Go over new builtins up to PolyLog

mathics/builtin/atomic/numbers.py

@@ -301,26 +301,37 @@ class NumberDigit(Builtin):
     https://reference.wolfram.com/language/ref/NumberDigit.html</url>
 
     <dl>
+      <dt>'NumberDigit[$x$, $n$]'
+      <dd>returns the digit coefficient of 10^$n$ for the real-valued number $x$.
+
       <dt>'NumberDigit[$x$, $n$, $b$]'
-      <dd>returns the coefficient of $b^n$ in the base-$b$ representation of $x$.
+      <dd>returns the coefficient of $b$^$n$ in the base-$b$ representation of $x$.
     </dl>
 
-    >> NumberDigit[123456, 2]
-     = 4
-    >> NumberDigit[12.3456, -1]
+    Get the 10^2 digit of a 210.345:
+    >> NumberDigit[210.345, 2]
+     = 2
+
+    Get the 10^-1 digit of a 210.345:
+    >> NumberDigit[210.345, -1]
      = 3
 
+    >> BaseForm[N[Pi], 2]
+     = 11.00100100001111110_2
+
+    Get the 2^0 bit of the Pi:
+     = 1
     """
 
     attributes = A_PROTECTED | A_READ_PROTECTED
 
-    summary_text = "digits of a real number"
-
     rules = {
         "NumberDigit[x_, n_Integer]": "NumberDigit[x, n, 10]",
         "NumberDigit[x_, n_Integer, b_Integer]": "RealDigits[x, b, 1, n][[1]][[1]]",
     }
 
+    summary_text = "get digits of a real number"
+
 
 class RealDigits(Builtin):
     """
@@ -776,7 +787,7 @@ class Precision(Builtin):
 
     summary_text = "find the precision of a number"
 
-    def eval(self, z, evaluation):
+    def eval(self, z, evaluation: Evaluation):
         """Precision[z_]"""
         if isinstance(z, MachineReal):
             return SymbolMachinePrecision

mathics/builtin/intfns/combinatorial.py

@@ -387,23 +387,39 @@ class PolygonalNumber(Builtin):
     :Polygonal number: https://en.wikipedia.org/wiki/Polygonal_number</url> (<url>
     :WMA: https://reference.wolfram.com/language/ref/PolygonalNumber.html</url>)
     <dl>
+      <dt>'PolygonalNumber[$n$]'
+      <dd>gives the $n$th triangular number.
+
       <dt>'PolygonalNumber[$r$, $n$]'
       <dd>gives the $n$th $r$-gonal number.
     </dl>
 
     >> Table[PolygonalNumber[n], {n, 10}]
      = {1, 3, 6, 10, 15, 21, 28, 36, 45, 55}
-    >> Table[PolygonalNumber[r, 10], {r, 3, 10}]
-     = {55, 100, 145, 190, 235, 280, 325, 370}
+
+    The sum of two consecutive Polygonal numbers is the square of the larger number:
+    >> Table[PolygonalNumber[n-1] + PolygonalNumber[n], {n, 10}]
+     = {1, 4, 9, 16, 25, 36, 49, 64, 81, 100}
+
+    'PolygonalNumber'[$r$, $n$] can be interpreted as the number of points arranged in the form of $n$-1 polygons of $r$ sides.
+
+    List the tenth $r-gonal number of regular polygons from 3 to 8:
+    >> Table[PolygonalNumber[r, 10], {r, 3, 8}]
+     = {55, 100, 145, 190, 235, 280}
+
+    See also <url>
+    :Binomial:
+    doc/reference-of-built-in-symbols/integer-functions/combinatorial-functions/binomial/</url>, and <url>
+    :RegularPolygon:
+    doc/reference-of-built-in-symbols/drawing-graphics/regularpolygon/</url>.
     """
 
     attributes = A_LISTABLE | A_NUMERIC_FUNCTION | A_PROTECTED | A_READ_PROTECTED
-    summary_text = "polygonal number"
-
     rules = {
         "PolygonalNumber[n_Integer]": "PolygonalNumber[3, n]",
         "PolygonalNumber[r_Integer, n_Integer]": "(1/2) n (n (r - 2) - r + 4)",
     }
+    summary_text = "get polygonal number"
 
 
 class RogersTanimotoDissimilarity(_BooleanDissimilarity):