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-rw-r--r--src/algebra/ffpoly.spad.pamphlet34
1 files changed, 17 insertions, 17 deletions
diff --git a/src/algebra/ffpoly.spad.pamphlet b/src/algebra/ffpoly.spad.pamphlet
index eba95386..acebb710 100644
--- a/src/algebra/ffpoly.spad.pamphlet
+++ b/src/algebra/ffpoly.spad.pamphlet
@@ -240,7 +240,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where
qexp.1:=h
for i in 2..m1 repeat
g:=0$SUP
- while h ^= 0 repeat
+ while h ~= 0 repeat
g:=g + leadingCoefficient(h) * qpow.degree(h)
h:=reductum(h)
qexp.i:=(h:=g)
@@ -282,7 +282,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where
-- -- determine the multiplicative order of q modulo n
-- e : PI := 1
-- qe : PI := q
--- while (qe rem n) ^= 1 repeat
+-- while (qe rem n) ~= 1 repeat
-- e := e + 1
-- qe := qe * q
-- ((qe - 1) ** ((eulerPhi(n) quo e) pretend PI) ) pretend PI
@@ -345,7 +345,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where
-- determine the multiplicative order of q modulo d
e : PI := 1
qe : PI := q
- while (qe rem d) ^= 1 repeat
+ while (qe rem d) ~= 1 repeat
e := e + 1
qe := qe * q
prod := prod * _
@@ -361,7 +361,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where
-- (cf. [LN] p.89, Th. 3.16, and p.87, following Th. 3.11)
n : NNI := degree f
n = 0 => false
- leadingCoefficient f ^= 1 => false
+ leadingCoefficient f ~= 1 => false
coefficient(f, 0) = 0 => false
q : PI := sizeGF
qn1: PI := (q**n - 1) :: NNI :: PI
@@ -371,7 +371,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where
-- may be improved by tabulating the residues x**(i*q)
-- for i = 0,...,n-1 :
--
- lift(x ** qn1)$MM ^= 1 => false -- X**(q**n - 1) rem f in GF[X]
+ lift(x ** qn1)$MM ~= 1 => false -- X**(q**n - 1) rem f in GF[X]
lrec : L Record(factor:I, exponent:I) := factors(factor qn1)
lfact : L PI := [] -- collect the prime factors
for rec in lrec repeat -- of q**n - 1
@@ -387,7 +387,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where
-- x, x**q, ... , x**(q**(n-1)) are linearly independent over GF
n : NNI := degree f
n = 0 => false
- leadingCoefficient f ^= 1 => false
+ leadingCoefficient f ~= 1 => false
coefficient(f, 0) = 0 => false
n = 1 => true
not irreducible? f => false
@@ -428,7 +428,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where
n : NNI := degree f
n = 0 => error "polynomial must have positive degree"
-- make f monic
- if (lcf := leadingCoefficient f) ^= 1 then f := (inv lcf) * f
+ if (lcf := leadingCoefficient f) ~= 1 then f := (inv lcf) * f
-- if f = fn*X**n + ... + f{i0}*X**{i0} with the fi non-zero
-- then fRepr := [[n,fn], ... , [i0,f{i0}]]
fRepr : Repr := f pretend Repr
@@ -438,7 +438,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where
-- a new value to one of its records
for term in fRepr repeat
fcopy := cons(copy term, fcopy)
- if term.expnt ^= 0 then
+ if term.expnt ~= 0 then
fcopy := cons([0,0]$Rec, fcopy)
tailpol : Repr := []
headpol : Repr := fcopy -- [[0,f0], ... , [n,fn]] where
@@ -505,7 +505,7 @@ 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 (lcf := leadingCoefficient f) ~= 1 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
@@ -515,7 +515,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where
-- a new value to one of its records
for term in fRepr repeat
fcopy := cons(copy term, fcopy)
- if term.expnt ^= 0 then
+ if term.expnt ~= 0 then
term := [0,0]$Rec
fcopy := cons(term, fcopy)
fcopy := reverse fcopy
@@ -624,7 +624,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where
n : NNI := degree f
n = 0 => error "polynomial must have positive degree"
-- make f monic
- if (lcf := leadingCoefficient f) ^= 1 then f := (inv lcf) * f
+ if (lcf := leadingCoefficient f) ~= 1 then f := (inv lcf) * f
-- if f = fn*X**n + ... + f{i0}*X**{i0} with the fi non-zero
-- then fRepr := [[n,fn], ... , [i0,f{i0}]]
fRepr : Repr := f pretend Repr
@@ -634,7 +634,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where
-- a new value to one of its records
for term in fRepr repeat
fcopy := cons(copy term, fcopy)
- if term.expnt ^= 0 then
+ if term.expnt ~= 0 then
term := [0,0]$Rec
fcopy := cons(term, fcopy)
fcopy := reverse fcopy -- [[n,1], [r,fr], ... , [0,f0]]
@@ -737,7 +737,7 @@ 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 (lcf := leadingCoefficient f) ~= 1 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
@@ -747,7 +747,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where
-- a new value to one of its records
for term in fRepr repeat
fcopy := cons(copy term, fcopy)
- if term.expnt ^= 0 then
+ if term.expnt ~= 0 then
term := [0,0]$Rec
fcopy := cons(term, fcopy)
fcopy := reverse fcopy -- [[n,1], [r,fr], ... , [0,f0]]
@@ -958,7 +958,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where
-- expt : NNI := #ragits
-- for i in ragits repeat
-- expt := (expt - 1) :: NNI
--- if i ^= 0 then pol := pol + monomial(index(i::PI)$GF, expt)
+-- if i ~= 0 then pol := pol + monomial(index(i::PI)$GF, expt)
-- pol
-- random == qAdicExpansion(random()$I)
@@ -967,7 +967,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where
-- pol := monomial(1,n)$SUP
-- n1 : NNI := (n - 1) :: NNI
-- for i in 0..n1 repeat
--- if (c := random()$GF) ^= 0 then
+-- if (c := random()$GF) ~= 0 then
-- pol := pol + monomial(c, i)$SUP
-- pol
@@ -975,7 +975,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where
polRepr : Repr := []
n1 : NNI := (n - 1) :: NNI
for i in 0..n1 repeat
- if (c := random()$GF) ^= 0 then
+ if (c := random()$GF) ~= 0 then
polRepr := cons([i, c]$Rec, polRepr)
cons([n, 1$GF]$Rec, polRepr) pretend SUP
generated by cgit v1.2.3 (git 2.39.1) at 2024-07-01 15:59:46 +0000