diff options
Diffstat (limited to 'src/algebra')
| -rw-r--r-- | src/algebra/ore.spad.pamphlet | 23 |
1 files changed, 11 insertions, 12 deletions
diff --git a/src/algebra/ore.spad.pamphlet b/src/algebra/ore.spad.pamphlet index e55b0eee..3aaeab04 100644 --- a/src/algebra/ore.spad.pamphlet +++ b/src/algebra/ore.spad.pamphlet @@ -296,26 +296,25 @@ Automorphism(R:Ring): Join(Group, Eltable(R, R)) with morphism: ((R, Integer) -> R) -> % ++ morphism(f) returns the morphism given by \spad{f^n(x) = f(x,n)}. == add + Rep == (R, Integer) -> R err: R -> R ident: (R, Integer) -> R iter: (R -> R, NonNegativeInteger, R) -> R iterat: (R -> R, R -> R, Integer, R) -> R - apply: (%, R, Integer) -> R - - Rep := ((R, Integer) -> R) - - 1 == ident + apply: (Rep, R, Integer) -> R + + 1 == per ident err r == error "Morphism is not invertible" ident(r, n) == r f = g == %peq(f,g)$Foreign(Builtin) - elt(f, r) == apply(f, r, 1) - inv f == apply(f, #1, - #2) - (f: %) ** (n: Integer) == apply(f, #1, n * #2) + elt(f, r) == apply(rep f, r, 1) + inv f == per apply(rep f, #1, - #2) + (f: %) ** (n: Integer) == per apply(rep f, #1, n * #2) coerce(f:%):OutputForm == message("R -> R") - morphism(f:(R, Integer) -> R):% == f + morphism(f:(R, Integer) -> R):% == per f morphism(f:R -> R):% == morphism(f, err) - morphism(f, g) == iterat(f, g, #2, #1) - apply(f, r, n) == (g := f pretend ((R, Integer) -> R); g(r, n)) + morphism(f, g) == per iterat(f, g, #2, #1) + apply(f, r, n) == f(r, n) iterat(f, g, n, r) == negative? n => iter(g, (-n)::NonNegativeInteger, r) @@ -327,7 +326,7 @@ Automorphism(R:Ring): Join(Group, Eltable(R, R)) with f * g == f = g => f**2 - iterat(f g #1, (inv g)(inv f) #1, #2, #1) + per iterat(f g #1, (inv g)(inv f) #1, #2, #1) @ \section{package OREPCTO UnivariateSkewPolynomialCategoryOps} |