Triangular numbers: Difference between revisions

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@@ Line 1,170: / Line 1,170: @@
 =={{header|Raku}}==
-<syntaxhighlight lang="raku" line>use Math::Root;
+<syntaxhighlight lang="raku" line>use Math::Root:ver<0.0.4>;
-my \ε = FatRat.new: 1, 10**24;
 sub binomial { [×] ($^n … 0) Z/ 1 .. $^p }
 sub polytopic (Int $r, @range) { @range.map: { binomial $_ + $r - 1, $r } }
-sub triangular-root ($x) { round ((8 × $x + 1).&root - 1) / 2, ε }
-sub tetrahedral-root ($x) {
-    ((3 × $x + (9 × $x² - 1/27).&root).&root(3) +
-     (3 × $x - (9 × $x² - 1/27).&root).&root(3) - 1).round: ε
-}
-sub pentatopic-root ($x) { round ((5 + 4 × (24 × $x + 1).&root).&root - 3) / 2, ε }
 sub display (@values) {
@@ Line 1,196: / Line 1,185: @@
 say '';
+my \ε = FatRat.new: 1, 10**24;
 for 7140, 21408696, 26728085384, 14545501785001 {
   say qq:to/R/;
   Roots of $_:
-    triangular-root: {.&triangular-root}
+    triangular-root: {.&triangular-root.round:  ε}
-   tetrahedral-root: {.&tetrahedral-root}
+   tetrahedral-root: {.&tetrahedral-root.round: ε}
-    pentatopic-root: {.&pentatopic-root}
+    pentatopic-root: {.&pentatopic-root.round:  ε}
   R
 }</syntaxhighlight>