How can I solve system of linear equations in SymPy?

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Sorry, I am pretty new to sympy and python in general.

I want to solve the following underdetermined linear system of equations:

x + y + z = 1 
x + y + 2z = 3

SymPy recently got a new Linear system solver: linsolve in sympy.solvers.solveset, you can use that as follows:

In [38]: from sympy import *

In [39]: from sympy.solvers.solveset import linsolve

In [40]: x, y, z = symbols('x, y, z')

List of Equations Form:

In [41]: linsolve([x + y + z - 1, x + y + 2*z - 3 ], (x, y, z))
Out[41]: {(-y - 1, y, 2)}

Augmented Matrix Form:

In [59]: linsolve(Matrix(([1, 1, 1, 1], [1, 1, 2, 3])), (x, y, z))
Out[59]: {(-y - 1, y, 2)}

A*x = b Form

In [59]: M = Matrix(((1, 1, 1, 1), (1, 1, 2, 3)))

In [60]: system = A, b = M[:, :-1], M[:, -1]

In [61]: linsolve(system, x, y, z)
Out[61]: {(-y - 1, y, 2)}

Note: Order of solution corresponds the order of given symbols.

How can I solve system of linear equations in SymPy?, The main function for solving algebraic equations is solveset . In the solveset module, the linear system of equations is solved using linsolve . In future we� In the solveset module, the linear system of equations is solved using linsolve.In future we would be able to use linsolve directly from solveset.Following is an example of the syntax of linsolve.

In addition to the great answers given by @AMiT Kumar and @Scott, SymPy 1.0 has added even further functionalities. For the underdetermined linear system of equations, I tried below and get it to work without going deeper into sympy.solvers.solveset. That being said, do go there if curiosity leads you.

from sympy import *
x, y, z = symbols('x, y, z')
eq1 = x + y + z
eq2 = x + y + 2*z
solve([eq1-1, eq2-3], (x, y,z))

That gives me {z: 2, x: -y - 1}. Again, great package, SymPy developers!

sympy, 5 Answers. List of Equations Form: In [41]: linsolve([x + y + z - 1, x + y + 2*z - 3 ], (x, y, z)) Out[41]: {(-y - 1, y, 2)} Augmented Matrix Form: In [59]: linsolve(Matrix(([1, 1, 1, 1], [1, 1, 2, 3])), (x, y, z)) Out[59]: {(-y - 1, y, 2)} (A solution for y is obtained because it is the first variable from the canonically sorted list of symbols that had a linear solution.) sympy.solvers.solvers.solve_linear_system (system, * symbols, ** flags) [source] ¶ Solve system of \(N\) linear equations with \(M\) variables, which means both under- and overdetermined systems are supported

import sympy as sp
x, y, z = sp.symbols('x, y, z')
eq1 = sp.Eq(x + y + z, 1)             # x + y + z  = 1
eq2 = sp.Eq(x + y + 2 * z, 3)         # x + y + 2z = 3
ans = sp.solve((eq1, eq2), (x, y, z))

this is similar to @PaulDong answer with some minor changes

  1. its a good practice getting used to not using import * (numpy has many similar functions)
  2. defining equations with sp.Eq() results in cleaner code later on

Solving Systems Of Equations Using Sympy And Numpy (Python , sympy Solve system of linear equations. Example#. import sympy as sy x1, x2 = sy.symbols("x1� The article explains how to solve a system of linear equations using Python's Numpy library. You can either use linalg.inv() and linalg.dot() methods in chain to solve a system of linear equations, or you can simply use the solve() method. The solve() method is the preferred way.

You can solve in matrix form Ax=b (in this case an underdetermined system but we can use solve_linear_system):

from sympy import Matrix, solve_linear_system

x, y, z = symbols('x, y, z')
A = Matrix(( (1, 1, 1, 1), (1, 1, 2, 3) ))
solve_linear_system(A, x, y, z)

{x: -y - 1, z: 2}

Or rewrite as (my editing, not sympy):

[x]=  [-1]   [-1]
[y]= y[1]  + [0]
[z]=  [0]    [2]

In the case of a square A we could define b and use A.LUsolve(b).

