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fredrikj.net | ||
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0fps.net
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| | | | | Last time, we showed how one can use symmetric tensors to conveniently represent homogeneous polynomials and Taylor series. Today, I am going to talk about how to actually implement a generic homogeneous polynomial/symmetric tensor class in C++. The goal of this implementation (for the moment) is not efficiency, but rather generality and correctness. If there... | |
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www.jeremykun.com
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| | | | | Problem: Compute the product of two polynomials efficiently. Solution: import numpy from numpy.fft import fft, ifft def poly_mul(p1, p2): """Multiply two polynomials. p1 and p2 are arrays of coefficients in degree-increasing order. """ deg1 = p1.shape[0] - 1 deg2 = p1.shape[0] - 1 # Would be 2*(deg1 + deg2) + 1, but the next-power-of-2 handles the +1 total_num_pts = 2 * (deg1 + deg2) next_power_of_2 = 1 << (total_num_pts - 1). | |
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cp4space.hatsya.com
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| | | | | At the end of the recent post on a combinatorial proof of Houston's identity, I ended with the following paragraph: This may seem paradoxical, but there's an analogous situation in fast matrix multiplication: the best known upper bound for the tensor rank of 4-by-4 matrix multiplication is 49, by applying two levels of Strassen's algorithm,... | |
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nurkiewicz.com
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| | | Yukihiro Matsumoto, the creator of Ruby programming language, famously said: | ||
