Hi Vladimir! On 06.04.20 14:34, Vladimir V. Kisil wrote:
Coming back to our previous discussion (with a long history) on the power law (e^x)^a=e^(x*a). I am attaching a patch which does not break the automatic simplification exp(x)/exp(x)=1.
Your new patch is much better since it doesn't break any existing test suite. Playing around with it, it still seems to raise some fundamental questions: What justifies treating exp(x)^a fundamentally different than any other (b^x)^a with a (positive) base b? With the patch, there seems to be this discrimination: exp(x)^5 is rewritten to exp(5*x) but (b^x)^5 is _not_ rewritten to b^(5*x). It's a nice pastime to fancy consequences of this. Let y=b^x, then normal((y^2-1)/(y+1)) returns b^x-1. But if y=exp(x), the patch prevents the normalization to exp(x)-1. Ugh. Or, consider this gedankenexperiment: If we didn't have exp(x) as a function but instead a symbol e, would it be justified to have special re-writing rules for (e^x)^a but not for (b^x)^a? I'm not sure... Best wishes, -richy. -- Richard B. Kreckel <https://in.terlu.de/~kreckel/>