On Tue, Oct 8, 2013 at 10:02 AM, Taylan Şengül <[email protected]> wrote:
> Hi all,
>
> I am quite new to sympy.
>
> When I type the following
>
> a = symbols('a')
> m = Matrix( [ [a, 0], [0, 1] ] )
> m.eigenvals()
>
> I expect the answer to
> {a: 1, 1: 1}
>
> But I get
>
> {a/2 + sqrt((a - 1)**2)/2 + 1/2: 1, a/2 - sqrt((a - 1)**2)/2 + 1/2: 1}
>
> I think first the characteristic polynomial is computed and then roots are
> found. This produces the mess. Wouldn't it be better to try to factor the
> characteristic polynomial first and then find roots?
SymPy assumes that "a" is complex, so no simplifications can be done, isn't it?
But you can tell SymPy that "a" is real, then some simplifications can be done:
In [1]: a = symbols('a')
In [2]: m = Matrix( [ [a, 0], [0, 1] ] )
In [3]: m.eigenvals()
Out[3]:
⎧ __________ __________ ⎫
⎪ ╱ 2 ╱ 2 ⎪
⎨a ╲╱ (a - 1) 1 a ╲╱ (a - 1) 1 ⎬
⎪─ - ───────────── + ─: 1, ─ + ───────────── + ─: 1⎪
⎩2 2 2 2 2 2 ⎭
In [4]: a = Symbol("a", real=True)
In [5]: m = Matrix( [ [a, 0], [0, 1] ] )
In [6]: m.eigenvals()
Out[6]:
⎧a │a - 1│ 1 a │a - 1│ 1 ⎫
⎨─ - ─────── + ─: 1, ─ + ─────── + ─: 1⎬
⎩2 2 2 2 2 2 ⎭
Ondrej
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