Solving symbolic equations with SymPy, In this video I go over two methods of solving systems of linear equations in python. One method Duration: 15:23 Posted: Jun 19, 2018 SymPy is a Python library for symbolic mathematics. It is one of the layers used in SageMath, the free open-source alternative to Maple/Mathematica/Matlab. When you have simple but big calculations that are tedious to be solved by hand, feed them to SymPy, and at least you can be sure it will make no calculation mistake ;-) The basic functionalities of SymPy are expansion/factorization

Another example on matrix linear system equations, lets assume we are solving for this system:

In SymPy we could do something like:

>>> import sympy as sy
... sy.init_printing()

>>> a, b, c, d = sy.symbols('a b c d')
... A = sy.Matrix([[a-b, b+c],[3*d + c, 2*a - 4*d]])
... A

⎡ a - b     b + c  ⎤
⎢                  ⎥
⎣c + 3⋅d  2⋅a - 4⋅d⎦


>>> B = sy.Matrix([[8, 1],[7, 6]])
... B

⎡8  1⎤
⎢    ⎥
⎣7  6⎦


>>> A - B

⎡ a - b - 8     b + c - 1  ⎤
⎢                          ⎥
⎣c + 3⋅d - 7  2⋅a - 4⋅d - 6⎦


>>> sy.solve(A - B, (a, b, c, d))
{a: 5, b: -3, c: 4, d: 1}

Solving simultaneous equations with sympy — reliability latest , SymPy is a Python library for symbolic mathematics. It is one of Solving a system of quadratic equations Consider the following system of quadratic equations:� Chapter 3: Equations Examples Solve system of linear equations import sympy as sy x1, x2 = sy.symbols("x1 x2") equations = [ sy.Eq( 2*x1 + 1*x2 , 10 ),

Solving Two Equations for Two Unknowns and a Statics Problem , This document is a tutorial for how to use the Python module sympy to solve simultaneous equations. Since sympy does this so well, there is no need to implement� Using symbolic math, we can define expressions and equations exactly in terms of symbolic variables. We reviewed how to create a SymPy expression and substitue values and variables into the expression. Then we created to SymPy equation objects and solved two equations for two unknowns using SymPy's solve() function.

Solving Equations and Writing Expressions with SymPy and Python , SymPy (http://www.sympy.org) is a Python library for symbolic math. To solve this system of two equations for the two unknows x and y, first� Systems of linear equations are a common and applicable subset of systems of equations. In the case of two variables, these systems can be thought of as lines drawn in two-dimensional space. If all lines converge to a common point, the system is said to be consistent and has a solution at this point of intersection.

Proper solution of linear equations with symbolic coefficients � Issue , SymPy (http://www.sympy.org) is a Python library for symbolic math. In symbolic math, symbols are used to represent mathematical expressions� I've create a linear system of equations in a for loop using sympy symbols and stored all equations in a numpy array. In the present moment I'm using sympy.linear_eq_to_matrix to "transform" the equations in to a matrix and solve then. But, this process using sympy.linear_eq_to_matrix is taking a long time when I've a lot of variables.

Comments
  • What have you tried so far? What has your research efforts yielded? A websearch appears to offer lots of examples. Please tell me you read the documentation and searched before asking.
  • I tried this: solve_linear_system(M, (x, y, z)), where M = Matrix(((1, 1, 1, - 1), (1, 1, 2, - 3))), It gave me an IndexError.
  • You have fewer equations than unknowns here. You need an SVD solver, not the usual linear solver when you have equal numbers of equations and unknowns. There's no guarantee of a unique solution.
  • It should be noted, that linsolve is not yet available in any release. Currently accessible only through the development version.
  • I am using sympy 0.7.6, First I could not get linsolve so used solve, Second The Augmented matrix and Ax = b form gives EMPTY LIST [ ] answer, only first method gives solution as like above, how can we fix this?
  • Adding further explanation would help readers understand why your answer is better than the others and enable them to vote for you. Expand your answer using the edit function.