Show code: [gcaops]

The sea of Poisson Structures and its Graph Complex flows

Index » Generic Poisson structure on $\mathbb{R}^2$

Alternative names:
  • Arbitrary Poisson structure on $\mathbb{R}^2$
  • Bi-vector field on $\mathbb{R}^2$
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Definition

Formula:$P = u \frac{\partial}{\partial x} \wedge \frac{\partial}{\partial y}$ where $u \in C^\infty(\mathbb{R}^2)$ is arbitrary.
Code (gcaops):
S.<xi1,xi2> = SuperfunctionAlgebra(SR, var('x,y'), simplify='expand', is_zero='is_trivial_zero')
P = function('u')(x,y)*xi1*xi2

Deformations