symbolic-equation 0.1.0.dev0

A class for multiline symbolic equations in the Jupyter Notebook

symbolic_equation

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 optionally 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.

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).set_tag("I - 2 II")
...     .apply(lambda v: v - 9, cont=True)
...     .apply(lambda v: v / (-3), cont=True, tag='y')
... )
>>> eq_y
9 - 3*y = 0     ('I - 2 II')
   -3*y = -9
      y = 3     ('y')

>>> eq_x = (
...     eq1.apply_mtd_to_lhs('subs', eq_y.as_dict, tag=r'y in I')
...     .apply(lambda v: v / 2, cont=True)
...     .apply(lambda v: v + 2, cont=True, tag='x')
... )
>>> eq_x
2*x - 4 = 0    ('y in I')
  x - 2 = 0
      x = 2    ('x')

Reference

>>> help(Eq)  # doctest: +NORMALIZE_WHITESPACE
Help on class Eq in module symbolic_equation:
<BLANKLINE>
class Eq(builtins.object)
 |  Eq(lhs, rhs=None, tag=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
 |
 |  Class Attributes:
 |      latex_renderer: If not None, a callable that must return a LaTeX
 |          representation (:class:`str`) of `lhs` and `rhs`.
 |
 |  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, _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)
 |
 |  apply(self, func, *args, cont=False, tag=None, **kwargs)
 |      Apply `func` 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`::
 |
 |          lhs=func(lhs, *args, **kwargs)
 |          rhs=func(rhs, *args, **kwargs)
 |
 |      If ``cont=True``, the resulting equation will keep a history of its
 |      previous state (resulting in multiple lines of equations when printed).
 |
 |      The resulting equation with have the given `tag`.
 |
 |  apply_mtd(self, mtd, *args, cont=False, tag=None, **kwargs)
 |      Call the method `mtd` on both sides of the equation.
 |
 |      That is, the left-hand-side and right-hand-side are replaced by::
 |
 |          lhs=lhs.<mtd>(*args, **kwargs)
 |          rhs=rhs.<mtd>(*args, **kwargs)
 |
 |      The `cont` and `tag` parameters are as in :meth:`apply`.
 |
 |  apply_mtd_to_lhs(self, mtd, *args, cont=False, tag=None, **kwargs)
 |      Call the method `mtd` on the :attr:`lhs` of the equation only.
 |
 |      Like :meth:`apply_mtd`, but modifying only the left-hand-side.
 |
 |  apply_mtd_to_rhs(self, mtd, *args, cont=False, tag=None, **kwargs)
 |      Call the method `mtd` on the :attr:`rhs` of the equation.
 |
 |      Like :meth:`apply_mtd`, but modifying only the right-hand-side.
 |
 |  apply_to_lhs(self, func, *args, cont=False, tag=None, **kwargs)
 |      Apply `func` to the :attr:`lhs` of the equation only.
 |
 |      Like :meth:`apply`, but modifying only the left-hand-side.
 |
 |  apply_to_rhs(self, func, *args, cont=False, tag=None, **kwargs)
 |      Apply `func` 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
 |
 |  set_tag(self, tag)
 |      Return a copy of the equation with a new `tag`.
 |
 |  ----------------------------------------------------------------------
 |  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.
 |
 |  tag
 |      A tag (equation number) to be shown when printing the equation, or
 |      None
 |
 |  ----------------------------------------------------------------------
 |  Data and other attributes defined here:
 |
 |  __hash__ = None
 |
 |  latex_renderer = None
<BLANKLINE>

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.

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

0.1.0-dev (2019-05-26)

• Initial release