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A class for multiline symbolic equations in the Jupyter Notebook

Project description

symbolic_equation

Source code on Github SymbolicEquation on the Python Package Index Travis Continuous Integration Coveralls BSD License

A simple Python package providing the Eq class for manipulating symbolic equations.

The Eq class defines an equation, and allows to apply arbitrary manipulations to the left-hand-side and/or right-hand-side of that equation. It keeps track all of these manipulations, and displays them neatly as a multi-line equation in an interactive interpreter session or a Jupyter notebook (using a LaTeX representation). It is mainly intended for use with SymPy.

Long calculations are expressed via method chaining, using .apply (apply function or method to both sides the equation), .apply_to_lhs, .apply_to_rhs (apply function or method only on the left hand side, respectively the right hand side), and .transform (apply function to the equation as a whole). For concise output, multiple steps in a calculation can be grouped with .amend and .reset. Tags (equation numbers or labels) set with .tag on any line of the equation will render in the text and LaTeX output.

Development of the symbolic_equation package happens on Github.

Installation

To install the latest released version of symbolic_equation, run this command in your terminal:

$ pip install symbolic_equation

This is the preferred method to install symbolic_equation, as it will always install the most recent stable release.

If you don’t have pip installed, the Python installation guide, respectively the Python Packaging User Guide can guide you through the process.

To install the latest development version of symbolic_equation from Github.

$ pip install git+https://github.com/goerz/symbolic_equation.git@master#egg=symbolic_equation

Example

>>> from symbolic_equation import Eq
>>> from sympy import symbols
>>> x, y = symbols('x y')
>>> eq1 = Eq(2*x - y - 1, tag='I')
>>> eq1
2*x - y - 1 = 0    ('I')

>>> eq2 = Eq(x + y - 5, tag='II')
>>> eq2
x + y - 5 = 0    ('II')

>>> eq_y = (
...     (eq1 - 2 * eq2).tag("I - 2 II")
...     .transform(lambda eq: eq - 9)
...     .transform(lambda eq: eq / (-3)).tag('y')
... )
>>> eq_y
9 - 3*y = 0     ('I - 2 II')
   -3*y = -9
      y = 3     ('y')

>>> eq_x = (
...     eq1.apply_to_lhs('subs', eq_y.as_dict).reset().tag(r'y in I')
...     .transform(lambda eq: eq / 2)
...     .transform(lambda eq: eq + 2).tag('x')
... )
>>> eq_x
2*x - 4 = 0    ('y in I')
  x - 2 = 0
      x = 2    ('x')

The reset() in the first line excludes ('I') from the output. It is also possible to “group” lines using amend, for less verbose output:

>>> eq_x = (
...     eq1.apply_to_lhs('subs', eq_y.as_dict).reset().tag(r'y in I')
...     .transform(lambda eq: eq / 2)
...     .transform(lambda eq: eq + 2).amend().tag('x')
... )
>>> eq_x
2*x - 4 = 0    ('y in I')
      x = 2    ('x')

