max125

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@tomleslie Thankyou for your reply.

Question. What is the exact difference between sort and collect. why do they work differently.

I have uploaded the document so you can view the differences. Here is a screenshot.

http://prntscr.com/8juzta

Here is the worksheet.

collect.mw

@Markiyan Hirnyk thankyou for youre reply

@Rouben Rostamian  

that seems work, thankyou.

but... there may be a situation where you can't use surd. I am looking for examples.

j:= x-> x^2.875

now i have problems with complex numbers

diff(j(x),x)

evalf(j(-2))  comes out complex answer

So i have to turn 2.875 into a rational number. 

I tried

j(-2) gave me

Oh nevermind, surd(x,8) is not defined for x<0 reals anyway.

which is complex

There are also possible problems if you raise a number to a square root

m:= x-> x^cuberoot 3

m(-2)

 

Also what exactly is the definition of the principal cube root of -1, it is necessarily a complex number?

I know the principal square root of 4 is 2.

 

Does (RealDomain); get you the same result with fractional exponents? I tried it and got a messy expression with signum's everywhere.

 

Also odd is the fact

evalf(surd(-2,8)) does not equal evalf((-2)^(1/8))

shouldn't they be equal since if x < 0 , the surd becomes complex

 

more observations:

does not simplify as well as your expression

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