/usr/share/axiom-20170501/src/algebra/ATTREG.spad is in axiom-source 20170501-3.
This file is owned by root:root, with mode 0o644.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 | )abbrev category ATTREG AttributeRegistry
++ Description:
++ This category exports the attributes in the AXIOM Library
AttributeRegistry() : Category == SIG where
SIG ==> with
finiteAggregate
++ \spad{finiteAggregate} is true if it is an aggregate with a
++ finite number of elements.
commutative("*")
++ \spad{commutative("*")} is true if it has an operation
++ \spad{"*": (D,D) -> D} which is commutative.
shallowlyMutable
++ \spad{shallowlyMutable} is true if its values
++ have immediate components that are updateable (mutable).
++ Note that the properties of any component domain are irrevelant
++ to the \spad{shallowlyMutable} proper.
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.
canonicalUnitNormal
++ \spad{canonicalUnitNormal} is true if we can choose a canonical
++ 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, For example, 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 which has the \spad{canonical} attribute means that two
++ objects are mathematically equal if and only if their data
++ structures are equal.
approximate
++ \spad{approximate} means "is an approximation to the real numbers".
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