Euler Identity in Home

[ColinJDenman]

oh dear, I'm breaking my word.

I won't coment hugely on the detail discussed though I think it has been an interesting and useful thread.

I'd note sin(n*pi) - sin(pi) for n=1...6000000 suggests there is no mapping of x to 0<= x < 2pi, which I do think is appropriately correctable for sin, as is the appropriate short circuiting of the internal algorithm for 'well known' values of x and sin. As the CAS notes, sin(pi) is 0. Why doesn't the Home calculator defer to this superior result by internally defining "Home.sin(x)=eval(CAS.sin(x)) figuratively speaking. In this, I perhaps don't understand the resource consumption of having Home.calc and the segregation between. The code for a better result is already in there somewhere.

If I process observational data, I should estimate the error margins in the result from observational errors and lose superfluous precision. Simple functions show rounding errors. What about the result from a more complex calculation of many operations such as might occur in a program. How do I estimate the computational error in each and every calculation I perform without considerable extra work, in order to estimate the result I get plus or minus a relevant margin?

My attitude from the beginning has been a concern that observable error in a one-shot simple calculation questions what the errors are in a more complex one. And how to estimate them and rely on the results I see..

You might like to try Cos(pi/2)/(sin(pi)

My silence over the week in part extends from a painful back injury last Monday. This is my first session online since. And probably the last for a bit longer :-(