diff options
Diffstat (limited to 'src/algebra/naalgc.spad.pamphlet')
| -rw-r--r-- | src/algebra/naalgc.spad.pamphlet | 21 |
1 files changed, 6 insertions, 15 deletions
diff --git a/src/algebra/naalgc.spad.pamphlet b/src/algebra/naalgc.spad.pamphlet index f5b56a47..3f85f7ef 100644 --- a/src/algebra/naalgc.spad.pamphlet +++ b/src/algebra/naalgc.spad.pamphlet @@ -78,8 +78,6 @@ Monad(): Category == SetCategory with ++ Axioms ++ leftIdentity("*":(%,%)->%,1) \tab{30} 1*x=x ++ rightIdentity("*":(%,%)->%,1) \tab{30} x*1=x -++ Common Additional Axioms -++ unitsKnown---if "recip" says "failed", that PROVES input wasn't a unit MonadWithUnit(): Category == Monad with --constants 1: constant -> % @@ -102,15 +100,15 @@ MonadWithUnit(): Category == Monad with ++ recip(a) returns an element, which is both a left and a right ++ inverse of \spad{a}, ++ or \spad{"failed"} if such an element doesn't exist or cannot - ++ be determined (see unitsKnown). + ++ be determined. leftRecip: % -> Union(%,"failed") ++ leftRecip(a) returns an element, which is a left inverse of \spad{a}, ++ or \spad{"failed"} if such an element doesn't exist or cannot - ++ be determined (see unitsKnown). + ++ be determined. rightRecip: % -> Union(%,"failed") ++ rightRecip(a) returns an element, which is a right inverse of ++ \spad{a}, or \spad{"failed"} if such an element doesn't exist - ++ or cannot be determined (see unitsKnown). + ++ or cannot be determined. add import RepeatedSquaring(%) one? x == x = 1 @@ -404,16 +402,16 @@ FiniteRankNonAssociativeAlgebra(R:CommutativeRing): ++ recip(a) returns an element, which is both a left and a right ++ inverse of \spad{a}, ++ or \spad{"failed"} if there is no unit element, if such an - ++ element doesn't exist or cannot be determined (see unitsKnown). + ++ element doesn't exist or cannot be determined. leftRecip: % -> Union(%,"failed") ++ leftRecip(a) returns an element, which is a left inverse of \spad{a}, ++ or \spad{"failed"} if there is no unit element, if such an - ++ element doesn't exist or cannot be determined (see unitsKnown). + ++ element doesn't exist or cannot be determined. rightRecip: % -> Union(%,"failed") ++ rightRecip(a) returns an element, which is a right inverse of ++ \spad{a}, ++ or \spad{"failed"} if there is no unit element, if such an - ++ element doesn't exist or cannot be determined (see unitsKnown). + ++ element doesn't exist or cannot be determined. associatorDependence:() -> List Vector R ++ associatorDependence() looks for the associator identities, i.e. ++ finds a basis of the solutions of the linear combinations of the @@ -450,13 +448,6 @@ FiniteRankNonAssociativeAlgebra(R:CommutativeRing): -- about characteristic -- if R has CharacteristicZero then CharacteristicZero -- if R has CharacteristicNonZero then CharacteristicNonZero - unitsKnown - ++ unitsKnown means that \spadfun{recip} truly yields reciprocal - ++ or \spad{"failed"} if not a unit, - ++ similarly for \spadfun{leftRecip} and - ++ \spadfun{rightRecip}. The reason is that we use left, respectively - ++ right, minimal polynomials to decide this question. - add --n := rank() --b := someBasis() |