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| author | dos-reis <gdr@axiomatics.org> | 2008-05-18 16:05:33 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2008-05-18 16:05:33 +0000 |
| commit | 38982ebf4d9b23fe336bd4880ef0f4d59dbc7684 (patch) | |
| tree | 84c5ecf37d692f6dfcd9328f9cc68b8410636ccf /src/algebra | |
| parent | b4858d7fc0bb4d55de5e7c1b51104c77cbae7109 (diff) | |
| download | open-axiom-38982ebf4d9b23fe336bd4880ef0f4d59dbc7684.tar.gz | |
Fix AW/313
* algebra/reclos.spad.pamphlet (sqrt$RealClosedField): Fix signature.
Diffstat (limited to 'src/algebra')
| -rw-r--r-- | src/algebra/reclos.spad.pamphlet | 9 |
1 files changed, 4 insertions, 5 deletions
diff --git a/src/algebra/reclos.spad.pamphlet b/src/algebra/reclos.spad.pamphlet index ff396d16..e5d2ece2 100644 --- a/src/algebra/reclos.spad.pamphlet +++ b/src/algebra/reclos.spad.pamphlet @@ -350,7 +350,7 @@ RealClosedField : Category == PUB where ++ \axiom{allRootsOf(pol)} creates all the roots ++ of \axiom{pol} naming each uniquely - sqrt: ($,N) -> $ + sqrt: ($,PI) -> $ ++ \axiom{sqrt(x,n)} is \axiom{x ** (1/n)} sqrt: $ -> $ @@ -394,7 +394,6 @@ RealClosedField : Category == PUB where sqrt(x,n) == - n = 0 => 1 n = 1 => x zero?(x) => 0 one?(x) => 1 @@ -407,12 +406,12 @@ RealClosedField : Category == PUB where n = 2 => rename(r,root(x::E)$E) rename(r,root(x :: E, n :: E)$E) - (x : $) ** (rn : RN) == sqrt(x**numer(rn),denom(rn)::N) + (x : $) ** (rn : RN) == sqrt(x**numer(rn),denom(rn)::PI) nthRoot(x, n) == zero?(n) => x - negative?(n) => inv(sqrt(x,(-n) :: N)) - sqrt(x,n :: N) + negative?(n) => inv(sqrt(x,(-n) :: PI)) + sqrt(x,n :: PI) allRootsOf(p:SUP(RN)) == allRootsOf(map(#1 :: $ ,p)$PACK(RN,$)) |