diff options
Diffstat (limited to 'src/algebra/lodop.spad.pamphlet')
| -rw-r--r-- | src/algebra/lodop.spad.pamphlet | 8 |
1 files changed, 4 insertions, 4 deletions
diff --git a/src/algebra/lodop.spad.pamphlet b/src/algebra/lodop.spad.pamphlet index f1e5eebb..680ed017 100644 --- a/src/algebra/lodop.spad.pamphlet +++ b/src/algebra/lodop.spad.pamphlet @@ -34,7 +34,7 @@ ++ ++ Note that multiplication is not necessarily commutative. ++ In fact, if \spad{a} is in \spad{R}, it is quite normal -++ to have \spad{a*G \^= G*a}. +++ to have \spad{a*G \~= G*a}. MonogenicLinearOperator(R): Category == Defn where E ==> NonNegativeInteger @@ -46,7 +46,7 @@ MonogenicLinearOperator(R): Category == Defn where ++ \spad{l = sum(monomial(a(i),i), i = 0..n)}. minimumDegree: $ -> E ++ minimumDegree(l) is the smallest \spad{k} such that - ++ \spad{a(k) \^= 0} if + ++ \spad{a(k) \~= 0} if ++ \spad{l = sum(monomial(a(i),i), i = 0..n)}. leadingCoefficient: $ -> R ++ leadingCoefficient(l) is \spad{a(n)} if @@ -163,7 +163,7 @@ NonCommutativeOperatorDivision(P, F): PDcat == PDdef where q: P := 0 r: P := a iv:F := inv leadingCoefficient b - while degree r >= degree b and r ^= 0 repeat + while degree r >= degree b and r ~= 0 repeat h := monomial(iv*leadingCoefficient r, (degree r - degree b)::NonNegativeInteger)$P r := r - b*h @@ -189,7 +189,7 @@ NonCommutativeOperatorDivision(P, F): PDcat == PDdef where b0 := b u := monomial(1,0)$P v := 0 - while leadingCoefficient b ^= 0 repeat + while leadingCoefficient b ~= 0 repeat qr := leftDivide(a,b) (a, b) := (b, qr.remainder) (u, v) := (u*qr.quotient+v, u) |