Merge pull request #740 from Mathics3/apply-reduction-4

apply->eval and doc stuff

mathics/builtin/attributes.py

@@ -1,6 +1,6 @@
 # -*- coding: utf-8 -*-
 """
-Attributes of Definitions
+Definition Attributes
 
 While a definition like 'cube[$x_$] = $x$^3' gives a way to specify \
 <em>values</em> of a function, <em>attributes</em> allow a way to \
@@ -13,6 +13,9 @@
 However in contrast to \Mathematica, you can set any symbol as an attribute.
 """
 
+# This tells documentation how to sort this module
+sort_order = "mathics.builtin.definition-attributes"
+
 
 from mathics.builtin.base import Builtin, Predefined
 from mathics.core.assignment import get_symbol_list

mathics/builtin/functional/composition.py

@@ -3,24 +3,36 @@
 """
 Functional Composition and Operator Forms
 
-<url>:Functional Composition: https://en.wikipedia.org/wiki/Function_composition_(computer_science)</url> is a way to combine simple functions to build more complicated ones.
-Like the usual composition of functions in mathematics, the result of each function is passed as the argument of the next, and the result of the last one is the result of the whole.
-
-The symbolic structure of Mathics makes it easy to create "operators" that can be composed and manipulated symbolically—forming "pipelines" of operations—and then applied to arguments.
-
-Some built-in functions also directly support a "curried" form, in which they can immediately be given as symbolic operators.
+<url>:Functional Composition:
+https://en.wikipedia.org/wiki/Function_composition_(computer_science)</url> is \
+a way to combine simple functions to build more complicated ones.
+Like the usual composition of functions in mathematics, the result of each \
+function is passed as the argument of the next, and the result of the last \
+one is the result of the whole.
+
+The symbolic structure of Mathics3 makes it easy to create "operators" that \
+can be composed and manipulated symbolically—forming "pipelines" of \
+operations—and then applied to arguments.
+
+Some built-in functions also directly support a "curried" form, in which they \
+can immediately be given as symbolic operators.
 """
 
 # This tells documentation how to sort this module
 sort_order = "mathics.builtin.functional-composition"
 
 from mathics.builtin.base import Builtin
 from mathics.core.attributes import A_FLAT, A_ONE_IDENTITY, A_PROTECTED
+from mathics.core.evaluation import Evaluation
 from mathics.core.expression import Expression
 
 
 class Composition(Builtin):
     """
+    <url>
+    :WMA link:
+    https://reference.wolfram.com/language/ref/Composition.html</url>
+
     <dl>
       <dt>'Composition[$f$, $g$]'
       <dd>returns the composition of two functions $f$ and $g$.
@@ -47,7 +59,7 @@ class Composition(Builtin):
     }
     summary_text = "the composition of two or more functions"
 
-    def apply(self, functions, args, evaluation):
+    def eval(self, functions, args, evaluation: Evaluation):
         "Composition[functions__][args___]"
 
         functions = functions.get_sequence()
@@ -60,6 +72,9 @@ def apply(self, functions, args, evaluation):
 
 class Identity(Builtin):
     """
+    <url>
+    :WMA link:
+    https://reference.wolfram.com/language/ref/Identity.html</url>
     <dl>
       <dt>'Identity[$x$]'
       <dd>is the identity function, which returns $x$ unchanged.

mathics/builtin/inout.py

@@ -6,6 +6,7 @@
 
 from mathics.builtin.base import Builtin, Predefined
 from mathics.core.attributes import A_NO_ATTRIBUTES
+from mathics.core.evaluation import Evaluation
 from mathics.core.expression import Expression
 from mathics.core.list import ListExpression
 from mathics.core.symbols import Symbol, SymbolNull
@@ -37,7 +38,9 @@ class Echo_(Predefined):
 
 class Print(Builtin):
     """
-    <url>:WMA link:https://reference.wolfram.com/language/ref/Print.html</url>
+    <url>
+    :WMA link:
+    https://reference.wolfram.com/language/ref/Print.html</url>
 
     <dl>
       <dt>'Print[$expr$, ...]'
@@ -56,7 +59,7 @@ class Print(Builtin):
 
     summary_text = "print strings and formatted text"
 
