diff options
Diffstat (limited to 'src/algebra/numtheor.spad.pamphlet')
| -rw-r--r-- | src/algebra/numtheor.spad.pamphlet | 8 |
1 files changed, 4 insertions, 4 deletions
diff --git a/src/algebra/numtheor.spad.pamphlet b/src/algebra/numtheor.spad.pamphlet index b5cf7404..6df112a7 100644 --- a/src/algebra/numtheor.spad.pamphlet +++ b/src/algebra/numtheor.spad.pamphlet @@ -126,12 +126,12 @@ Using the half extended Euclidean algorithm we compute 1/a mod b. borg:I:=b c1:I := 1 d1:I := 0 - while b ^= 0 repeat + while b ~= 0 repeat q:I := a quo b r:I := a-q*b (a,b):=(b,r) (c1,d1):=(d1,c1-q*d1) - a ^= 1 => error("moduli are not relatively prime") + a ~= 1 => error("moduli are not relatively prime") positiveRemainder(c1,borg) @ @@ -287,7 +287,7 @@ IntegerNumberTheoryFunctions(): Exports == Implementation where jacobi : (I,I) -> I ++ \spad{jacobi(a,b)} returns the Jacobi symbol \spad{J(a/b)}. ++ When b is odd, \spad{J(a/b) = product(L(a/p) for p in factor b )}. - ++ Note: by convention, 0 is returned if \spad{gcd(a,b) ^= 1}. + ++ Note: by convention, 0 is returned if \spad{gcd(a,b) ~= 1}. ++ Iterative \spad{O(log(b)^2)} version coded by Michael Monagan June 1987. legendre : (I,I) -> I ++ \spad{legendre(a,p)} returns the Legendre symbol \spad{L(a/p)}. @@ -560,7 +560,7 @@ PolynomialNumberTheoryFunctions(): Exports == Implementation where MonicQuotient: (SUP(I),SUP(I)) -> SUP(I) MonicQuotient (a,b) == - leadingCoefficient(b) ^= 1 => error "divisor must be monic" + leadingCoefficient(b) ~= 1 => error "divisor must be monic" b = 1 => a da := degree a db := degree b -- assertion: degree b > 0 |