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Fungrim entry: d9a187

χ(n)=χq. ⁣(n)   where χ=χq.\chi(n) = \chi_{q \, . \, \ell}\!\left(n\right)\; \text{ where } \chi = \chi_{q \, . \, \ell}
This is simply a syntactical definition of character evaluation.
Assumptions:qZ1  and  {1,2,,max ⁣(q,2)1}  and  gcd ⁣(,q)=1  and  nZq \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; \ell \in \{1, 2, \ldots, \max\!\left(q, 2\right) - 1\} \;\mathbin{\operatorname{and}}\; \gcd\!\left(\ell, q\right) = 1 \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}
\chi(n) = \chi_{q \, . \, \ell}\!\left(n\right)\; \text{ where } \chi = \chi_{q \, . \, \ell}

q \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; \ell \in \{1, 2, \ldots, \max\!\left(q, 2\right) - 1\} \;\mathbin{\operatorname{and}}\; \gcd\!\left(\ell, q\right) = 1 \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}
Fungrim symbol Notation Short description
DirichletCharacterχq.\chi_{q \, . \, \ell} Dirichlet character
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Range{a,a+1,,b}\{a, a + 1, \ldots, b\} Integers between given endpoints
GCDgcd ⁣(a,b)\gcd\!\left(a, b\right) Greatest common divisor
ZZZ\mathbb{Z} Integers
Source code for this entry:
    Formula(Where(Equal(chi(n), DirichletCharacter(q, ell, n)), Equal(chi, DirichletCharacter(q, ell)))),
    Description("This is simply a syntactical definition of character evaluation."),
    Variables(q, ell, n),
    Assumptions(And(Element(q, ZZGreaterEqual(1)), Element(ell, Range(1, Sub(Max(q, 2), 1))), Equal(GCD(ell, q), 1), Element(n, ZZ))))

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2021-03-15 19:12:00.328586 UTC