def rref_solve(matlist, variable, constant, K):
"""
Solves a system of equations using reduced row echelon form given
a matrix of coefficients, a vector of variables and a vector of constants.
Examples
========
>>> from sympy.matrices.densesolve import rref_solve
>>> from sympy import QQ
>>> from sympy import Dummy
>>> x, y, z = Dummy('x'), Dummy('y'), Dummy('z')
>>> coefficients = [
... [QQ(25), QQ(15), QQ(-5)],
... [QQ(15), QQ(18), QQ(0)],
... [QQ(-5), QQ(0), QQ(11)]]
>>> constants = [
... [QQ(2)],
... [QQ(3)],
... [QQ(1)]]
>>> variables = [
... [x],
... [y],
... [z]]
>>> rref_solve(coefficients, variables, constants, QQ)
[[-1/225], [23/135], [4/45]]
See Also
========
row_echelon
augment
"""
new_matlist = copy.deepcopy(matlist)
augmented = augment(new_matlist, constant, K)
solution = rref(augmented, K)
return col(solution, -1)
def rref_solve(matlist, variable, constant, K):
"""
Solves a system of equations using reduced row echelon form given
a matrix of coefficients, a vector of variables and a vector of constants.
Examples
========
>>> from sympy.matrices.densesolve import rref_solve
>>> from sympy import QQ
>>> from sympy import Dummy
>>> x, y, z = Dummy('x'), Dummy('y'), Dummy('z')
>>> coefficients = [
... [QQ(25), QQ(15), QQ(-5)],
... [QQ(15), QQ(18), QQ(0)],
... [QQ(-5), QQ(0), QQ(11)]]
>>> constants = [
... [QQ(2)],
... [QQ(3)],
... [QQ(1)]]
>>> variables = [
... [x],
... [y],
... [z]]
>>> rref_solve(coefficients, variables, constants, QQ)
[[-1/225], [23/135], [4/45]]
See Also
========
row_echelon
augment
"""
new_matlist = copy.deepcopy(matlist)
augmented = augment(new_matlist, constant, K)
solution = rref(augmented, K)
return col(solution, -1)