Reference

class Eq(builtins.object)
 |  symbolic_equation.Eq(lhs, rhs=None, tag=None, eq_sym_str=None, eq_sym_tex=None, _prev_lhs=None, _prev_rhs=None, _prev_tags=None)
 |
 |  Symbolic equation.
 |
 |  This class keeps track of the :attr:`lhs` and :attr:`rhs` of an equation
 |  across arbitrary manipulations.
 |
 |  Args:
 |      lhs: the left-hand-side of the equation
 |      rhs: the right-hand-side of the equation. If None, defaults to zero.
 |      tag: a tag (equation number) to be shown when printing
 |           the equation
 |      eq_sym_str: If given, a value that overrides the `eq_sym_str` class
 |          attribute for this particular instance.
 |      eq_sym_tex: If given, a value that overrides the `eq_sym_tex` class
 |          attribute for this particular instance.
 |
 |  Class Attributes:
 |      latex_renderer: If not None, a callable that must return a LaTeX
 |          representation (:class:`str`) of `lhs` and `rhs`. When overriding
 |          this, wrap the function with `staticmethod`.
 |      eq_sym_str: default representation of the "equal" when rendering the
 |          equation as a str
 |      eq_sym_tex: default representation of the "equal" when rendering the
 |          equation in latex
 |
 |  Methods defined here:
 |
 |  __add__(self, other)
 |      Add another equation, or a constant.
 |
 |  __eq__(self, other)
 |      Compare to another equation, or a constant.
 |
 |      This does not take into account any mathematical knowledge, it merely
 |      checks if the :attr:`lhs` and :attr:`rhs` are exactly equal. If
 |      comparing against a constant, the :attr:`rhs` must be exactly equal to
 |      that constant.
 |
 |  __init__(self, lhs, rhs=None, tag=None, eq_sym_str=None, eq_sym_tex=None, _prev_lhs=None, _prev_rhs=None, _prev_tags=None)
 |      Initialize self.  See help(type(self)) for accurate signature.
 |
 |  __mul__(self, other)
 |
 |  __radd__ = __add__(self, other)
 |
 |  __repr__(self)
 |      Return repr(self).
 |
 |  __rmul__(self, other)
 |
 |  __rsub__(self, other)
 |
 |  __str__(self)
 |      Return str(self).
 |
 |  __sub__(self, other)
 |
 |  __truediv__(self, other)
 |
 |  amend(self, previous_lines=1)
 |      Amend the previous lhs and rhs with the current ones.
 |
 |      If `previous_lines` is greater than 1, overwrite the corresponding
 |      number of previous lines.
 |
 |      This can be chained to e.g. an :meth:`apply` call to group multiple
 |      steps so that they don't show up a separate lines in the output.
 |
 |  apply(self, func_or_mtd, *args, **kwargs)
 |      Apply `func_or_mtd` to both sides of the equation.
 |
 |      Returns a new equation where the left-hand-side and right-hand side
 |      are replaced by the application of `func_or_mtd`, depending on its
 |      type.
 |
 |      * If `func_or_mtd` is a string, it must be the name of a method `mtd`,
 |        and equation is modified as
 |
 |        ::
 |
 |            lhs=lhs.mtd(*args, **kwargs)
 |            rhs=rhs.mtd(*args, **kwargs)
 |
 |      * If `func_or_mtd` is a callable `func`, the equation is modified as
 |
 |        ::
 |
 |            lhs=func(lhs, *args, **kwargs)
 |            rhs=func(rhs, *args, **kwargs)
 |
 |  apply_to_lhs(self, func_or_mtd, *args, **kwargs)
 |      Apply `func_or_mtd` to the :attr:`lhs` of the equation only.
 |
 |      Like :meth:`apply`, but modifying only the left-hand-side.
 |
 |  apply_to_rhs(self, func_or_mtd, *args, **kwargs)
 |      Apply `func_or_mtd` to the :attr:`rhs` of the equation only.
 |
 |      Like :meth:`apply`, but modifying only the right-hand-side.
 |
 |  copy(self)
 |      Return a copy of the equation, including its history.
 |
 |  reset(self)
 |      Discard the equation history.
 |
 |  tag(self, tag)
 |      Set the tag for the last line in the equation.
 |
 |  transform(self, func, *args, **kwargs)
 |      Apply `func` to the entire equation.
 |
 |      The lhs and the rhs of the equation is replaced with the lhs and rhs of
 |      the equation returned by ``func(self, *args, **kwargs)``.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  __dict__
 |      dictionary for instance variables (if defined)
 |
 |  __weakref__
 |      list of weak references to the object (if defined)
 |
 |  as_dict
 |      Mapping of the lhs to the rhs.
 |
 |      This allows to plug an equation into another expression.
 |
 |  lhs
 |      The left-hand-side of the equation.
 |
 |  rhs
 |      The right-hand-side of the equation.
 |
 |  ----------------------------------------------------------------------
 |  Data and other attributes defined here:
 |
 |  __hash__ = None
 |
 |  eq_sym_str = '='
 |
 |  eq_sym_tex = '='
 |
 |  latex_renderer = None

Use in the Jupyter notebook

In a Jupyter notebook, equations will be rendered in LaTeX. See examples.ipynb.

The rendering presumes that both the lhs and the rhs have a LaTeX representation. If the Eq class has a latex_renderer attribute defined, that renderer will be used to obtain the LaTeX representation of the lhs and rhs. Otherwise:

  • If the lhs or rhs object has a _latex method, that method will be called; or lastly,
  • The lhs and rhs will be passed to sympy.latex.

Use with QAlgebra

To properly render equations that contain QAlgebra expressions, you must register QAlgebra’s latex renderer:

from symbolic_equation import Eq
from qalgebra import latex
Eq.latex_renderer = staticmethod(latex)

Relation to SymPy’s Eq class

The SymPy package also provides an Eq class that represents equality between two SymPy expressions. The class provided by SymPy and the class provided by this package are not interchangeable: SymPy’s Eq does not track modifications or print out as multiline equations. While the symbolic_equation.Eq class is not a SymPy expression, it can be converted to a sympy.Eq instance via the sympy.sympify function.

History

0.3.0 (2020-11-22)

  • Added: eq_sym_str and eq_sym_tex attributes

0.2.0 (2020-06-28)

  • Removed: apply_mtd, apply_mtd_to_lhs, apply_mtd_to_rhs methods. The functionality is now included in apply, apply_to_lhs, apply_to_rhs, which can now receive a function or a method name
  • Added: amend and reset methods for controlling which lines are included in the history of an equation (“grouping”)
  • Changed: The set_tag method was renamed to tag
  • Removed: cont and tag arguments. The cont behavior (preserving the equation history) is now on by default, and the old cont=False can be achieved with reset.
  • Removed: tag property (tag is now a method for setting the equation tag).
  • Added: transform method for transforming the equation as a whole.

0.1.0-dev (2019-05-26)

  • Initial release

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