Dear Mitch,

I am sorry but I still do not understand why you are expecting this to evaluate to $\sqrt{29}$ for all $t$. It is true that this should evaluate to $\sqrt{29}$ if $t$ was real, but if it wasn't it is a mistake to make that particular simplification. For example:

FullSimplify[Norm[r'[t]] /. t -> 1] 

gives $\sqrt{29}$, but if I substitute another perfectly valid number for $t$ this expression does not evaluate to $\sqrt{29}$:

FullSimplify[Norm[r'[t]] /. t -> I]

So if, without further information, Mathematica were to reduce the equation to $\sqrt{29}$, that would be incorrect, because it does not hold for complex numbers in general. So I think that Mathematica does not simplify the equation in the way you wish it to do, because it would be incorrect in general. So I would think that this can definitely not be reported as broken code, but rather as expected and desired behaviour.

Or am I missing the point here?

Cheers,

Marco

Thanks so much, that worked great!

Mitch Sandlin

Hi Macro;

I tried the Simplify[ ] command with the Reals definition on both the Norm[ ] and Normalize[ ] commands without any change to either output - see attached. If I am doing something wrong, I certainly can't figure it out.

Thanks,

Mitch Sandlin

Attachments:

Hi;

Attached is yet another example of the Norm[ ] command not reducing to the correct answer when using Trig functions. As can be seen by inspection the answer should be SqRoot(29). However it appears that the subsequent Integrate[ ] command produced the correct answer. In using the Norm[ ] command, I have tried Simplify[ ], FullSimplify[ ] and TrigReduce[ ] commands and they all produce very similar answers to just using the Norm[ ] command by itself. I realize that I am using the Norm[ ] command in a very simplistic manner, but it still seems that it should produce the expected reduced answer.

Is there someone at Mathematica that can tell me what I am doing wrong, if I am in fact doing something wrong, or can this be reported as possibly broken code. By the way, I am using version 9 of Mathematica.

Thanks,

Mitch Sandlin

Attachments:

Hi Sander,

It is my understanding that the Norm is a scalar length of a vector (or magnitude). It converts the vector into a scalar by summing the squares of the individual vector components and then takes the square root, and this is what I am assuming that the Norm[ ] command does in Mathematica.

My end goal is to normalize the vector, which I would do by dividing the individual vector values by the norm. Incidentally, I tried to use the Normalize[ ] command in Mathematica, and it didn’t give me the expected results either – see attached.

In the attached, the answers are somewhat correct. However, the denominators are not reduced. In this example, the denominators should simplify to 2.

Thanks so much, I certainly appreciate your time in helping me with this.

Mitch Sandlin

Attachments:

As you say, you need a vector, you gave it a formula, that simplify doesn't work the way you want it to. Perhaps you want to normalize using an integral over a certain domain?

Your notebook does not contain Sin[x]^2 + Cos[x]^2. Even if it did, as Sander says, it is not a convention that Norm simplifies trig expressions. However:

In[9]:= TrigReduce[Sin[x]^2 + Cos[x]^2]

Out[9]= 1

In[10]:= Simplify[Sin[x]^2 + Cos[x]^2]

Out[10]= 1