merge

.github/workflows/consistency-checks.yml

@@ -15,7 +15,7 @@ jobs:
     steps:
     - uses: actions/checkout@v3
     - name: Set up Python ${{ matrix.python-version }}
-      uses: actions/setup-python@v2
+      uses: actions/setup-python@v4
       with:
         python-version: ${{ matrix.python-version }}
     - name: Install dependencies

.github/workflows/isort-and-black-checks.yml

@@ -11,7 +11,7 @@ jobs:
     steps:
       - uses: actions/checkout@v3
       - name: Set up Python 3.11
-        uses: actions/setup-python@v2
+        uses: actions/setup-python@v4
         with:
           python-version: 3.11
       - name: Install click, black and isort

.github/workflows/osx.yml

@@ -19,7 +19,7 @@ jobs:
     steps:
     - uses: actions/checkout@v3
     - name: Set up Python ${{ matrix.python-version }}
-      uses: actions/setup-python@v2
+      uses: actions/setup-python@v4
       with:
         python-version: ${{ matrix.python-version }}
     - name: Install OS dependencies

.github/workflows/ubuntu.yml

@@ -15,7 +15,7 @@ jobs:
     steps:
     - uses: actions/checkout@v3
     - name: Set up Python ${{ matrix.python-version }}
-      uses: actions/setup-python@v3
+      uses: actions/setup-python@v4
       with:
         python-version: ${{ matrix.python-version }}
     - name: Install OS dependencies

.github/workflows/windows.yml

@@ -16,7 +16,7 @@ jobs:
     steps:
     - uses: actions/checkout@v3
     - name: Set up Python ${{ matrix.python-version }}
-      uses: actions/setup-python@v3
+      uses: actions/setup-python@v4
       with:
         python-version: ${{ matrix.python-version }}
     - name: Install OS dependencies

.gitignore

@@ -14,9 +14,10 @@
 .settings
 .vscode
 /.cache
+/.gdbinit
 /.python-version
-/Mathics3.egg-info
 /Mathics.egg-info
+/Mathics3.egg-info
 ChangeLog
 Documents/
 Homepage/
@@ -33,9 +34,9 @@ mathics/doc/tex/logo-heptatom.pdf
 mathics/doc/tex/logo-text-nodrop.pdf
 mathics/doc/tex/mathics-*.asy
 mathics/doc/tex/mathics-*.dvi
+mathics/doc/tex/mathics-*.dvi
 mathics/doc/tex/mathics-*.eps
 mathics/doc/tex/mathics-*.pdf
-mathics/doc/tex/mathics-*.dvi
 mathics/doc/tex/mathics-*.tex
 mathics/doc/tex/mathics.aux
 mathics/doc/tex/mathics.dvi

CHANGES.rst

@@ -9,7 +9,7 @@ New Builtins
 
 
 * `Elements`
-
+* `RealAbs` and `RealSign`
 
 Compatibility
 -------------
@@ -24,7 +24,7 @@ Internals
 * ``eval_abs`` and ``eval_sign`` extracted from ``Abs`` and ``Sign`` and added to ``mathics.eval.arithmetic``.
 * Maximum number of digits allowed in a string set to 7000 and can be adjusted using environment variable
   ``MATHICS_MAX_STR_DIGITS`` on Python versions that don't adjust automatically (like pyston).
-
+* Real number comparisons implemented is based now in the internal implementation of `RealSign`.
 
