We present symbolic and numerical methods for computing Poisson brackets on the spaces of measures with positive densities of the plane, the 2-torus, and the 2-sphere. We apply our methods to compute symplectic areas of finite regions for the case of the 2-sphere, including an explicit example for Gaussian measures with positive densities.

翻译：我们用象征性和数字方法计算波瓦森括号在平面、平面、平面和两层的正密度的测量空间上。 我们用我们的方法计算2层的定点区域的间隙区域,包括一个带有正密度的高斯措施的明显例子。