-    def apply(self, expr, evaluation):
+    def eval(self, expr, evaluation: Evaluation):
         "Print[expr__]"
 
         expr = expr.get_sequence()

mathics/builtin/intfns/divlike.py

@@ -23,26 +23,32 @@
 )
 from mathics.core.convert.expression import to_mathics_list
 from mathics.core.convert.python import from_bool
+from mathics.core.evaluation import Evaluation
 from mathics.core.expression import Expression
-from mathics.core.symbols import Symbol, SymbolFalse, SymbolTrue
-from mathics.core.systemsymbols import SymbolComplexInfinity
-
-SymbolQuotient = Symbol("Quotient")
-SymbolQuotientRemainder = Symbol("QuotientRemainder")
+from mathics.core.symbols import SymbolFalse, SymbolTrue
+from mathics.core.systemsymbols import (
+    SymbolComplexInfinity,
+    SymbolQuotient,
+    SymbolQuotientRemainder,
+)
 
 
 class CompositeQ(Builtin):
     """
-    <url>:WMA link:https://reference.wolfram.com/language/ref/CompositeQ.html</url>
+    <url>
+    :WMA link:
+    https://reference.wolfram.com/language/ref/CompositeQ.html</url>
 
     <dl>
       <dt>'CompositeQ[$n$]'
       <dd>returns True if $n$ is a composite number
     </dl>
 
     <ul>
-      <li>A composite number is a positive number that is the product of two integers other than 1.
-      <li>For negative integer $n$, 'CompositeQ[$n$]' is effectively equivalent to 'CompositeQ[-$n$]'.
+      <li>A composite number is a positive number that is the product of two \
+          integers other than 1.
+      <li>For negative integer $n$, 'CompositeQ[$n$]' is effectively equivalent \
+          to 'CompositeQ[-$n$]'.
     </ul>
 
     >> Table[CompositeQ[n], {n, 0, 10}]
@@ -52,7 +58,7 @@ class CompositeQ(Builtin):
     attributes = A_LISTABLE | A_PROTECTED
     summary_text = "test whether a number is composite"
 
-    def apply(self, n, evaluation):
+    def eval(self, n: Integer, evaluation: Evaluation):
         "CompositeQ[n_Integer]"
         return from_bool(ask(Q.composite(n.value)))
 
@@ -63,7 +69,8 @@ class CoprimeQ(Builtin):
 
     <dl>
       <dt>'CoprimeQ[$x$, $y$]'
-      <dd>tests whether $x$ and $y$ are coprime by computing their greatest common divisor.
+      <dd>tests whether $x$ and $y$ are coprime by computing their greatest \
+          common divisor.
     </dl>
 
     >> CoprimeQ[7, 9]
@@ -92,7 +99,7 @@ class CoprimeQ(Builtin):
     attributes = A_LISTABLE | A_PROTECTED
     summary_text = "test whether elements are coprime"
 
-    def apply(self, args, evaluation):
+    def eval(self, args, evaluation: Evaluation):
         "CoprimeQ[args__]"
 
         py_args = [arg.to_python() for arg in args.get_sequence()]
@@ -183,7 +190,7 @@ class GCD(Builtin):
     attributes = A_FLAT | A_LISTABLE | A_ONE_IDENTITY | A_ORDERLESS | A_PROTECTED
     summary_text = "greatest common divisor"
 
-    def apply(self, ns, evaluation):
+    def eval(self, ns, evaluation: Evaluation):
         "GCD[ns___Integer]"
 
         ns = ns.get_sequence()
@@ -214,7 +221,7 @@ class LCM(Builtin):
     attributes = A_FLAT | A_LISTABLE | A_ONE_IDENTITY | A_ORDERLESS | A_PROTECTED
     summary_text = "least common multiple"
 
-    def apply(self, ns: List[Integer], evaluation):
+    def eval(self, ns: List[Integer], evaluation: Evaluation):
         "LCM[ns___Integer]"
 
         ns = ns.get_sequence()
@@ -250,7 +257,7 @@ class Mod(Builtin):
     attributes = A_LISTABLE | A_NUMERIC_FUNCTION | A_PROTECTED
     summary_text = "the remainder in an integer division"
 
