diff options
Diffstat (limited to 'src/algebra/catdef.spad.pamphlet')
| -rw-r--r-- | src/algebra/catdef.spad.pamphlet | 16 |
1 files changed, 8 insertions, 8 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) @ |