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Apr 22, 2025, 14:07:18

The old me is the young me if you think about it.

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Articles

  • Monkey-patching graciously

    Monkey-patching is a powerful tool in programming. In this article, I used techniques of Ruby metaprogramming to define a series of methods def_after, def_before, etc. to help monkey-patching. They look graciously in that we can use it to shorten the codes for monkey-patching (avoiding aliasing and repeating codes).

  • Amazing Siteleaf

    I have been using Siteleaf to manage my blog. It is just convenient and amazing.

  • Hyperellipsoids in barycentric coordinates

    In this article, I introduce the barycentric coordinates: it is an elegant way to represent geometric shapes related to a simplex. By using it, given a simplex, we can construct a hyperellipsoid with the properties: its surface passes every vertex of the simplex, and its tangent hyperplane at each vertex is parallel to the hyperplane containing all other vertices.

  • Use complex numbers as canonical variables

    In this article, I try exploring an idea: using complex numbers to combine pairs of canonical variables into complex variables: cαq+iβp\mathbf c\coloneqq\alpha\mathbf q+\mathrm i\beta\mathbf p. It turns out that we can write canonical equations dcdt=2iαβHc\frac{\mathrm d\mathbf c}{\mathrm dt}=-2\mathrm i\alpha\beta\frac{\partial\mathcal H}{\partial\mathbf c^*}, Poisson brackets {f,g}=2iαβ(fcgcfcgc)\left\{f,g\right\}=-2\mathrm i\alpha\beta \left(\frac{\partial f}{\partial\mathbf c}\cdot \frac{\partial g}{\partial\mathbf c^*}- \frac{\partial f}{\partial\mathbf c^*}\cdot \frac{\partial g}{\partial\mathbf c}\right), and canonical transformations cc=cc,cc=cc\frac{\partial\mathbf c^*}{\partial\mathbf c'^*}= \frac{\partial\mathbf c'}{\partial\mathbf c}, \frac{\partial\mathbf c}{\partial\mathbf c'^*}= -\frac{\partial\mathbf c'}{\partial\mathbf c^*} in these complex numbers. Finally, I show two examples of using them in real problems: a free particle, and a harmonic oscillator.

  • Giving birth to my own blog

    This is my first blog! I will share interesting things in my life here.

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