Start to correct the binomials. (#914)

* Start to correct the binomials. * remove the dodgy tests
oscar-system · Dec 20, 2021 · 5db4abf · 5db4abf
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diff --git a/docs/src/Rings/integer.md b/docs/src/Rings/integer.md
@@ -551,8 +551,8 @@ bell(ZZ(20))
 
 * `binomial(n::fmpz, k::fmpz) -> fmpz`
 
-Returns the binomial coefficient ``\frac{n!}{k!(n - k)!}``. If ``n, k < 0`` or
-``k > n`` we return zero.
+Returns the binomial coefficient ``\frac{n (n-1) \cdots (n-k+1)}{k!}`` for
+``k \ge 0`` and returns `0` for `k < 0`.
 
 !!! note
     Julia already defines the `binomial` function for `Int`, which throws an

diff --git a/test/Rings/integer-test.jl b/test/Rings/integer-test.jl
@@ -621,8 +621,6 @@ end
    @test binomial(ZZ(1), ZZ(0)) == 1
    @test binomial(ZZ(1), ZZ(1)) == 1
 
-   @test binomial(ZZ(-3), ZZ(2)) == 0
-   @test binomial(ZZ(-3), ZZ(0)) == 0
    @test binomial(ZZ(2), ZZ(-3)) == 0
    @test binomial(ZZ(0), ZZ(-3)) == 0
    @test binomial(ZZ(-1), ZZ(-1)) == 0