Go over drawing.plot and ... (#1130)

add links to functional_iteration

Author: rocky

mathics/builtin/drawing/plot.py

@@ -28,6 +28,7 @@
 from mathics.core.list import ListExpression
 from mathics.core.symbols import Symbol, SymbolList, SymbolTrue
 from mathics.core.systemsymbols import (
+    SymbolBlack,
     SymbolBlend,
     SymbolColorData,
     SymbolEdgeForm,
@@ -308,7 +309,16 @@ def eval(self, points, evaluation: Evaluation, options: dict):
                 )
             )
 
-        all_points = eval_N(points, evaluation).to_python()
+        # If "points" is a literal value with a Python representation,
+        # it has a ".value" attribute with a non-None value. So here,
+        # we don't have to eval_N().to_python().
+
+        all_points = (
+            points.value
+            if hasattr(points, "value") and points.value is not None
+            else eval_N(points, evaluation).to_python()
+        )
+
         # FIXME: arrange for self to have a .symbolname property or attribute
         expr = Expression(Symbol(self.get_name()), points, *options_to_rules(options))
 
@@ -1176,7 +1186,7 @@ def boxes():
                 x += 0.2
 
         def rectangles():
-            yield Expression(SymbolEdgeForm, Symbol("Black"))
+            yield Expression(SymbolEdgeForm, SymbolBlack)
 
             last_x1 = 0
 
@@ -1198,7 +1208,7 @@ def rectangles():
             )
 
         def axes():
-            yield Expression(SymbolFaceForm, Symbol("Black"))
+            yield Expression(SymbolFaceForm, SymbolBlack)
 
             def points(x):
                 return ListExpression(vector2(x, 0), vector2(x, MTwoTenths))
@@ -1210,7 +1220,7 @@ def points(x):
                     yield Expression(SymbolLine, points(x1))
 
         def labels(names):
-            yield Expression(SymbolFaceForm, Symbol("Black"))
+            yield Expression(SymbolFaceForm, SymbolBlack)
 
             for (k, n), x0, x1, y in boxes():
                 if k <= len(names):
@@ -2362,7 +2372,7 @@ def phis(values):
                 phi0 = phi1
 
         def segments():
-            yield Expression(SymbolEdgeForm, Symbol("Black"))
+            yield Expression(SymbolEdgeForm, SymbolBlack)
 
             origin = vector2(0.0, 0.0)
 
@@ -2386,7 +2396,7 @@ def segments():
                     )
 
         def labels(names):
-            yield Expression(SymbolFaceForm, Symbol("Black"))
+            yield Expression(SymbolFaceForm, SymbolBlack)
 
             for values, (r0, r1) in zip(data, radii()):
                 for name, (phi0, phi1) in zip(names, phis(values)):

mathics/builtin/functional/functional_iteration.py

@@ -5,20 +5,23 @@
 Functional iteration is an elegant way to represent repeated operations that is used a lot.
 """
 
-from mathics.core.atoms import Integer1
 from mathics.core.builtin import Builtin
 from mathics.core.convert.python import from_python
 from mathics.core.evaluation import Evaluation
 from mathics.core.expression import Expression
 from mathics.core.expression_predefined import MATHICS3_INFINITY
 from mathics.core.symbols import Symbol, SymbolTrue
+from mathics.core.systemsymbols import SymbolAll
 
 # This tells documentation how to sort this module
 sort_order = "mathics.builtin.iteratively-applying-functions"
 
 
 class FixedPoint(Builtin):
     """
+    <url>:WMA link:
+      https://reference.wolfram.com/language/ref/FixedPoint.html</url>
+
     <dl>
       <dt>'FixedPoint[$f$, $expr$]'
       <dd>starting with $expr$, iteratively applies $f$ until the result no longer changes.
@@ -84,9 +87,13 @@ def eval(self, f, expr, n, evaluation: Evaluation, options: dict):
 
 class FixedPointList(Builtin):
     """
+    <url>:WMA link:
+      https://reference.wolfram.com/language/ref/FixedPointList.html</url>
+
     <dl>
       <dt>'FixedPointList[$f$, $expr$]'
-      <dd>starting with $expr$, iteratively applies $f$ until the result no longer changes, and returns a list of all intermediate results.
+      <dd>starting with $expr$, iteratively applies $f$ until the result no longer changes, \
+          and returns a list of all intermediate results.
 
