# Expansión de series multivariadas en sympy

Does anyone know if there is a built-in function in sympy to obtain a multivariate series expansion of the form

``````f(x,y) = a + b*x + c*y + d*x**2 + e*x*y + f*y**2 + ...
``````

i.e. by ascending order in all variables?

Gracias de antemano.

preguntado el 09 de septiembre de 13 a las 23:09

What do you start with (a polynomial, some other (analytic) function)? What kind of output do you expect? (A polynomial, a list of monomials, something different?) -

Hi Piotr, I am interested in power series expansions of any multivariate function, as a multivariate variant of "series": -

I had meant to continue with an example: something like (exp(x)*exp(y)).series() giving 1 + x + y + x2/2 + x*y + y2/2 + ... -

## 2 Respuestas

It is maybe too late but here is what I would do. It is not exactly a builtin function but it does the job. The idea is to introduce a temporary variable (eps) using substitutions and to expand the series over it. Here is an example:

``````import sympy
x, y , eps = sympy.symbols('x y eps')
f = sympy.exp(x-y)
f.subs(x,x*eps).subs(y,y*eps).series(eps).removeO().subs(eps,1)
``````

Note that using this technique you can have "asymmetric" expansions in x and y. For instance: `f.subs(x,x*eps).subs(y,y*eps**2)` ...

Respondido el 04 de diciembre de 14 a las 13:12

The short answer is that currently (sympy build 0.7.5), there is no built-in function in sympy that will handle multivariate series expansions.

There appears to be support for series expansion of multivariate functions in . solo variables. You can see this in the docstring of `_eval_nseries` en el capítulo respecto a la `function` documentación aquí. If this is important to you, you can comment on the Rastreador de problemas o unirse a la lista de correo.

So, to be clear, this works:

``````In : import sympy as sp
In : x, y = sp.symbols('x,y')
In : g = sp.exp(-x*y)
In : g
Out: exp(-x*y)
In : g.series(x, 0)
Out: 1 - x*y + x**2*y**2/2 - x**3*y**3/6 + x**4*y**4/24 - x**5*y**5/120 + O(x**6)
In : g.series(y, 0)
Out: 1 - x*y + x**2*y**2/2 - x**3*y**3/6 + x**4*y**4/24 - x**5*y**5/120 + O(y**6)
``````

but there is none of your desired functionality in any of the following:

``````In : g.series((x, y), (0, 0))
Out: exp(-x*y)

In : g.series((x, 0), (y, 0))
Out: exp(-x*y)

In : g.series(x, 0, y, 0)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-21-20c1ab732928> in <module>()
----> 1 g.series(x, 0, y, 0)

/usr/lib/python2.7/dist-packages/sympy/core/expr.pyc in series(self, x, x0, n, dir, logx)
2401                 return self
2402
-> 2403         if len(dir) != 1 or dir not in '+-':
2404             raise ValueError("Dir must be '+' or '-'")
2405

TypeError: object of type 'int' has no len()

In : g.series(x, y, 0, 0)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-22-32b57736cd3d> in <module>()
----> 1 g.series(x, y, 0, 0)

/usr/lib/python2.7/dist-packages/sympy/core/expr.pyc in series(self, x, x0, n, dir, logx)
2401                 return self
2402
-> 2403         if len(dir) != 1 or dir not in '+-':
2404             raise ValueError("Dir must be '+' or '-'")
2405

TypeError: object of type 'int' has no len()
``````

contestado el 12 de mayo de 14 a las 23:05

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