diff options
Diffstat (limited to 'src/algebra/pfo.spad.pamphlet')
| -rw-r--r-- | src/algebra/pfo.spad.pamphlet | 18 |
1 files changed, 6 insertions, 12 deletions
diff --git a/src/algebra/pfo.spad.pamphlet b/src/algebra/pfo.spad.pamphlet index 493a68e4..5a36f184 100644 --- a/src/algebra/pfo.spad.pamphlet +++ b/src/algebra/pfo.spad.pamphlet @@ -190,8 +190,7 @@ PointsOfFiniteOrderRational(UP, UPUP, R): Exports == Implementation where n := rat(modulus, d, p := getGoodPrime bad) -- if n > 1 then it is cheaper to compute the order modulo a second prime, -- since computing n * d could be very expensive --- one? n => n - (n = 1) => n + one? n => n m := rat(modulus, d, getGoodPrime(p * bad)) n = m => n 0 @@ -203,8 +202,7 @@ PointsOfFiniteOrderRational(UP, UPUP, R): Exports == Implementation where -- returns the potential order of d, 0 if d is of infinite order possibleOrder d == --- zero?(genus()) or one?(#(numer ideal d)) => 1 - zero?(genus()) or (#(numer ideal d) = 1) => 1 + zero?(genus()) or one?(#(numer ideal d)) => 1 r := polyred definingPolynomial()$R ratcurve(d, r, doubleDisc r) @@ -447,8 +445,7 @@ PointsOfFiniteOrder(R0, F, UP, UPUP, R): Exports == Implementation where gf := InnerPrimeField p m := map(retract(#1)@Z :: gf, mm)$SparseUnivariatePolynomialFunctions2(Q, gf) --- one? degree m => - (degree m = 1) => + one? degree m => alpha := - coefficient(m, 0) / leadingCoefficient m order(d, pp, (map(numer(#1)::gf / denom(#1)::gf, @@ -476,8 +473,7 @@ PointsOfFiniteOrder(R0, F, UP, UPUP, R): Exports == Implementation where n := rat(pp, d, p := getGoodPrime bad) -- if n > 1 then it is cheaper to compute the order modulo a second prime, -- since computing n * d could be very expensive --- one? n => n - (n = 1) => n + one? n => n m := rat(pp, d, getGoodPrime(p * bad)) n = m => n 0 @@ -490,8 +486,7 @@ PointsOfFiniteOrder(R0, F, UP, UPUP, R): Exports == Implementation where -- returns the potential order of d, 0 if d is of infinite order possibleOrder d == --- zero?(genus()) or one?(#(numer ideal d)) => 1 - zero?(genus()) or (#(numer ideal d) = 1) => 1 + zero?(genus()) or one?(#(numer ideal d)) => 1 empty?(la := alglist d) => ratcurve(d, selIntegers()) not(empty? rest la) => error "PFO::possibleOrder: more than 1 algebraic constant" @@ -548,8 +543,7 @@ PointsOfFiniteOrder(R0, F, UP, UPUP, R): Exports == Implementation where l := [f.factor for f in factors factor(map(retract(#1)@Z :: gf, rec.dfpoly)$SparseUnivariatePolynomialFunctions2(Q, gf))$DistinctDegreeFactorize(gf, --- SparseUnivariatePolynomial gf) | one?(f.exponent)] - SparseUnivariatePolynomial gf) | (f.exponent = 1)] + SparseUnivariatePolynomial gf) | one?(f.exponent)] empty? l => "failed" mdg := first l for ff in rest l repeat |