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Add linsolve sphinx docs #9587

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merged 3 commits into from Aug 8, 2015
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Add linsolve sphinx docs #9587

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444e7da
Add linsolve sphinx docs
aktech Jun 30, 2015
eaf87a6
Fix 'unexpected unindent' Sphinx error
aktech Jun 30, 2015
a31aebc
Fix rendering of Matrix in docs using literal block
aktech Aug 7, 2015
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11 changes: 11 additions & 0 deletions doc/src/modules/solvers/solveset.rst
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Expand Up @@ -34,8 +34,19 @@ is the symbol that we want to solve the equation for.

.. autofunction:: sympy.solvers.solveset.domain_check


linear_eq_to_matrix
-------------------

.. autofunction:: sympy.solvers.solveset.linear_eq_to_matrix


linsolve
--------

.. autofunction:: sympy.solvers.solveset.linsolve


Diophantine Equations (DEs)
---------------------------

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50 changes: 26 additions & 24 deletions sympy/solvers/solveset.py
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Expand Up @@ -914,23 +914,24 @@ def linear_eq_to_matrix(equations, *symbols):
The Matrix form corresponds to the augmented matrix form.
For example:

4.x + 2.y + 3.z = 1
3.x + y + z = -6
2.x + 4.y + 9.z = 2
.. math:: 4x + 2y + 3z = 1
.. math:: 3x + y + z = -6
.. math:: 2x + 4y + 9z = 2

This system would return A & b as given below:
This system would return `A` & `b` as given below:

[ 4 2 3 ] [ 1 ]
[ 3 1 1 ] [-6 ]
[ 2 4 9 ] [ 2 ]
::

[ 4 2 3 ] [ 1 ]
A = [ 3 1 1 ] b = [-6 ]
[ 2 4 9 ] [ 2 ]

Examples
========

>>> from sympy.solvers.solveset import linear_eq_to_matrix
>>> from sympy import symbols
>>> x, y, z = symbols('x, y, z')

>>> eqns = [x + 2*y + 3*z - 1, 3*x + y + z + 6, 2*x + 4*y + 9*z - 2]
>>> A, b = linear_eq_to_matrix(eqns, [x, y, z])
>>> A
Expand All @@ -943,7 +944,6 @@ def linear_eq_to_matrix(equations, *symbols):
[ 1],
[-6],
[ 2]])

>>> eqns = [x + z - 1, y + z, x - y]
>>> A, b = linear_eq_to_matrix(eqns, [x, y, z])
>>> A
Expand Down Expand Up @@ -1022,27 +1022,31 @@ def linsolve(system, *symbols):
For the given set of Equations, the respective input types
are given below:

3*x + 2*y - z = 1
2*x - 2*y + 4*z = -2
2*x - y + 2*z = 0
.. math:: 3x + 2y - z = 1
.. math:: 2x - 2y + 4z = -2
.. math:: 2x - y + 2z = 0

* Augmented Matrix Form, `system` given below:

* Augmented Matrix Form
::

[3 2 -1 1]
system = [2 -2 4 -2] (Matrix)
[2 -1 2 0]
[3 2 -1 1]
system = [2 -2 4 -2]
[2 -1 2 0]

* List Of Equations Form

system = [3*x + 2*y - z - 1, 2*x - 2*y + 4*z + 2, 2*x - y + 2*z]
`system = [3x + 2y - z - 1, 2x - 2y + 4z + 2, 2x - y + 2z]`

* Input A & b Matrix Form (from Ax = b)
* Input A & b Matrix Form (from Ax = b) are given as below:

[3 2 -1 ] [ 1 ]
A = [2 -2 4 ] b = [ -2 ]
[2 -1 2 ] [ 0 ]
::

system = (A, b)
[3 2 -1 ] [ 1 ]
A = [2 -2 4 ] b = [ -2 ]
[2 -1 2 ] [ 0 ]

`system = (A, b)`

Symbols to solve for should be given as input in all the
cases either in an iterable or as comma separated arguments.
Expand Down Expand Up @@ -1085,7 +1089,6 @@ def linsolve(system, *symbols):
>>> from sympy import Matrix, S
>>> from sympy import symbols
>>> x, y, z = symbols("x, y, z")

>>> A = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 10]])
>>> b = Matrix([3, 6, 9])
>>> A
Expand All @@ -1098,7 +1101,6 @@ def linsolve(system, *symbols):
[3],
[6],
[9]])

>>> linsolve((A, b), [x, y, z])
{(-1, 2, 0)}

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