diff options
Diffstat (limited to 'src/algebra')
| -rw-r--r-- | src/algebra/catdef.spad.pamphlet | 16 | ||||
| -rw-r--r-- | src/algebra/integer.spad.pamphlet | 20 | ||||
| -rw-r--r-- | src/algebra/si.spad.pamphlet | 10 |
3 files changed, 25 insertions, 21 deletions
diff --git a/src/algebra/catdef.spad.pamphlet b/src/algebra/catdef.spad.pamphlet index 26aa0469..668b63b7 100644 --- a/src/algebra/catdef.spad.pamphlet +++ b/src/algebra/catdef.spad.pamphlet @@ -822,14 +822,14 @@ EuclideanDomain(): Category == PrincipalIdealDomain with u:= extendedEuclidean(first l,v.generator) [[u.coef1,:[u.coef2*vv for vv in v.coef]],u.generator] expressIdealMember(l,z) == - z = 0 => just [0 for v in l] + zero? z => just [0 for v in l] pid := principalIdeal l (q := z exquo (pid.generator)) case "failed" => nothing just [q*v for v in pid.coef] multiEuclidean(l,z) == n := #l zero? n => error "empty list passed to multiEuclidean" - n = 1 => [z] + one? n => [z] l1 := copy l l2 := split!(l1, n quo 2) u:= extendedEuclidean(*/l1, */l2, z) @@ -883,7 +883,7 @@ Field(): Category == Join(EuclideanDomain,UniqueFactorizationDomain, unitCanonical(x) == if zero? x then x else 1 associates?(x,y) == if zero? x then zero? y else not(zero? y) inv x ==((u:=recip x) case "failed" => error "not invertible"; u) - x exquo y == (y=0 => "failed"; x / y) + x exquo y == (zero? y => "failed"; x / y) gcd(x,y) == 1 euclideanSize(x) == 0 prime? x == false @@ -1001,8 +1001,8 @@ GcdDomain(): Category == IntegralDomain with ++ univariate polynomials over the domain add lcm(x: %,y: %) == - y = 0 => 0 - x = 0 => 0 + zero? y => 0 + zero? x => 0 LCM : Union(%,"failed") := y exquo gcd(x,y) LCM case % => x * LCM error "bad gcd in lcm computation" @@ -1021,9 +1021,9 @@ GcdDomain(): Category == IntegralDomain with p2:=(p2 exquo monomial(1,e2))::SUP % e1:=min(e1,e2); c1:=gcd(c1,c2) p1:= - degree p1 = 0 or degree p2 = 0 => monomial(c1,0) + zero? degree p1 or zero? degree p2 => monomial(c1,0) p:= subResultantGcd(p1,p2) - degree p = 0 => monomial(c1,0) + zero? degree p => monomial(c1,0) c2:= gcd(leadingCoefficient p1,leadingCoefficient p2) unitCanonical(c1 * primitivePart(((c2*p) exquo leadingCoefficient p)::SUP %)) zero? e1 => p1 @@ -2014,7 +2014,7 @@ UniqueFactorizationDomain(): Category == GcdDomain with squareFreePart x == unit(s := squareFree x) * _*/[f.factor for f in factors s] - prime? x == # factorList factor x = 1 + prime? x == one?(# factorList factor x) @ diff --git a/src/algebra/integer.spad.pamphlet b/src/algebra/integer.spad.pamphlet index 0d7e8f0b..cc3fbff5 100644 --- a/src/algebra/integer.spad.pamphlet +++ b/src/algebra/integer.spad.pamphlet @@ -88,6 +88,7 @@ Integer: Join(IntegerNumberSystem, ConvertibleTo String, OpenMath) with import %iabs: % -> % from Foreign Builtin import %irandom: % -> % from Foreign Builtin import %iodd?: % -> Boolean from Foreign Builtin + import %ieven?: % -> Boolean from Foreign Builtin import %hash: % -> SingleInteger from Foreign Builtin import %iadd: (%,%) -> % from Foreign Builtin import %isub: (%,%) -> % from Foreign Builtin @@ -152,17 +153,17 @@ Integer: Join(IntegerNumberSystem, ConvertibleTo String, OpenMath) with