Roughly it can be viewed as a change of coordinates and then recognizing the symmetry. Say you had a 2D function of x and y and transformed it to r and theta and then noticed that it was independent of theta. You go from an 2D problem to a 1D one.
In this case we’re transforming a 7D problem into a sum of a discrete set of 2D problems. With more algebra we could get it down to a 1D problem but that would take more human work that wouldn’t be paid off later in CPU time. If their project ends up scaling and the 1D transformation makes sense, we’ll do it.
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Roughly it can be viewed as a change of coordinates and then recognizing the symmetry. Say you had a 2D function of x and y and transformed it to r and theta and then noticed that it was independent of theta. You go from an 2D problem to a 1D one.
In this case we’re transforming a 7D problem into a sum of a discrete set of 2D problems. With more algebra we could get it down to a 1D problem but that would take more human work that wouldn’t be paid off later in CPU time. If their project ends up scaling and the 1D transformation makes sense, we’ll do it.
What field of mathematics is this?