diff options
Diffstat (limited to 'src')
| -rw-r--r-- | src/ChangeLog | 8 | ||||
| -rw-r--r-- | src/algebra/attreg.spad.pamphlet | 29 | ||||
| -rw-r--r-- | src/algebra/catdef.spad.pamphlet | 16 | ||||
| -rw-r--r-- | src/algebra/integer.spad.pamphlet | 8 | ||||
| -rw-r--r-- | src/algebra/lie.spad.pamphlet | 2 | ||||
| -rw-r--r-- | src/algebra/matrix.spad.pamphlet | 7 | ||||
| -rw-r--r-- | src/algebra/naalgc.spad.pamphlet | 21 | ||||
| -rw-r--r-- | src/algebra/si.spad.pamphlet | 6 | ||||
| -rw-r--r-- | src/algebra/vector.spad.pamphlet | 1 | ||||
| -rw-r--r-- | src/algebra/xlpoly.spad.pamphlet | 5 | ||||
| -rw-r--r-- | src/algebra/xpoly.spad.pamphlet | 1 | ||||
| -rw-r--r-- | src/interp/Makefile.in | 4 | ||||
| -rw-r--r-- | src/interp/functor.boot | 2 | ||||
| -rw-r--r-- | src/interp/nruncomp.boot | 2 | ||||
| -rw-r--r-- | src/interp/sys-constants.boot | 10 |
15 files changed, 25 insertions, 97 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index bec1627b..a2fdd2b4 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,3 +1,11 @@ +2015-12-30 Gabriel Dos Reis <gdr@axiomatics.org> + + * algebra/attreg.spad.pamphlet (AttributeRegistry): Remove + unitsKnown, leftUnitary, rightUnitary, canonicalsClosed, + central, noetherian, NullSquare, JacobiIdentity. + Adjust users. + * interp/sys-constants.boot ($BuiltinAttributes): Likewise. + 2015-12-29 Gabriel Dos Reis <gdr@axiomatics.org> * interp/nruncomp.boot ($AddChainIndex): Define. 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 diff --git a/src/algebra/catdef.spad.pamphlet b/src/algebra/catdef.spad.pamphlet index 9e6a8102..1e9370df 100644 --- a/src/algebra/catdef.spad.pamphlet +++ b/src/algebra/catdef.spad.pamphlet @@ -489,9 +489,7 @@ OrderedStructure(T: Type,f: (T,T) -> Boolean): Public == Private where ++ Axiom: ++ \spad{ r*(x*s) = (r*x)*s } BiModule(R:Ring,S:Ring):Category == - Join(LeftModule(R),RightModule(S)) with - leftUnitary ++ \spad{1 * x = x} - rightUnitary ++ \spad{x * 1 = x} + Join(LeftModule(R),RightModule(S)) @ \section{category CABMON CancellationAbelianMonoid} @@ -1033,7 +1031,6 @@ Field(): Category == Join(EuclideanDomain,UniqueFactorizationDomain, ++ x/y divides the element x by the element y. ++ Error: if y is 0. canonicalUnitNormal ++ either 0 or 1. - canonicalsClosed ++ since \spad{0*0=0}, \spad{1*1=1} add --declarations x,y: % @@ -1224,8 +1221,6 @@ Group(): Category == Monoid with inv: % -> % ++ inv(x) returns the inverse of x. /: (%,%) -> % ++ x/y is the same as x times the inverse of y. **: (%,Integer) -> % ++ x**n returns x raised to the integer power n. - unitsKnown ++ unitsKnown asserts that recip only returns - ++ "failed" for non-units. conjugate: (%,%) -> % ++ conjugate(p,q) computes \spad{inv(q) * p * q}; this is 'right action ++ by conjugation'. @@ -1261,7 +1256,6 @@ Group(): Category == Monoid with ++ ++ Conditional attributes: ++ canonicalUnitNormal\tab{20}the canonical field is the same for all associates -++ canonicalsClosed\tab{20}the product of two canonicals is itself canonical IntegralDomain(): Category == Join(CommutativeRing, Algebra(%), EntireRing) with @@ -1411,8 +1405,6 @@ Module(R:CommutativeRing): Category == Join(BiModule(R,R), LinearSet R) ++ \spad{leftIdentity("*":(%,%)->%,1)}\tab{30}\spad{1*x=x} ++ \spad{rightIdentity("*":(%,%)->%,1)}\tab{30}\spad{x*1=x} ++ -++ Conditional attributes: -++ unitsKnown\tab{15}\spadfun{recip} only returns "failed" on non-units Monoid(): Category == SemiGroup with --operations 1: % ++ 1 is the multiplicative identity. @@ -1422,7 +1414,7 @@ Monoid(): Category == SemiGroup with ++ of x n times, i.e. exponentiation. recip: % -> Union(%,"failed") ++ recip(x) tries to compute the multiplicative inverse for x - ++ or "failed" if it cannot find the inverse (see unitsKnown). + ++ or "failed" if it cannot find the