if wholeObj then OMputEndObject(dev) - zero? x == x = 0@% - one? x == x = 1@% + zero? x == x = %icst0 + one? x == x = %icst1 0 == %icst0 1 == %icst1 base() == 2 pretend % copy x == x - inc x == x + 1@% - dec x == x - 1@% + inc x == x + %icst1 + dec x == x - %icst1 hash x == %hash x - negative? x == x < 0@% - positive? x == 0 < x + negative? x == x < %icst0 + positive? x == %icst0 < x coerce(x):OutputForm == outputForm(x pretend Integer) coerce(m:Integer):% == m pretend % convert(x:%):Integer == x pretend Integer @@ -183,7 +184,7 @@ Integer: Join(IntegerNumberSystem, ConvertibleTo String, OpenMath) with latex(x:%):String == s : String := convert x - -1 < x and x < 10 => s + -%icst1 < x and x < 10 => s %strconc("{", %strconc(s, "}")) positiveRemainder(a, b) == @@ -214,6 +215,7 @@ Integer: Join(IntegerNumberSystem, ConvertibleTo String, OpenMath) with (m:Integer) * (y:%) == %imul(m,y) -- for subsumption problem x ** n == %ipow(x,n)$Foreign(Builtin) odd? x == %iodd? x + even? x == %ieven? x max(x,y) == %imax(x,y) min(x,y) == %imin(x,y) divide(x,y) == %idivide(x,y)$Foreign(Builtin) @@ -224,8 +226,8 @@ Integer: Join(IntegerNumberSystem, ConvertibleTo String, OpenMath) with gcd(x,y) == %igcd(x,y) UCA ==> Record(unit:%,canonical:%,associate:%) unitNormal x == - negative? x => [-1@%,-x,-1@%]$UCA - [1@%,x,1@%]$UCA + negative? x => [-%icst1,-x,-%icst1]$UCA + [%icst1,x,%icst1]$UCA unitCanonical x == abs x solveLinearPolynomialEquation(lp:List ZP,p:ZP):Union(List ZP,"failed") == solveLinearPolynomialEquation(lp pretend List ZZP, diff --git a/src/algebra/si.spad.pamphlet b/src/algebra/si.spad.pamphlet index 888a40f3..f8296439 100644 --- a/src/algebra/si.spad.pamphlet +++ b/src/algebra/si.spad.pamphlet @@ -226,6 +226,7 @@ SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,BooleanLogic,OpenMath) w import %hash: % -> SingleInteger from Foreign Builtin import %ilength: % -> % from Foreign Builtin import %iodd?: % -> Boolean from Foreign Builtin + import %ieven?: % -> Boolean from Foreign Builtin import %ieq: (%,%) -> Boolean from Foreign Builtin import %ilt: (%,%) -> Boolean from Foreign Builtin import %ile: (%,%) -> Boolean from Foreign Builtin @@ -319,6 +320,7 @@ SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,BooleanLogic,OpenMath) w gcd(x,y) == %igcd(x,y) abs(x) == %iabs x odd?(x) == %iodd? x + even?(x) == %ieven? x zero?(x) == %ieq(x,%icst0) one?(x) == %ieq(x,%icst1) max(x,y) == %imax(x,y) @@ -334,7 +336,7 @@ SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,BooleanLogic,OpenMath) w (%icstmax - %icstmin + %icst1) pretend NonNegativeInteger index i == per(i + rep %icstmin - rep %icst1) lookup x == - (x - %icstmin + %icst1) pretend PositiveInteger + (rep x - rep %icstmin + rep %icst1) pretend PositiveInteger reducedSystem(m: Matrix %, v: Vector %) == @@ -353,9 +355,9 @@ SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,BooleanLogic,OpenMath) w UCA ==> Record(unit:%,canonical:%,associate:%) unitNormal x == - negative? x => [-1@%,-x,-1@%]$UCA - [1@%,x,1@%]$UCA - positive? x == 0 < x + negative? x => [-%icst1,-x,-%icst1]$UCA + [%icst1,x,%icst1]$UCA + positive? x == %icst0 < x @ |