Faulhaber's formula: Difference between revisions

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@@ Line 2,824: / Line 2,824: @@
 =={{header|Sidef}}==
-<syntaxhighlight lang="ruby">const AnyNum = require('Math::AnyNum')
+<syntaxhighlight lang="ruby">func faulhaber_formula(p) {
-const Poly   = require('Math::Polynomial')
-Poly.string_config(Hash(
-    fold_sign => true, prefix => "",
-    suffix => "", variable => "n"
-))
-func anynum(n) {
-    AnyNum.new(n.as_rat)
-}
-func faulhaber_formula(p) {
     (p+1).of { |j|
-        Poly.monomial(p - j + 1)\
+        Poly(p - j + 1 => 1) * bernoulli(j) * binomial(p+1, j)
+    }.sum / (p+1)
-            .mul_const(anynum(bernoulli(j)))\
-            .mul_const(anynum(binomial(p+1, j)))
-    }.reduce(:add).div_const(p+1)
 }
@@ Line 2,849: / Line 2,835: @@
 {{out}}
 <pre>
-: n
+: x
-: 1/2 n^2 + 1/2 n
+: 1/2*x^2 + 1/2*x
-: 1/3 n^3 + 1/2 n^2 + 1/6 n
+: 1/3*x^3 + 1/2*x^2 + 1/6*x
-: 1/4 n^4 + 1/2 n^3 + 1/4 n^2
+: 1/4*x^4 + 1/2*x^3 + 1/4*x^2
-: 1/5 n^5 + 1/2 n^4 + 1/3 n^3 - 1/30 n
+: 1/5*x^5 + 1/2*x^4 + 1/3*x^3 - 1/30*x
-: 1/6 n^6 + 1/2 n^5 + 5/12 n^4 - 1/12 n^2
+: 1/6*x^6 + 1/2*x^5 + 5/12*x^4 - 1/12*x^2
-: 1/7 n^7 + 1/2 n^6 + 1/2 n^5 - 1/6 n^3 + 1/42 n
+: 1/7*x^7 + 1/2*x^6 + 1/2*x^5 - 1/6*x^3 + 1/42*x
-: 1/8 n^8 + 1/2 n^7 + 7/12 n^6 - 7/24 n^4 + 1/12 n^2
+: 1/8*x^8 + 1/2*x^7 + 7/12*x^6 - 7/24*x^4 + 1/12*x^2
-: 1/9 n^9 + 1/2 n^8 + 2/3 n^7 - 7/15 n^5 + 2/9 n^3 - 1/30 n
+: 1/9*x^9 + 1/2*x^8 + 2/3*x^7 - 7/15*x^5 + 2/9*x^3 - 1/30*x
-: 1/10 n^10 + 1/2 n^9 + 3/4 n^8 - 7/10 n^6 + 1/2 n^4 - 3/20 n^2
+: 1/10*x^10 + 1/2*x^9 + 3/4*x^8 - 7/10*x^6 + 1/2*x^4 - 3/20*x^2
 </pre>