diff options
Diffstat (limited to 'src/algebra/curve.spad.pamphlet')
| -rw-r--r-- | src/algebra/curve.spad.pamphlet | 20 |
1 files changed, 10 insertions, 10 deletions
diff --git a/src/algebra/curve.spad.pamphlet b/src/algebra/curve.spad.pamphlet index 5ca9495b..d216b16d 100644 --- a/src/algebra/curve.spad.pamphlet +++ b/src/algebra/curve.spad.pamphlet @@ -168,13 +168,13 @@ FunctionFieldCategory(F, UP, UPUP): Category == Definition where Q2RF q == numer(q)::UP / denom(q)::UP infOrder f == (degree denom f)::Z - (degree numer f)::Z integral? f == ground?(integralCoordinates(f).den) - integral?(f:$, a:F) == (integralCoordinates(f).den)(a) ^= 0 + integral?(f:$, a:F) == (integralCoordinates(f).den)(a) ~= 0 -- absolutelyIrreducible? == one? numberOfComponents() absolutelyIrreducible? == numberOfComponents() = 1 yCoordinates f == splitDenominator coordinates f hyperelliptic() == - degree(f := definingPolynomial()) ^= 2 => "failed" + degree(f := definingPolynomial()) ~= 2 => "failed" (u:=retractIfCan(reductum f)@Union(RF,"failed")) case "failed" => "failed" (v := retractIfCan(-(u::RF) / leadingCoefficient f)@Union(UP, "failed")) case "failed" => "failed" @@ -299,7 +299,7 @@ FunctionFieldCategory(F, UP, UPUP): Category == Definition where nostart:Boolean := true ans:Z := 0 r := row(m, i) - for j in minIndex r .. maxIndex r | qelt(r, j) ^= 0 repeat + for j in minIndex r .. maxIndex r | qelt(r, j) ~= 0 repeat ans := nostart => (nostart := false; infOrder qelt(r, j)) min(ans, infOrder qelt(r,j)) @@ -321,7 +321,7 @@ FunctionFieldCategory(F, UP, UPUP): Category == Definition where nostart:Boolean := true k:Z := 0 ii := minRowIndex m - (i0 := minIndex v) - for i in minIndex v .. maxIndex v | qelt(v, i) ^= 0 repeat + for i in minIndex v .. maxIndex v | qelt(v, i) ~= 0 repeat nk := repOrder(m, i + ii) if nostart then (nostart := false; k := nk; i0 := i) else @@ -476,7 +476,7 @@ ChangeOfVariable(F, UP, UPUP): Exports == Implementation where infIntegral?: (UPUP, UPUP) -> Boolean eval(p, x, y) == map(#1 x, p) monomial(y, 1) - good?(a, p, q) == p(a) ^= 0 and q(a) ^= 0 + good?(a, p, q) == p(a) ~= 0 and q(a) ~= 0 algPoly p == ground?(a:= retract(leadingCoefficient(q:=clearDenominator p))@UP) @@ -514,7 +514,7 @@ ChangeOfVariable(F, UP, UPUP): Exports == Implementation where ninv := inv(r.deg::Q) degy:Q := degree(retract(r.radicand)@UP) * ninv degp:Q := 0 - while p ^= 0 repeat + while p ~= 0 repeat c := leadingCoefficient p degp := max(degp, (2 + degree(numer c)::Z - degree(denom c)::Z)::Q + degree(p) * degy) @@ -666,7 +666,7 @@ RadicalFunctionField(F, UP, UPUP, radicnd, n): Exports == Impl where -- is a local integral basis at infinity for the curve y**d = p inftyBasis(p, m) == rt := rootPoly(p(x := inv(monomial(1, 1)$UP :: RF)), m) - m ^= rt.exponent => + m ~= rt.exponent => error "Curve not irreducible after change of variable 0 -> infinity" a := (rt.coef) x b:RF := 1 @@ -678,7 +678,7 @@ RadicalFunctionField(F, UP, UPUP, radicnd, n): Exports == Impl where w charPintbas(p, c, v, w) == - degree(p) ^= n => error "charPintbas: should not happen" + degree(p) ~= n => error "charPintbas: should not happen" q:UP2 := map(retract(#1)@UP, p) ib := integralBasis()$FunctionFieldIntegralBasis(UP, UP2, SimpleAlgebraicExtension(UP, UP2, q)) @@ -712,7 +712,7 @@ RadicalFunctionField(F, UP, UPUP, radicnd, n): Exports == Impl where char0StartUp() == rp := rootPoly(radicnd, n) - rp.exponent ^= n => error "RadicalFunctionField: curve is not irreducible" + rp.exponent ~= n => error "RadicalFunctionField: curve is not irreducible" newrad() := rp.radicand ib := iBasis(newrad(), n) infb := inftyBasis(radicnd, n) @@ -831,7 +831,7 @@ AlgebraicFunctionField(F, UP, UPUP, modulus): Exports == Impl where x := inv(monomial(1, 1)$UP :: RF) invmod := map(#1 x, modulus) r := mkIntegral invmod - degree(r.poly) ^= n => error "Should not happen" + degree(r.poly) ~= n => error "Should not happen" ninvmod:UP2 := map(retract(#1)@UP, r.poly) alpha := [(r.coef ** i) x for i in 0..n1]$Vector(RF) invalpha := [inv qelt(alpha, i) |