prime(n) is the n-th prime, and valuation(n, p) the p-adic valuation

BREAKING-CHANGES.md

@@ -867,6 +867,8 @@ prime, `17` ([#1450](https://github.com/asc-community/AngouriMath/issues/1450)).
 | `"PP intersect [1; 30]".ToEntity().Evaled` | as written | `{ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 }` |
 | `"min(ZZ+)".ToEntity().Evaled` | `ZZ+` | `1` |
 | `"max(x, x in PP and x < 14)".ToEntity().Evaled` | as written | `13` |
+| `"prime(25)".ToEntity().Evaled` | `prime * 25` — juxtaposition of a variable `prime` | `97`; `prime(n)` is the `n`-th prime, `NaN` off the positive whole numbers |
+| `"valuation(12, 2)".ToEntity().Evaled` | `UnrecognizedFunctionParseException` | `2`; `valuation(n, p)` is the `p`-adic valuation, `+oo` at `0` and `NaN` off the primes |
 
 ### `binomial(n, k)` is a function
 

Sources/AngouriMath/Convenience/MathS.cs

@@ -50,6 +50,40 @@ public static class NumberTheory
             /// </example>
             public static Entity Phi(Entity integer) => new Phif(integer);
 
+            /// <summary>
+            /// The <c>n</c>-th prime, <c>prime(n)</c>: <c>prime(1)</c> is <c>2</c> and
+            /// <c>prime(25)</c> is <c>97</c>. Defined on the positive whole numbers, and a
+            /// function rather than an operation on the set <c>PP</c>, which carries no order.
+            /// https://github.com/asc-community/AngouriMath/issues/1450
+            /// </summary>
+            /// <example>
+            /// <code>
+            /// Console.WriteLine(MathS.NumberTheory.Prime(25).Evaled);
+            /// </code>
+            /// Prints
+            /// <code>
+            /// 97
+            /// </code>
+            /// </example>
+            public static Entity Prime(Entity index) => new Primef(index);
+
+            /// <summary>
+            /// The <c>p</c>-adic valuation of a whole number, <c>valuation(n, p)</c>: the exponent
+            /// of the prime <c>p</c> in <c>n</c>. <c>valuation(12, 2)</c> is <c>2</c>,
+            /// <c>valuation(12, 5)</c> is <c>0</c>, and at <c>n = 0</c> it is <c>+oo</c>.
+            /// https://github.com/asc-community/AngouriMath/issues/1450
+            /// </summary>
+            /// <example>
+            /// <code>
+            /// Console.WriteLine(MathS.NumberTheory.Valuation(12, 2).Evaled);
+            /// </code>
+            /// Prints
+            /// <code>
+            /// 2
+            /// </code>
+            /// </example>
+            public static Entity Valuation(Entity argument, Entity prime) => new Valuationf(argument, prime);
+
             /// <summary>
             /// The statement that <paramref name="divisor"/> divides <paramref name="dividend"/>,
             /// written <c>a divides b</c>: for integers, that <c>b mod a = 0</c>.

Sources/AngouriMath/Core/Antlr/AngouriMath.g

@@ -570,6 +570,8 @@ atom returns[Entity value]
     | 'sign(' args = function_arguments ')' { Assert("sign", 1, $args.list.Count); $value = MathS.Signum($args.list[0]); }
     | 'abs(' args = function_arguments ')' { Assert("abs", 1, $args.list.Count); $value = MathS.Abs($args.list[0]); }
     | 'phi(' args = function_arguments ')' { Assert("phi", 1, $args.list.Count); $value = MathS.NumberTheory.Phi($args.list[0]); }
+    | 'prime(' args = function_arguments ')' { Assert("prime", 1, $args.list.Count); $value = MathS.NumberTheory.Prime($args.list[0]); }
+    | 'valuation(' args = function_arguments ')' { Assert("valuation", 2, $args.list.Count); $value = MathS.NumberTheory.Valuation($args.list[0], $args.list[1]); }
     | 'card(' args = function_arguments ')' { Assert("card", 1, $args.list.Count); $value = MathS.Sets.Card($args.list[0]); }
     | 'powerset(' args = function_arguments ')' { Assert("powerset", 1, $args.list.Count); $value = MathS.Sets.PowerSet($args.list[0]); }
     | 'union(' args = function_arguments ')' { Assert("union", 2, $args.list.Count); $value = $args.list[1] is Entity.Set.Inf { Element: Variable } unionRange ? MathS.Sets.IndexedUnion($args.list[0], unionRange.Element, unionRange.SupSet) : throw new InvalidArgumentParseException("union expects its second argument to say which name ranges over which set, as in union(A_i, i in I)"); }

Sources/AngouriMath/Core/Antlr/AngouriMath.tokens

@@ -169,14 +169,16 @@ T__167=168
 T__168=169
 T__169=170
 T__170=171
-NEWLINE=172
-NUMBER=173
-SPECIALSET=174
-BOOLEAN=175
-NAN=176
-VARIABLE=177
-COMMENT=178
-WS=179
+T__171=172
+T__172=173
+NEWLINE=174
+NUMBER=175
+SPECIALSET=176
+BOOLEAN=177
+NAN=178
+VARIABLE=179
+COMMENT=180
+WS=181
 '!'=1
 '^'=2
 '-'=3
@@ -323,29 +325,31 @@ WS=179
 'sign('=144
 'abs('=145
 'phi('=146
-'card('=147
-'powerset('=148
-'union('=149
-'intersection('=150
-'complement('=151
-'image('=152
-'preimage('=153
-'floor('=154
-'ceil('=155
-'ceiling('=156
-'round('=157
-'min('=158
-'max('=159
-'argmax('=160
-'argmin('=161
-'gcd('=162
-'lcm('=163
-'binomial('=164
-'trunc('=165
-'erf('=166
-'conjugate('=167
-'domain('=168
-'piecewise('=169
-'apply('=170
-'lambda('=171
-'NaN'=176
+'prime('=147
+'valuation('=148
+'card('=149
+'powerset('=150
+'union('=151
+'intersection('=152
+'complement('=153
+'image('=154
+'preimage('=155
+'floor('=156
+'ceil('=157
+'ceiling('=158
+'round('=159
+'min('=160
+'max('=161
+'argmax('=162
+'argmin('=163
+'gcd('=164
+'lcm('=165
+'binomial('=166
+'trunc('=167
+'erf('=168
+'conjugate('=169
+'domain('=170
+'piecewise('=171
+'apply('=172
+'lambda('=173
+'NaN'=178