diff options
Diffstat (limited to 'src/algebra/attreg.spad.pamphlet')
| -rw-r--r-- | src/algebra/attreg.spad.pamphlet | 29 |
1 files changed, 0 insertions, 29 deletions
diff --git a/src/algebra/attreg.spad.pamphlet b/src/algebra/attreg.spad.pamphlet index b8853786..68028a29 100644 --- a/src/algebra/attreg.spad.pamphlet +++ b/src/algebra/attreg.spad.pamphlet @@ -18,15 +18,6 @@ AttributeRegistry(): Category == with commutative("*") ++ \spad{commutative("*")} is true if it has an operation ++ \spad{"*": (D,D) -> D} which is commutative. - unitsKnown - ++ \spad{unitsKnown} is true if a monoid (a multiplicative semigroup - ++ with a 1) has \spad{unitsKnown} means that - ++ the operation \spadfun{recip} can only return "failed" - ++ if its argument is not a unit. - leftUnitary - ++ \spad{leftUnitary} is true if \spad{1 * x = x} for all x. - rightUnitary - ++ \spad{rightUnitary} is true if \spad{x * 1 = x} for all x. noZeroDivisors ++ \spad{noZeroDivisors} is true if \spad{x * y \~~= 0} implies ++ both x and y are non-zero. @@ -35,37 +26,17 @@ AttributeRegistry(): Category == with ++ representative for each class of associate elements, that is ++ \spad{associates?(a,b)} returns true if and only if ++ \spad{unitCanonical(a) = unitCanonical(b)}. - canonicalsClosed - ++ \spad{canonicalsClosed} is true if - ++ \spad{unitCanonical(a)*unitCanonical(b) = unitCanonical(a*b)}. - arbitraryPrecision - ++ \spad{arbitraryPrecision} means the user can set the - ++ precision for subsequent calculations. partiallyOrderedSet ++ \spad{partiallyOrderedSet} is true if ++ a set with \spadop{<} which is transitive, ++ but \spad{not(a < b or a = b)} ++ does not necessarily imply \spad{b<a}. - central - ++ \spad{central} is true if, given an algebra over a ring R, - ++ the image of R is the center - ++ of the algebra, i.e. the set of members of the algebra which commute - ++ with all others is precisely the image of R in the algebra. - noetherian - ++ \spad{noetherian} is true if all of its ideals are finitely generated. additiveValuation ++ \spad{additiveValuation} implies ++ \spad{euclideanSize(a*b)=euclideanSize(a)+euclideanSize(b)}. multiplicativeValuation ++ \spad{multiplicativeValuation} implies ++ \spad{euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b)}. - NullSquare - ++ \axiom{NullSquare} means that \axiom{[x,x] = 0} holds. - ++ See \axiomType{LieAlgebra}. - JacobiIdentity - ++ \axiom{JacobiIdentity} means that - ++ \axiom{[x,[y,z]]+[y,[z,x]]+[z,[x,y]] = 0} holds. - ++ See \axiomType{LieAlgebra}. canonical ++ \spad{canonical} is true if and only if distinct elements have ++ distinct data structures. For example, a domain of mathematical objects |