       <dt>'FixedPointList[$f$, $expr$, $n$]'
       <dd>performs at most $n$ iterations.
@@ -100,12 +107,17 @@ class FixedPointList(Builtin):
     >> newton[9]
      = {1., 5., 3.4, 3.02353, 3.00009, 3., 3., 3.}
 
-    Plot the "hailstone" sequence of a number:
+    Compute the <url>:Hailstone Number:
+    https://mathworld.wolfram.com/HailstoneNumber.html</url>: for 14:
+
     >> collatz[1] := 1;
     >> collatz[x_ ? EvenQ] := x / 2;
     >> collatz[x_] := 3 x + 1;
     >> list = FixedPointList[collatz, 14]
      = {14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, 1}
+
+    Plot this:
+
     >> ListLinePlot[list]
      = -Graphics-
     """
@@ -143,6 +155,9 @@ def eval(self, f, expr, n, evaluation: Evaluation):
 
 class Fold(Builtin):
     """
+    <url>:WMA link:
+      https://reference.wolfram.com/language/ref/Fold.html</url>
+
     <dl>
       <dt>'Fold[$f$, $x$, $list$]'
       <dd>returns the result of iteratively applying the binary
@@ -166,6 +181,9 @@ class Fold(Builtin):
 
 class FoldList(Builtin):
     """
+    <url>:WMA link:
+      https://reference.wolfram.com/language/ref/FoldList.html</url>
+
     <dl>
       <dt>'FoldList[$f$, $x$, $list$]'
       <dd>returns a list starting with $x$, where each element is
@@ -190,6 +208,9 @@ class FoldList(Builtin):
 
 class Nest(Builtin):
     """
+    <url>:WMA link:
+      https://reference.wolfram.com/language/ref/Nest.html</url>
+
     <dl>
       <dt>'Nest[$f$, $expr$, $n$]'
       <dd>starting with $expr$, iteratively applies $f$ $n$ times and returns the final result.
@@ -217,6 +238,9 @@ def eval(self, f, expr, n, evaluation):
 
 class NestList(Builtin):
     """
+    <url>:WMA link:
+      https://reference.wolfram.com/language/ref/NestList.html</url>
+
     <dl>
       <dt>'NestList[$f$, $expr$, $n$]'
       <dd>starting with $expr$, iteratively applies $f$ $n$ times and \
@@ -257,6 +281,9 @@ def eval(self, f, expr, n, evaluation):
 
 class NestWhile(Builtin):
     """
+    <url>:WMA link:
+      https://reference.wolfram.com/language/ref/NestWhile.html</url>
+
     <dl>
       <dt>'NestWhile[$f$, $expr$, $test$]'
       <dd>applies a function $f$ repeatedly on an expression $expr$, until \
@@ -302,7 +329,7 @@ def eval(self, f, expr, test, m, evaluation: Evaluation):
 
         results = [expr]
         while True:
-            if m.get_name() == "System`All":
+            if m is SymbolAll:
                 test_elements = results
             else:
                 test_elements = results[-m.value :]

mathics/core/builtin.py

@@ -830,6 +830,7 @@ def eval_symbol(self, expr, iterator, evaluation):
 
     def eval_range(self, expr, i, imax, evaluation):
         "%(name)s[expr_, {i_Symbol, imax_}]"
+
         imax = imax.evaluate(evaluation)
         if imax.has_form("Range", None):
             # FIXME: this should work as an iterator in Python3, not
@@ -965,6 +966,7 @@ def eval_iter(self, expr, i, imin, imax, di, evaluation):
 
     def eval_list(self, expr, i, items, evaluation):
         "%(name)s[expr_, {i_Symbol, {items___}}]"
+
         items = items.evaluate(evaluation).get_sequence()
         result = []
         for item in items:

mathics/core/list.py

@@ -110,12 +110,7 @@ def evaluate_elements(self, evaluation: Evaluation) -> Expression:
             return self
 
         new_list = ListExpression(*elements)
-        # TODO: we could have a specialized version of this
-        # that keeps self.value up to date when that is
-        # easy to do. That is left of some future time to
-        # decide whether doing this this is warranted.
         new_list._build_elements_properties()
-        new_list.value = None
         return new_list
 
     @property

mathics/core/systemsymbols.py

@@ -40,6 +40,7 @@
 SymbolAttributes = Symbol("System`Attributes")
 SymbolAutomatic = Symbol("System`Automatic")
 SymbolBaseForm = Symbol("System`BaseForm")
+SymbolBlack = Symbol("System`Black")
 SymbolBlank = Symbol("System`Blank")
 SymbolBlankNullSequence = Symbol("System`BlankNullSequence")
 SymbolBlankSequence = Symbol("System`BlankSequence")

mathics/eval/drawing/plot.py

@@ -158,7 +158,7 @@ def eval_ListPlot(
       options: miscellaneous graphics options from underlying M-Expression
     """
 
-    if not isinstance(plot_groups, list) or len(plot_groups) == 0:
+    if not isinstance(plot_groups, (list, tuple)) or len(plot_groups) == 0:
         return
 
     # Classify the kind of data that "point" is, and