inverse. add import RepeatedSquaring(%) one? x == x = 1 @@ -2012,10 +2004,6 @@ Ring(): Category == Join(Rng,SemiRing,LeftModule(%),CoercibleFrom Integer) 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 - unitsKnown - ++ recip truly yields - ++ reciprocal or "failed" if not a unit. - ++ Note: \spad{recip(0) = "failed"}. add n:Integer coerce(n) == n * 1$% diff --git a/src/algebra/integer.spad.pamphlet b/src/algebra/integer.spad.pamphlet index ba924720..df709373 100644 --- a/src/algebra/integer.spad.pamphlet +++ b/src/algebra/integer.spad.pamphlet @@ -73,10 +73,6 @@ IntegerSolveLinearPolynomialEquation(): C ==T Integer: IntegerNumberSystem with canonical ++ mathematical equality is data structure equality. - canonicalsClosed - ++ two positives multiply to give positive. - noetherian - ++ ascending chain condition on ideals. == add ZP ==> SparseUnivariatePolynomial % ZZP ==> SparseUnivariatePolynomial Integer @@ -298,10 +294,6 @@ PositiveInteger: Join(OrderedAbelianSemiGroup,Monoid) with RomanNumeral(): Join(IntegerNumberSystem,ConvertibleFrom Symbol) with canonical ++ mathematical equality is data structure equality. - canonicalsClosed - ++ two positives multiply to give positive. - noetherian - ++ ascending chain condition on ideals. roman : Symbol -> % ++ roman(n) creates a roman numeral for symbol n. roman : Integer -> % diff --git a/src/algebra/lie.spad.pamphlet b/src/algebra/lie.spad.pamphlet index d039c5ef..a8d2c857 100644 --- a/src/algebra/lie.spad.pamphlet +++ b/src/algebra/lie.spad.pamphlet @@ -201,8 +201,6 @@ LieSquareMatrix(n,R): Exports == Implementation where -- symdecomp : % -> Record(sym:%,antisym:%) -- if R has commutative("*") then -- minorsVect: -> Vector(Union(R,"uncomputed")) --range: 1..2**n-1 --- if R has commutative("*") then central --- if R has commutative("*") and R has unitsKnown then unitsKnown @ \section{License} diff --git a/src/algebra/matrix.spad.pamphlet b/src/algebra/matrix.spad.pamphlet index 6aded198..159f0217 100644 --- a/src/algebra/matrix.spad.pamphlet +++ b/src/algebra/matrix.spad.pamphlet @@ -310,13 +310,6 @@ SquareMatrix(ndim,R): Exports == Implementation where -- if R has commutative("*") then -- minorsVect: -> Vector(Union(R,"uncomputed")) --range: 1..2**n-1 -- ++ \spad{minorsVect(m)} returns a vector of the minors of the matrix m - if R has commutative("*") then central - ++ the elements of the Ring R, viewed as diagonal matrices, commute - ++ with all matrices and, indeed, are the only matrices which commute - ++ with all matrices. - if R has commutative("*") and R has unitsKnown then unitsKnown - ++ the invertible matrices are simply the matrices whose determinants - ++ are units in the Ring R. if R has ConvertibleTo InputForm then ConvertibleTo InputForm Implementation ==> Matrix R add 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() diff --git a/src/algebra/si.spad.pamphlet b/src/algebra/si.spad.pamphlet index 795a75ed..561fc89e 100644 --- a/src/algebra/si.spad.pamphlet +++ b/src/algebra/si.spad.pamphlet @@ -182,12 +182,6 @@ IntegerNumberSystem(): Category == SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,BooleanLogic) with canonical ++ \spad{canonical} means that mathematical equality is implied by data structure equality. - canonicalsClosed - ++ \spad{canonicalClosed} means two positives multiply to give positive. - noetherian - ++ \spad{noetherian} all ideals are finitely generated (in fact principal). - - -- bit operations xor: (%, %) -> % ++ xor(n,m) returns the bit-by-bit logical {\em xor} of ++ the single integers n and m. diff --git a/src/algebra/vector.spad.pamphlet b/src/algebra/vector.spad.pamphlet index ea83ba12..7d143b7a 100644 --- a/src/algebra/vector.spad.pamphlet +++ b/src/algebra/vector.spad.pamphlet @@ -238,7 +238,6 @@ DirectProductCategory(dim:NonNegativeInteger, R:Type): Category == if R has Monoid then LinearSet R if R has Finite then Finite if R has CommutativeRing then Module R - if R has unitsKnown then unitsKnown if R has OrderedSet then OrderedSet if R has OrderedAbelianMonoidSup then OrderedAbelianMonoidSup if R has Field then VectorSpace R diff --git a/src/algebra/xlpoly.spad.pamphlet b/src/algebra/xlpoly.spad.pamphlet index f607199d..6090799a 100644 --- a/src/algebra/xlpoly.spad.pamphlet +++ b/src/algebra/xlpoly.spad.pamphlet @@ -353,11 +353,6 @@ import Field ++ \axiomType{LiePolynomial} and ++ \axiomType{XPBWPolynomial}. \newline Author : Michel Petitot (petitot@lifl.fr). LieAlgebra(R: CommutativeRing): Category == Module(R) with - --attributes - NullSquare - ++ \axiom{NullSquare} means that \axiom{[x,x] = 0} holds. - JacobiIdentity - ++ \axiom{JacobiIdentity} means that \axiom{[x,[y,z]]+[y,[z,x]]+[z,[x,y]] = 0} holds. --exports construct: ($,$) -> $ ++ \axiom{construct(x,y)} returns the Lie bracket of \axiom{x} and \axiom{y}. diff --git a/src/algebra/xpoly.spad.pamphlet b/src/algebra/xpoly.spad.pamphlet index b2021bf8..dbaf46dc 100644 --- a/src/algebra/xpoly.spad.pamphlet +++ b/src/algebra/xpoly.spad.pamphlet @@ -536,7 +536,6 @@ XPolynomialRing(R:Ring,E:OrderedMonoid): T == C where --assertions if R has noZeroDivisors then noZeroDivisors - if R has unitsKnown then unitsKnown if R has canonicalUnitNormal then canonicalUnitNormal ++ canonicalUnitNormal guarantees that the function ++ unitCanonical returns the same representative for all diff --git a/src/interp/Makefile.in b/src/interp/Makefile.in index b0b9c507..ef249649 100644 --- a/src/interp/Makefile.in +++ b/src/interp/Makefile.in @@ -294,12 +294,12 @@ setvart.$(FASLEXT): sys-macros.$(FASLEXT) ## OpenAxiom's compiler compiler.$(FASLEXT): msgdb.$(FASLEXT) pathname.$(FASLEXT) define.$(FASLEXT) nrunfast.$(FASLEXT): c-util.$(FASLEXT) -nruncomp.$(FASLEXT): profile.$(FASLEXT) simpbool.$(FASLEXT) functor.$(FASLEXT) +nruncomp.$(FASLEXT): profile.$(FASLEXT) simpbool.$(FASLEXT) nrunfast.$(FASLEXT) define.$(FASLEXT): g-error.$(FASLEXT) nruncomp.$(FASLEXT) database.$(FASLEXT) database.$(FASLEXT): clam.$(FASLEXT) nlib.$(FASLEXT) \ cattable.$(FASLEXT) compat.$(FASLEXT) g-cndata.$(FASLEXT) \ c-util.$(FASLEXT) -functor.$(FASLEXT): category.$(FASLEXT) lisplib.$(FASLEXT) nrunfast.$(FASLEXT) +functor.$(FASLEXT): category.$(FASLEXT) lisplib.$(FASLEXT) nruncomp.$(FASLEXT) category.$(FASLEXT): c-util.$(FASLEXT) g-cndata.$(FASLEXT) cattable.$(FASLEXT): simpbool.$(FASLEXT) c-util.$(FASLEXT) compat.$(FASLEXT): pathname.$(FASLEXT) diff --git a/src/interp/functor.boot b/src/interp/functor.boot index c6185c94..950fb3b1 100644 --- a/src/interp/functor.boot +++ b/src/interp/functor.boot @@ -33,7 +33,7 @@ import lisplib -import nrunfast +import nruncomp import category namespace BOOT diff --git a/src/interp/nruncomp.boot b/src/interp/nruncomp.boot index 459472d2..2b6c7ad4 100644 --- a/src/interp/nruncomp.boot +++ b/src/interp/nruncomp.boot @@ -34,7 +34,7 @@ import simpbool import profile -import functor +import nrunfast namespace BOOT ++ The "add-chain" index for a functor instance. diff --git a/src/interp/sys-constants.boot b/src/interp/sys-constants.boot index 44515be3..673e0b2d 100644 --- a/src/interp/sys-constants.boot +++ b/src/interp/sys-constants.boot @@ -627,11 +627,11 @@ $FILETYPE_-TABLE == +++ $BuiltinAttributes == - '(nil infinite arbitraryExponent approximate complex - canonical noetherian central - partiallyOrderedSet arbitraryPrecision canonicalsClosed - noZeroDivisors rightUnitary leftUnitary - additiveValuation unitsKnown canonicalUnitNormal + '(nil arbitraryExponent approximate complex + canonical + partiallyOrderedSet arbitraryPrecision + noZeroDivisors + additiveValuation canonicalUnitNormal multiplicativeValuation commutative) +++ |