4c82a578-6a63-41fb-ac07-9601fe834b17 6 6 5 auto

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Sanity check Mathematica 4.0

Y 1.3 2.4 1.7 4.1 2.9 1.7 5.1 2.7 18 mat transpose :

Fourier complex  from sampled  Y vector [Numeric] Y fft N Y length : i 1 - sqrt : n 0 N range D n 1 + el 1 N sqrt / Y k 1 + el e i 2 π * n * N / (* k *^* (k 0 N 1 - sum * : for D 41 line :

Symbolic F Y fft :

Fraction => Auto F 7.742819 0.740685 - 0.677082 i * - 0.919239 - 0.954594 i * - 0.390685 - 1.727082 i * + 0.035355 0.390685 - 1.727082 i * - 0.919239 - 0.954594 i * + 0.740685 - 0.677082 i * + 7.742819 91 mat

Y 1 - 1 - 1 - 1 - 111118 mat transpose :

F Y fft :

These two sanity check

F 0 0.707107 - 1.707107 i * - 0 0.707107 - 0.292893 i * - 0 0.707107 - 0.292893 i * + 0 0.707107 - 1.707107 i * + 091 mat

yy 0 0.707107 - 1.707107 i * - 0 0.707107 - 0.292893 i * - 0 0.707107 - 0.292893 i * + 0 0.707107 - 1.707107 i * + 091 mat :

=> copy/paste =>

Numeric vec ifft N vec length 1 - : i 1 - sqrt : n 0 N 1 - range ID n 1 + el 1 N sqrt / vec k 1 + el i - (2 π * n * N / (* k * exp * (k 0 N 1 - sum * : for ID 41 line :

Symbolic sanity yy ifft :

Fraction Auto sanity transpose 1 - 1 - 1 - 1 - 111118 mat

Y 11 - 113 mat transpose :

Symbolic F Y fft :

Fraction => Auto F 0.57735 0.57735 i - 0.57735 i + 0.57735 41 mat

q 0.57735 0.57735 i - 0.57735 i + 0.57735 41 mat :

Symbolic sanity q ifft :

=> copy/paste =>

Fraction Auto sanity transpose 11 - 113 mat