 Bugs
 ----

SYMBOLS_MANIFEST.txt

@@ -824,8 +824,10 @@ System`Read
 System`ReadList
 System`ReadProtected
 System`Real
+System`RealAbs
 System`RealDigits
 System`RealNumberQ
+System`RealSign
 System`Reals
 System`Reap
 System`Record

admin-tools/build_and_check_manifest.py

@@ -2,7 +2,14 @@
 
 import sys
 
-from mathics.builtin import Builtin, modules, name_is_builtin_symbol
+from mathics.builtin.base import Builtin
+from mathics.core.load_builtin import (
+    import_and_load_builtins,
+    modules,
+    name_is_builtin_symbol,
+)
+
+import_and_load_builtins()
 
 
 def generate_available_builtins_names():

examples/symbolic_logic/gries_schneider/test_gs.py

@@ -4,8 +4,10 @@
 
 from mathics.core.definitions import Definitions
 from mathics.core.evaluation import Evaluation
+from mathics.core.load_builtin import import_and_load_builtins
 from mathics.core.parser import MathicsSingleLineFeeder, parse
 
+import_and_load_builtins()
 definitions = Definitions(add_builtin=True)
 
 for i in range(0, 4):

mathics/builtin/__init__.py

@@ -15,38 +15,3 @@
 builtin class such as the Builtin's Attributes, its Information text,
 among other things.
 """
-
-import os
-import os.path as osp
-
-from mathics.core.load_builtin import (
-    add_builtins_from_builtin_modules,
-    get_module_names,
-    import_builtin_subdirectories,
-    import_builtins,
-    initialize_display_operators_set,
-)
-from mathics.settings import ENABLE_FILES_MODULE
-
-# Get import modules in this directory of Python modules that contain
-# Mathics3 Builtin class definitions.
-
-builtin_path = osp.dirname(__file__)
-exclude_files = {"codetables", "base"}
-module_names = get_module_names(builtin_path, exclude_files)
-modules = []
-import_builtins(module_names, modules)
-
-# Get import modules in subdirectories of this directory of Python
-# modules that contain Mathics3 Builtin class definitions.
-
-# The files_io module handles local file access, reading and writing..
-# In some sandboxed settings, such as running Mathics from as a remote
-# server, we disallow local file access.
-disable_file_module_names = set() if ENABLE_FILES_MODULE else {"files_io"}
-
-subdirectories = next(os.walk(builtin_path))[1]
-import_builtin_subdirectories(subdirectories, disable_file_module_names, modules)
-
-add_builtins_from_builtin_modules(modules)
-initialize_display_operators_set()

mathics/builtin/arithmetic.py

@@ -77,7 +77,13 @@
     SymbolTable,
     SymbolUndefined,
 )
-from mathics.eval.arithmetic import eval_Abs, eval_mpmath_function, eval_Sign
+from mathics.eval.arithmetic import (
+    eval_Abs,
+    eval_mpmath_function,
+    eval_negate_number,
+    eval_RealSign,
+    eval_Sign,
+)
 from mathics.eval.nevaluator import eval_N
 from mathics.eval.numerify import numerify
 
@@ -1207,6 +1213,44 @@ class Real_(Builtin):
     name = "Real"
 
 
+class RealAbs(Builtin):
+    """
+    <url>:WMA link:https://reference.wolfram.com/language/ref/RealAbs.html</url>
+
+    <dl>
+      <dt>'RealAbs[$x$]'
+      <dd>returns the absolute value of a real number $x$.
+    </dl>
+    'RealAbs' is also known as modulus. It is evaluated if $x$ can be compared \
+    with $0$.
+
+    >> RealAbs[-3.]
+     = 3.
+    'RealAbs[$z$]' is left unevaluated for complex $z$:
+    >> RealAbs[2. + 3. I]
+     = RealAbs[2. + 3. I]
+    >> D[RealAbs[x ^ 2], x]
+     = 2 x ^ 3 / RealAbs[x ^ 2]
+    """
+
+    attributes = A_LISTABLE | A_NUMERIC_FUNCTION | A_PROTECTED
+    rules = {
+        "D[RealAbs[x_],x_]": "x/RealAbs[x]",
+        "Integrate[RealAbs[x_],x_]": "1/2 x RealAbs[x]",
+        "Integrate[RealAbs[u_],{u_,a_,b_}]": "1/2 b RealAbs[b]-1/2 a RealAbs[a]",
+    }
+    summary_text = "real absolute value"
+
+    def eval(self, x: BaseElement, evaluation: Evaluation):
+        """RealAbs[x_]"""
+        real_sign = eval_RealSign(x)
+        if real_sign is IntegerM1:
+            return eval_negate_number(x)
+        if real_sign is None:
+            return
+        return x
+
+
 class RealNumberQ(Test):
     """
     ## Not found in WMA
@@ -1237,6 +1281,42 @@ def test(self, expr) -> bool:
         return isinstance(expr, (Integer, Rational, Real))
 
