diff options
Diffstat (limited to 'src/algebra/catdef.spad.pamphlet')
| -rw-r--r-- | src/algebra/catdef.spad.pamphlet | 10 |
1 files changed, 2 insertions, 8 deletions
diff --git a/src/algebra/catdef.spad.pamphlet b/src/algebra/catdef.spad.pamphlet index 56860d9f..45d087d0 100644 --- a/src/algebra/catdef.spad.pamphlet +++ b/src/algebra/catdef.spad.pamphlet @@ -149,10 +149,7 @@ AbelianSemiGroup(): Category == SetCategory with ++ \spad{b*x = (b::%)*x} ++ \spad{r*(a*b) = (r*a)*b = a*(r*b)} Algebra(R:CommutativeRing): Category == - Join(Ring, Module R) with - --operations - coerce: R -> % - ++ coerce(r) maps the ring element r to a member of the algebra. + Join(Ring, Module R, CoercibleFrom R) add coerce(x:R):% == x * 1$% @@ -1529,7 +1526,7 @@ RightModule(R:Rng):Category == AbelianGroup with ++ not necessarily commutative. --Ring(): Category == Join(Rng,Monoid,LeftModule(%:Rng)) with -Ring(): Category == Join(Rng,Monoid,LeftModule(%)) with +Ring(): Category == Join(Rng,Monoid,LeftModule(%),CoercibleFrom Integer) with --operations characteristic: () -> NonNegativeInteger ++ characteristic() returns the characteristic of the ring @@ -1537,9 +1534,6 @@ Ring(): Category == Join(Rng,Monoid,LeftModule(%)) with ++ \spad{n*x=0} for all x in the ring, or zero if no such n ++ exists. --We can not make this a constant, since some domains are mutable - coerce: Integer -> % - ++ coerce(i) converts the integer i to a member of the given domain. --- recip: % -> Union(%,"failed") -- inherited from Monoid unitsKnown ++ recip truly yields ++ reciprocal or "failed" if not a unit. |