diff options
Diffstat (limited to 'src/algebra/ffpoly.spad.pamphlet')
| -rw-r--r-- | src/algebra/ffpoly.spad.pamphlet | 16 |
1 files changed, 8 insertions, 8 deletions
diff --git a/src/algebra/ffpoly.spad.pamphlet b/src/algebra/ffpoly.spad.pamphlet index db79d30e..c4f0c586 100644 --- a/src/algebra/ffpoly.spad.pamphlet +++ b/src/algebra/ffpoly.spad.pamphlet @@ -345,7 +345,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where -- determine the multiplicative order of q modulo d e : PI := 1 qe : PI := q - while (qe rem d) ~= 1 repeat + while not one?(qe rem d) repeat e := e + 1 qe := qe * q prod := prod * _ @@ -361,7 +361,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where -- (cf. [LN] p.89, Th. 3.16, and p.87, following Th. 3.11) n : NNI := degree f n = 0 => false - leadingCoefficient f ~= 1 => false + not one? leadingCoefficient f => false coefficient(f, 0) = 0 => false q : PI := sizeGF qn1: PI := (q**n - 1) :: NNI :: PI @@ -371,7 +371,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where -- may be improved by tabulating the residues x**(i*q) -- for i = 0,...,n-1 : -- - lift(x ** qn1)$MM ~= 1 => false -- X**(q**n - 1) rem f in GF[X] + not one? lift(x ** qn1)$MM => false -- X**(q**n - 1) rem f in GF[X] lrec : L Record(factor:I, exponent:I) := factors(factor qn1) lfact : L PI := [] -- collect the prime factors for rec in lrec repeat -- of q**n - 1 @@ -387,7 +387,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where -- x, x**q, ... , x**(q**(n-1)) are linearly independent over GF n : NNI := degree f n = 0 => false - leadingCoefficient f ~= 1 => false + not one? leadingCoefficient f => false coefficient(f, 0) = 0 => false n = 1 => true not irreducible? f => false @@ -428,7 +428,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where n : NNI := degree f n = 0 => error "polynomial must have positive degree" -- make f monic - if (lcf := leadingCoefficient f) ~= 1 then f := (inv lcf) * f + if not one?(lcf := leadingCoefficient f) then f := (inv lcf) * f -- if f = fn*X**n + ... + f{i0}*X**{i0} with the fi non-zero -- then fRepr := [[n,fn], ... , [i0,f{i0}]] fRepr : Repr := f pretend Repr @@ -506,7 +506,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where n : NNI := degree f n = 0 => error "polynomial must have positive degree" -- make f monic - if (lcf := leadingCoefficient f) ~= 1 then f := (inv lcf) * f + if not one?(lcf := leadingCoefficient f) then f := (inv lcf) * f -- if f = fn*X**n + ... + f{i0}*X**{i0} with the fi non-zero -- then fRepr := [[n,fn], ... , [i0,f{i0}]] fRepr : Repr := f pretend Repr @@ -626,7 +626,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where n : NNI := degree f n = 0 => error "polynomial must have positive degree" -- make f monic - if (lcf := leadingCoefficient f) ~= 1 then f := (inv lcf) * f + if not one?(lcf := leadingCoefficient f) then f := (inv lcf) * f -- if f = fn*X**n + ... + f{i0}*X**{i0} with the fi non-zero -- then fRepr := [[n,fn], ... , [i0,f{i0}]] fRepr : Repr := f pretend Repr @@ -740,7 +740,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where n : NNI := degree f n = 0 => error "polynomial must have positive degree" -- make f monic - if (lcf := leadingCoefficient f) ~= 1 then f := (inv lcf) * f + if not one?(lcf := leadingCoefficient f) then f := (inv lcf) * f -- if f = fn*X**n + ... + f{i0}*X**{i0} with the fi non-zero -- then fRepr := [[n,fn], ... , [i0,f{i0}]] fRepr : Repr := f pretend Repr |