NumberTheory
KroneckerSymbol
generalized Jacobi symbol
JacobiSymbol
generalized Legendre symbol
LegendreSymbol
quadratic residuosity
Calling Sequence
Parameters
Description
Examples
Compatibility
KroneckerSymbol(a, n)
JacobiSymbol(a, m)
LegendreSymbol(a, m)
a
-
integer
n
m
positive odd integer
The KroneckerSymbol(a, n) command computes the Kronecker symbol of a and n.
The alternative calling sequences, JacobiSymbol(a, m) and LegendreSymbol(a, m), have return values equal to KroneckerSymbol(a, m), but m must be a positive odd integer.
The Legendre symbol is typically defined only for second arguments that are prime, but due to primality checking being expensive, here LegendreSymbol is an alias of JacobiSymbol.
If n is equal to where is or and the are distinct primes, then the Kronecker symbol is given by , where is the usual Legendre symbol, except for the following cases.
is equal to if is equal to or . Otherwise it is equal to .
is equal to if is less than . Otherwise it is equal to .
is always equal to .
is equal to if is odd. Otherwise it is equal to .
is congruent to modulo .
is a quadratic residue modulo .
is a quadratic non-residue modulo .
is congruent to modulo and is a quadratic non-residue modulo .
The NumberTheory[KroneckerSymbol], NumberTheory[JacobiSymbol] and NumberTheory[LegendreSymbol] commands were introduced in Maple 2016.
For more information on Maple 2016 changes, see Updates in Maple 2016.
See Also
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