-    def apply(self, n: Integer, m: Integer, evaluation):
+    def eval(self, n: Integer, m: Integer, evaluation: Evaluation):
         "Mod[n_Integer, m_Integer]"
 
         n, m = n.value, m.value
@@ -262,14 +269,20 @@ def apply(self, n: Integer, m: Integer, evaluation):
 
 class ModularInverse(SympyFunction):
     """
-    <url>:Modular multiplicative inverse: https://en.wikipedia.org/wiki/Modular_multiplicative_inverse</url> (<url>:SymPy: https://docs.sympy.org/latest/modules/core.html#sympy.core.numbers.mod_inverse</url>, <url>:WMA: https://reference.wolfram.com/language/ref/ModularInverse.html</url>)
+    <url>
+    :Modular multiplicative inverse:
+    https://en.wikipedia.org/wiki/Modular_multiplicative_inverse</url> (<url>
+    :SymPy: https://docs.sympy.org/latest/modules/core.html#sympy.core.numbers.mod_inverse</url>, <url>
+    :WMA: https://reference.wolfram.com/language/ref/ModularInverse.html
+    </url>)
 
     <dl>
       <dt>'ModularInverse[$k$, $n$]'
       <dd>returns the modular inverse $k$^(-1) mod $n$.
     </dl>
 
-    'ModularInverse[$k$,$n$]' gives the smallest positive integer $r$ where the remainder of the division of $r$ x $k$ by $n$ is equal to 1.
+    'ModularInverse[$k$,$n$]' gives the smallest positive integer $r$ where the remainder \
+    of the division of $r$ x $k$ by $n$ is equal to 1.
 
     >> ModularInverse[2, 3]
      = 2
@@ -289,7 +302,7 @@ class ModularInverse(SympyFunction):
     summary_text = "returns the modular inverse $k^(-1)$ mod $n$"
     sympy_name = "mod_inverse"
 
-    def apply_k_n(self, k: Integer, n: Integer, evaluation):
+    def eval_k_n(self, k: Integer, n: Integer, evaluation: Evaluation):
         "ModularInverse[k_Integer, n_Integer]"
         try:
             r = sympy.mod_inverse(k.value, n.value)
@@ -352,7 +365,7 @@ class PowerMod(Builtin):
     }
     summary_text = "modular exponentiation"
 
-    def apply(self, a: Integer, b: Integer, m: Integer, evaluation):
+    def eval(self, a: Integer, b: Integer, m: Integer, evaluation: Evaluation):
         "PowerMod[a_Integer, b_Integer, m_Integer]"
 
         a_int = a
@@ -411,7 +424,7 @@ class PrimeQ(SympyFunction):
     sympy_name = "isprime"
     summary_text = "test whether elements are prime numbers"
 
-    def apply(self, n, evaluation):
+    def eval(self, n, evaluation: Evaluation):
         "PrimeQ[n_]"
 
         n = n.get_int_value()
@@ -455,7 +468,7 @@ class Quotient(Builtin):
     }
     summary_text = "integer quotient"
 
-    def apply(self, m: Integer, n: Integer, evaluation):
+    def eval(self, m: Integer, n: Integer, evaluation: Evaluation):
         "Quotient[m_Integer, n_Integer]"
         py_m = m.value
         py_n = n.value
@@ -503,7 +516,7 @@ class QuotientRemainder(Builtin):
     }
     summary_text = "integer quotient and remainder"
 
-    def apply(self, m, n, evaluation):
+    def eval(self, m, n, evaluation: Evaluation):
         "QuotientRemainder[m_, n_]"
         if m.is_numeric(evaluation) and n.is_numeric():
             py_m = m.to_python()

mathics/builtin/intfns/recurrence.py

@@ -2,7 +2,10 @@
 """
 Recurrence and Sum Functions
 
-A recurrence relation is an equation that recursively defines a sequence or multidimensional array of values, once one or more initial terms are given; each further term of the sequence or array is defined as a function of the preceding terms.
+A recurrence relation is an equation that recursively defines a \
+sequence or multidimensional array of values, once one or more initial \
+terms are given; each further term of the sequence or array is defined \
+as a function of the preceding terms.
 """
 
