diff options
Diffstat (limited to 'src/algebra/mring.spad.pamphlet')
| -rw-r--r-- | src/algebra/mring.spad.pamphlet | 18 |
1 files changed, 9 insertions, 9 deletions
diff --git a/src/algebra/mring.spad.pamphlet b/src/algebra/mring.spad.pamphlet index 04c50f32..3d2ca1c7 100644 --- a/src/algebra/mring.spad.pamphlet +++ b/src/algebra/mring.spad.pamphlet @@ -109,7 +109,7 @@ MonoidRing(R: Ring, M: Monoid): MRcategory == MRdefinition where for j in 0.. while i > 0 repeat h := i rem p -- we use index(p) = 0$R - if h ^= 0 then + if h ~= 0 then c : R := index(h :: PositiveInteger)$R m : M := index((j+n) :: PositiveInteger)$M --ans := ans + c *$% m @@ -161,7 +161,7 @@ MonoidRing(R: Ring, M: Monoid): MRcategory == MRdefinition where else (r:R) * (a:%) == r = 0 => 0 - [[rt, t.Mn] for t in a | (rt:=r*t.Cf) ^= 0] + [[rt, t.Mn] for t in a | (rt:=r*t.Cf) ~= 0] if R has noZeroDivisors then (n:Integer) * (a:%) == @@ -170,8 +170,8 @@ MonoidRing(R: Ring, M: Monoid): MRcategory == MRdefinition where else (n:Integer) * (a:%) == n = 0 => 0 - [[nt, t.Mn] for t in a | (nt:=n*t.Cf) ^= 0] - map(f, a) == [[ft, t.Mn] for t in a | (ft:=f(t.Cf)) ^= 0] + [[nt, t.Mn] for t in a | (nt:=n*t.Cf) ~= 0] + map(f, a) == [[ft, t.Mn] for t in a | (ft:=f(t.Cf)) ~= 0] numberOfMonomials a == #a retractIfCan(a:%):Union(M, "failed") == @@ -188,13 +188,13 @@ MonoidRing(R: Ring, M: Monoid): MRcategory == MRdefinition where if M has Group then recip a == lt := terms a - #lt ^= 1 => "failed" + #lt ~= 1 => "failed" (u := recip lt.first.Cf) case "failed" => "failed" --(u::R) * inv lt.first.Mn monomial((u::R), inv lt.first.Mn)$% else recip a == - #a ^= 1 or a.first.Mn ^= 1 => "failed" + #a ~= 1 or a.first.Mn ~= 1 => "failed" (u := recip a.first.Cf) case "failed" => "failed" u::R::% @@ -215,9 +215,9 @@ MonoidRing(R: Ring, M: Monoid): MRcategory == MRdefinition where reductum a == (empty? a => a; rest a) a = b == - #a ^= #b => false + #a ~= #b => false for ta in a for tb in b repeat - ta.Cf ^= tb.Cf or ta.Mn ^= tb.Mn => return false + ta.Cf ~= tb.Cf or ta.Mn ~= tb.Mn => return false true a + b == @@ -298,7 +298,7 @@ MonoidRing(R: Ring, M: Monoid): MRcategory == MRdefinition where else -- M hasn't OrderedSet -- Terms are stored in random order. a = b == - #a ^= #b => false + #a ~= #b => false brace(a pretend List(Term)) =$Set(Term) brace(b pretend List(Term)) coefficient(a, m) == |