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taylor(1/(x^8+1),x,rectform(exp(%i*%pi/8)),1) incorrect #298

Open rtoy opened 2 days ago

rtoy commented 2 days ago

Imported from SourceForge on 2024-07-02 15:30:45 Created by rtoy on 2012-07-25 02:23:40 Original: https://sourceforge.net/p/maxima/bugs/2453

The expansion of taylor(1/(x^8+1),x,rectform(exp(%i*%pi/8)),1) appears to be incorrect. The expansion only contains powers of (x-exp(%i*%pi/8)). However, taylor(1/(x^8+1),x,exp(%i*%pi/8),1) appears to be correct and very different from the first result.

rtoy commented 2 days ago

Imported from SourceForge on 2024-07-02 15:30:46 Created by rtoy on 2012-07-26 16:23:21 Original: https://sourceforge.net/p/maxima/bugs/2453/#00d5

If you look at the expansion with rectform, the leading term is free of x. If you run trigreduce and expand on it, you'll get a division by 0 error. I'm guessing taylor returns the wrong result because it couldn't determine that the expression has a pole there.