 
@@ -17,6 +20,7 @@
     A_PROTECTED,
     A_READ_PROTECTED,
 )
+from mathics.core.evaluation import Evaluation
 
 
 class Fibonacci(_MPMathFunction):
@@ -51,7 +55,7 @@ class HarmonicNumber(_MPMathFunction):
     <url>:WMA link:https://reference.wolfram.com/language/ref/HarmonicNumber.html</url>)
 
     <dl>
-    <dt>'HarmonicNumber[n]'
+      <dt>'HarmonicNumber[n]'
       <dd>returns the $n$th harmonic number.
     </dl>
 
@@ -76,8 +80,12 @@ class HarmonicNumber(_MPMathFunction):
 # Note: WL allows StirlingS1[{2, 4, 6}, 2], but we don't (yet).
 class StirlingS1(Builtin):
     """
-    <url>:Stirling numbers of first kind:https://en.wikipedia.org/wiki/Stirling_numbers_of_the_first_kind</url> \
-    (<url>:WMA link:https://reference.wolfram.com/language/ref/StirlingS1.html</url>)
+    <url>
+    :Stirling numbers of first kind:
+    https://en.wikipedia.org/wiki/Stirling_numbers_of_the_first_kind</url> \
+    (<url>
+    :WMA link:
+    https://reference.wolfram.com/language/ref/StirlingS1.html</url>)
 
     <dl>
       <dt>'StirlingS1[$n$, $m$]'
@@ -98,24 +106,29 @@ class StirlingS1(Builtin):
     sympy_name = "functions.combinatorial.stirling"
     mpmath_name = "stirling1"
 
-    def apply(self, n, m, evaluation):
+    def eval(self, n: Integer, m: Integer, evaluation: Evaluation):
         "%(name)s[n_Integer, m_Integer]"
-        n_value = n.get_int_value()
-        m_value = m.get_int_value()
+        n_value = n.value
+        m_value = m.value
         return Integer(stirling(n_value, m_value, kind=1, signed=True))
 
 
 class StirlingS2(Builtin):
     """
-    <url>:Stirling numbers of first kind:https://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind</url> \
-    (<url>:WMA link:https://reference.wolfram.com/language/ref/StirlingS2.html</url>)
+    <url>
+    :Stirling numbers of second kind:
+    https://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind</url> \
+    (<url>
+    :WMA link
+    :https://reference.wolfram.com/language/ref/StirlingS2.html</url>)
 
-      <dl>
+    <dl>
       <dt>'StirlingS2[$n$, $m$]'
       <dd>gives the Stirling number of the second kind  _n^m.
     </dl>
 
-    returns the number of ways of partitioning a set of $n$ elements into $m$ non empty subsets.
+    returns the number of ways of partitioning a set of $n$ elements into $m$ \
+    non empty subsets.
 
     >> Table[StirlingS2[10, m], {m, 10}]
     = {1, 511, 9330, 34105, 42525, 22827, 5880, 750, 45, 1}
@@ -127,8 +140,8 @@ class StirlingS2(Builtin):
     mpmath_name = "stirling2"
     summary_text = "Stirling numbers of the second kind"
 
-    def apply(self, m, n, evaluation):
+    def eval(self, m: Integer, n: Integer, evaluation: Evaluation):
         "%(name)s[n_Integer, m_Integer]"
-        n_value = n.get_int_value()
-        m_value = m.get_int_value()
+        n_value = n.value
+        m_value = m.value
         return Integer(stirling(n_value, m_value, kind=2))

mathics/core/systemsymbols.py

@@ -172,6 +172,8 @@
 SymbolPrecision = Symbol("System`Precision")
 SymbolQuantity = Symbol("System`Quantity")
 SymbolQuiet = Symbol("System`Quiet")
+SymbolQuotient = Symbol("System`Quotient")
+SymbolQuotientRemainder = Symbol("System`QuotientRemainder")
 SymbolRGBColor = Symbol("System`RGBColor")
 SymbolRandomComplex = Symbol("System`RandomComplex")
 SymbolRandomReal = Symbol("System`RandomReal")