 
+class RealSign(Builtin):
+    """
+    <url>:WMA link:https://reference.wolfram.com/language/ref/RealAbs.html</url>
+
+    <dl>
+      <dt>'RealSign[$x$]'
+      <dd>returns $-1$, $0$ or $1$ depending on whether $x$ is negative,
+    zero or positive.
+    </dl>
+    'RealSign' is also known as $sgn$ or $signum$ function.
+
+    >> RealSign[-3.]
+     = -1
+    'RealSign[$z$]' is left unevaluated for complex $z$:
+    >> RealSign[2. + 3. I]
+     = RealSign[2. + 3. I]
+
+    >> D[RealSign[x^2],x]
+     = 2 x Piecewise[{{0, x ^ 2 != 0}}, Indeterminate]
+    >> Integrate[RealSign[u],{u,0,x}]
+     = RealAbs[x]
+    """
+
+    attributes = A_LISTABLE | A_NUMERIC_FUNCTION | A_PROTECTED
+    rules = {
+        "D[RealSign[x_],x_]": "Piecewise[{{0, x!=0}}, Indeterminate]",
+        "Integrate[RealSign[x_],x_]": "RealAbs[x]",
+        "Integrate[RealSign[u_],{u_, a_, b_}]": "RealAbs[b]-RealSign[a]",
+    }
+    summary_text = "real sign"
+
+    def eval(self, x: Number, evaluation: Evaluation) -> Optional[Integer]:
+        """RealSign[x_]"""
+        return eval_RealSign(x)
+
+
 class Sign(SympyFunction):
     """
     <url>:WMA link:https://reference.wolfram.com/language/ref/Sign.html</url>

mathics/builtin/optiondoc.py → mathics/builtin/drawing/drawing_options.py

@@ -18,7 +18,7 @@
 from mathics.builtin.base import Builtin
 
 # This tells documentation how to sort this module
-sort_order = "mathics.builtin.drawing-options-and-option-values"
+sort_order = "mathics.builtin.graphing-and-drawing.drawing-options-and-option-values"
 
 
 class Automatic(Builtin):

mathics/builtin/drawing/graphics3d.py

@@ -69,8 +69,8 @@ class Graphics3D(Graphics):
           <dt>'Graphics3D[$primitives$, $options$]'
           <dd>represents a three-dimensional graphic.
 
-          See also the <url>:Drawing Option and Option Values:
-    /doc/reference-of-built-in-symbols/drawing-options-and-option-values
+          See <url>:Drawing Option and Option Values:
+    /doc/reference-of-built-in-symbols/graphics-and-drawing/drawing-options-and-option-values
     </url> for a list of Plot options.
         </dl>
 

mathics/builtin/drawing/plot.py

@@ -1100,6 +1100,7 @@ class BarChart(_Chart):
         <dt>'BarChart[{$b1$, $b2$ ...}]'
         <dd>makes a bar chart with lengths $b1$, $b2$, ....
     </dl>
+
     Drawing options include -
     Charting:
     <ul>
@@ -2563,24 +2564,11 @@ class Plot3D(_Plot3D):
       <dd>creates a three-dimensional plot of $f$ with $x$ ranging from $xmin$ to \
           $xmax$ and $y$ ranging from $ymin$ to $ymax$.
 
