A computer algebra system written in pure Python http://sympy.org/ . To get started to with contributing https://github.com/sympy/sympy/wiki/Introduction-to-contributing
smichr on master
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smichr on master
Make ArrayAdd.as_explicit() wor… Merge pull request #22147 from … (compare)
r.subs(tau0, 0)
, both complain about tau0
not being defined
mysolution
is a numpy array as you could notice.
If no symbols are given, internally generated symbols will be used.
tau0
.
solution_as_list
, didn't returns a list per se, but a set with a tuple, as in: {(-0.916666666666667, 0.708333333333333, 0.375, -0.208333333333333, 0.0416666666666667, 0)}
of type sympy.sets.sets.FiniteSet
.
flatten
anyway... Never mind then
Actually,
solution = np.array(*[e for e in r_tmp]).astype(float)
should flatten it as well
wow. :-( Given the matrix PI
array([[ -0.917, 0.042, 0. , 0. , -1. ],
[ 0.708, -1.125, 0.042, 0. , 5. ],
[ 0.375, 1.125, -1.125, 0.042, -10. ],
[ -0.208, -0.042, 1.125, -1.125, 10. ],
[ 0.042, 0. , -0.042, 1.125, -5. ],
[ 0. , 0. , 0. , -0.042, 1. ]])
and the vector c
array([-1. , 0. , 0. , -0.042, 1.083, -0.042])
the solution given by
linsolve(Matrix(np.c_[PI,c]))
returns an EmptySet()
while the same operation in Maple 16 returns non empty, and exactly
np.array([649/576, 143/192, 75/64, 551/576, -25/13824])
that in float is around
array([ 1.127, 0.745, 1.172, 0.957, -0.002])
Any ideas?
PI = np.array([
[-11/12, 1/24, 0, 0, -1],
[ 17/24, -9/8, 1/24, 0 ,5],
[3/8, 9/8, -9/8, 1/24, -10],
[-5/24, -1/24, 9/8, -9/8, 10],
[1/24, 0, -1/24, 9/8, -5],
[0, 0, 0, -1/24, 1]
])
It seems that your system is over-determined. It has 6 equations in 5 variables. It can have solutions only if the determinant of the extended system is 0.
>>> P = Matrix([[ -0.917, 0.042, 0. , 0. , -1. ],
... [ 0.708, -1.125, 0.042, 0. , 5. ],
... [ 0.375, 1.125, -1.125, 0.042, -10. ],
... [ -0.208, -0.042, 1.125, -1.125, 10. ],
... [ 0.042, 0. , -0.042, 1.125, -5. ],
... [ 0. , 0. , 0. , -0.042, 1. ]])
>>> c = Matrix([-1. , 0. , 0. , -0.042, 1.083, -0.042])
>>> Pc = P.row_join(c)
>>> Pc.det()
0.000998125750125132
In this example, the determinant not 0 because of the inaccuracy of floating point numbers. Hence there is no solution.
A potential solution could be to define
rationalize = lambda x: [nsimplify(e) for e in x]
(this will turn numbers from a list into rationals). And then do
PI = Matrix(map(rationalize, [
[-11/12, 1/24, 0, 0, -1],
[ 17/24, -9/8, 1/24, 0 ,5],
[3/8, 9/8, -9/8, 1/24, -10],
[-5/24, -1/24, 9/8, -9/8, 10],
[1/24, 0, -1/24, 9/8, -5],
[0, 0, 0, -1/24, 1]
]))
and similarly for c
. I've just checked and this returns the right solutions
mrationalize = lambda x: [nsimplify(e) for e in [r for r in x]]
that I do not like much the fell.
I have a problem with calculating eigenvectors for a simple 3x3 matrix in sympy. Trying to execute
q = symbols("q", positive=True)
m = Matrix([[-2, exp(-q), 1], [exp(q), -2, 1], [1, 1, -2]])
#m.eigenvects(simplify=True)
m.eigenvals()
results in very complicated expressions for the eigenvalues, trying to get the eigenvectors fails with a NotImplementedError. I expect the latter to be due to the former. However, when trying to do the same thing in Mathematica, I get much simpler expressions for everything. Is there some option / flag that I can set to have sympy compute these eigenvalues and eigenvectors? Is there currently some form of limitation within sympy that prevents me from doing this?
simplify