Add 2 new routines to Maths category

Added IsPalindromic & IsNarcissistic function to Mathematics category

Added new source code .dat file for the functions.

Updated maths.ini with meta data for both functions.

Author: delphidabbler

collection/660.dat

@@ -0,0 +1,13 @@
+function IsPalindromic(const N: Int64; const Base: Byte = 10): Boolean;
+var
+  Digits: SysUtils.TBytes;
+  Idx: Integer;
+  PartitionSize: Integer;
+begin
+  Digits := DigitsOf(N, Base); // raises exception for Base < 2
+  Result := True;
+  PartitionSize := Length(Digits) div 2;
+  for Idx := 0 to Pred(PartitionSize) do
+    if Digits[Idx] <> Digits[Length(Digits) - Idx - 1] then
+      Exit(False);
+end;

collection/662.dat

@@ -0,0 +1,8 @@
+function IsNarcissistic(N: Integer; const Base: Byte = 10): Boolean;
+var
+  Sum: Int64;
+begin
+  N := Abs(N);
+  Sum := DigitPowerSum(N, Base, DigitCountBase(N, Base));
+  Result := N = Sum;
+end;

collection/maths.ini

@@ -1812,3 +1812,32 @@ AdvancedTest.URL="https://github.com/delphidabbler/code-snippets/tree/master/tes
 Snip=661.dat
 DelphiXE=Y
 Delphi12A=Y
+
+[IsPalindromic]
+DisplayName="IsPalindromic"
+DescEx="<p>Checks if the absolute value of integer <var>N</var> is palindromic in base <var>Base</var>.</p><p>Bases up to 255 are supported. If <var>Base</var> &lt; 2 then an <var>EArgumentException</var> exception is raised.</p>"
+Extra="<p>A number expressed in a specified base is palindromic if it remains unchanged when its digits are reversed. See <a href="https://en.m.wikipedia.org/wiki/Palindromic_number">Wikipedia</a> for a formal definition and examples.</p><p>Strictly speaking a palindromic number should be non-negative. However, <var>IsPalindromic</var> considers negative numbers to be palindromic if and only if their absolute value is palindromic.</p>"
+Kind=routine
+Units=SysUtils
+Depends=DigitsOf
+SeeAlso=IsNarcissistic
+TestInfo=advanced
+AdvancedTest.Level=unit-tests
+AdvancedTest.URL="https://github.com/delphidabbler/code-snippets/tree/master/tests/Cat-Maths"
+Snip=660.dat
+DelphiXE=Y
+Delphi12A=Y
+
+[IsNarcissistic]
+DisplayName=IsNarcissistic
+DescEx="<p>Checks if the absolute value of integer <var>N</var> is a narcissistic number in base <var>Base</var>.</p><p>Bases up to 255 are supported. If <var>Base</var> &lt;= 2 then an <var>EArgumentException</var> exception is raised. An <var>EOverflow</var> exception may be raised for large numbers and bases.</p>"
+Extra="<p>A narcissistic number in a given number base is a number that is the sum of its own digits each raised to the power of the number of digits. See <a href="https://en.wikipedia.org/wiki/Narcissistic_number">Wikipedia</a> for a formal definition and examples.</p><p>Strictly speaking a palindromic number should be non-negative. However, <var>IsNarcissistic</var> considers negative numbers to be narcissistic if and only if their absolute value is narcissistic.</p>"
+Kind=routine
+Depends=DigitCountBase,DigitPowerSum
+SeeAlso=IsPalindromic
+TestInfo=advanced
+AdvancedTest.Level=unit-tests
+AdvancedTest.URL="https://github.com/delphidabbler/code-snippets/tree/master/tests/Cat-Maths"
+Snip=662.dat
+DelphiXE=Y
+Delphi12A=Y