+          See <url>:Drawing Option and Option Values:
+    /doc/reference-of-built-in-symbols/graphics-and-drawing/drawing-options-and-option-values
+    </url> for a list of Plot options.
     </dl>
 
-    Plot3D has the same options as <url>:Graphics3D:
-/doc/reference-of-built-in-symbols/graphics-and-drawing/three-dimensional-graphics/graphics3d</url>,\
-    in particular:
-    <ul>
-    <li><url>
-    :Mesh:
-    /doc/reference-of-built-in-symbols/drawing-options-and-option-values/mesh</url>
-    <li><url>
-    :PlotPoints:
-    /doc/reference-of-built-in-symbols/drawing-options-and-option-values/plotpoints</url>
-    <li><url>
-    :MaxRecursion:
-    /doc/reference-of-built-in-symbols/drawing-options-and-option-values/maxrecursion</url>
-    </ul>
-
-
     >> Plot3D[x ^ 2 + 1 / y, {x, -1, 1}, {y, 1, 4}]
      = -Graphics3D-
 

mathics/builtin/options.py

@@ -59,7 +59,7 @@ class All(Predefined):
     /doc/reference-of-built-in-symbols/graphics-and-drawing/plotting-data/plot</url>, \
     setting the <url>
     :Mesh:
-    /doc/reference-of-built-in-symbols/drawing-options-and-option-values/mesh</url> \
+/doc/reference-of-built-in-symbols/graphics-and-drawing/drawing-options-and-option-values/mesh</url> \
     option to 'All' will show the specific plot points:
 
     >> Plot[x^2, {x, -1, 1}, MaxRecursion->5, Mesh->All]
@@ -180,7 +180,7 @@ class None_(Predefined):
 
         Plot3D shows the mesh grid between computed points by default. This the <url>
         :Mesh:
-    /doc/reference-of-built-in-symbols/drawing-options-and-option-values/mesh</url> option.
+/doc/reference-of-built-in-symbols/graphics-and-drawing/drawing-options-and-option-values/mesh</url> \
 
         However, you hide the mesh by setting the 'Mesh' option value to 'None':
 

mathics/builtin/tensors.py

@@ -216,7 +216,7 @@ class Inner(Builtin):
     messages = {
         "incom": (
             "Length `1` of dimension `2` in `3` is incommensurate with "
-            "length `4` of dimension 1 in `5."
+            "length `4` of dimension 1 in `5`."
         ),
     }
 

mathics/builtin/testing_expressions/equality_inequality.py

@@ -70,7 +70,7 @@ def numerify_args(items, evaluation) -> list:
             for item in items:
                 if not isinstance(item, Number):
                     # TODO: use $MaxExtraPrecision insterad of hard-coded 50
-                    item = eval_N(item, evaluation, SymbolMaxPrecision)
+                    item = eval_N(item, evaluation, SymbolMaxExtraPrecision)
                 n_items.append(item)
             items = n_items
         else:

mathics/core/definitions.py

@@ -15,9 +15,10 @@
 from mathics.core.convert.expression import to_mathics_list
 from mathics.core.element import fully_qualified_symbol_name
 from mathics.core.expression import Expression
-from mathics.core.load_builtin import definition_contribute
+from mathics.core.load_builtin import definition_contribute, mathics3_builtins_modules
 from mathics.core.symbols import Atom, Symbol, strip_context
 from mathics.core.systemsymbols import SymbolGet
+from mathics.settings import ROOT_DIR
 
 type_compiled_pattern = type(re.compile("a.a"))
 
@@ -138,12 +139,12 @@ def __init__(
         self.timing_trace_evaluation = False
 
         if add_builtin:
-            from mathics.builtin import modules
-            from mathics.settings import ROOT_DIR
-
             loaded = False
             if builtin_filename is not None:
-                builtin_dates = [get_file_time(module.__file__) for module in modules]
+                builtin_dates = [
+                    get_file_time(module.__file__)
+                    for module in mathics3_builtins_modules
+                ]
                 builtin_time = max(builtin_dates)
                 if get_file_time(builtin_filename) > builtin_time:
                     builtin_file = open(builtin_filename, "rb")
@@ -770,7 +771,6 @@ def __init__(
         builtin=None,
         is_numeric=False,
     ) -> None:
-
         super(Definition, self).__init__()
         self.name = name