- a/src/algebra/sttaylor.spad.pamphlet +++ b/src/algebra/sttaylor.spad.pamphlet @@ -48,29 +48,29 @@ StreamTaylorSeriesOperations(A): Exports == Implementation where YS ==> Y$ParadoxicalCombinatorsForStreams(A) UN ==> Union(ST A,"failed") Exports ==> with - "+" : (ST A,ST A) -> ST A + + : (ST A,ST A) -> ST A ++ a + b returns the power series sum of \spad{a} and \spad{b}: ++ \spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]} - "-" : (ST A,ST A) -> ST A + - : (ST A,ST A) -> ST A ++ a - b returns the power series difference of \spad{a} and ++ \spad{b}: \spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]} - "-" : ST A -> ST A + - : ST A -> ST A ++ - a returns the power series negative of \spad{a}: ++ \spad{- [a0,a1,...] = [- a0,- a1,...]} - "*" : (ST A,ST A) -> ST A + * : (ST A,ST A) -> ST A ++ a * b returns the power series (Cauchy) product of \spad{a} and b: ++ \spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where ++ \spad{ck = sum(i + j = k,ai * bk)}. - "*" : (A,ST A) -> ST A + * : (A,ST A) -> ST A ++ r * a returns the power series scalar multiplication of r by \spad{a}: ++ \spad{r * [a0,a1,...] = [r * a0,r * a1,...]} - "*" : (ST A,A) -> ST A + * : (ST A,A) -> ST A ++ a * r returns the power series scalar multiplication of \spad{a} by r: ++ \spad{[a0,a1,...] * r = [a0 * r,a1 * r,...]} - "exquo" : (ST A,ST A) -> Union(ST A,"failed") + exquo : (ST A,ST A) -> Union(ST A,"failed") ++ exquo(a,b) returns the power series quotient of \spad{a} by b, ++ if the quotient exists, and "failed" otherwise - "/" : (ST A,ST A) -> ST A + / : (ST A,ST A) -> ST A ++ a / b returns the power series quotient of \spad{a} by b. ++ An error message is returned if \spad{b} is not invertible. ++ This function is used in fixed point computations. |