## 178 Reputation

17 years, 122 days

## Primes...

Daniel, I'm glad the links were helpful. I can't comment beyond that because I am not knowledgeable enough in these areas. Fortunately, Jacques was able to respond before I read your post. Thomas

## Random...

Also, and perhaps better information at plab and "Randomness for crypto" from Berkeley

## Random...

Also, and perhaps better information at plab and "Randomness for crypto" from Berkeley

## name...

It seems appropriate in the sense of "unappply" an application of some sort. But I trust that in these matters your judgment is much better than mine. BTW you are very close to 700. I think it is time to start the drum roll.

## name...

It seems appropriate in the sense of "unappply" an application of some sort. But I trust that in these matters your judgment is much better than mine. BTW you are very close to 700. I think it is time to start the drum roll.

## unapply...

I don't mean to quibble, but after reading the posts by Jacques and Dave I think it is an appropriately chosen term. Thomas

## unapply...

I don't mean to quibble, but after reading the posts by Jacques and Dave I think it is an appropriately chosen term. Thomas

## RootOf...

William, do not hesitate to ask questions, that's why Maplesoft created this site. Chances are that every question you ask will help at least one other person. In this case it forced me to take a better look at RootOf. Here is a simple example that may help you or anyone else looking at this thread to better understand RootOf.

> restart:

> R:=RootOf(z^3-8);

So R is just a set containing the three roots which are evenly spaced around to circle of radius 2 in the complex plane. To see them we can do

> allvalues(R);

Maple keeps track of the roots by using an index. To see a list do

> S:=[seq(RootOf(z^3-8, index=i), i=1..3)];

>

> allvalues(S);

But, if I understand correctly the real benefit of these objects is that you can continue to work symbolically with any expressions that contain them. This helps keep the expressions manageable and at the same time you can continue to do exact aritmetic. Here is a simple example

> ex1:=x^3*R;

> diff(ex1,x);

> allvalues(%);

> int(ex1,x);

> allvalues(%);

So from this I can see that there are real advantages in using RootOf.

Hope this helps,

Thomas

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## RootOf...

William, do not hesitate to ask questions, that's why Maplesoft created this site. Chances are that every question you ask will help at least one other person. In this case it forced me to take a better look at RootOf. Here is a simple example that may help you or anyone else looking at this thread to better understand RootOf.

> restart:

> R:=RootOf(z^3-8);

So R is just a set containing the three roots which are evenly spaced around to circle of radius 2 in the complex plane. To see them we can do

> allvalues(R);

Maple keeps track of the roots by using an index. To see a list do

> S:=[seq(RootOf(z^3-8, index=i), i=1..3)];

>

> allvalues(S);

But, if I understand correctly the real benefit of these objects is that you can continue to work symbolically with any expressions that contain them. This helps keep the expressions manageable and at the same time you can continue to do exact aritmetic. Here is a simple example

> ex1:=x^3*R;

> diff(ex1,x);

> allvalues(%);

> int(ex1,x);

> allvalues(%);

So from this I can see that there are real advantages in using RootOf.

Hope this helps,

Thomas

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## RootOf...

This is not unique to Maple. Mathematica does the same thing with Root Objects. My impression from reading post in both groups is that experienced users prefer this representation. Representation in terms of radicals often becomes to unwieldy. One of the hard things to get used to with a CAS is that the methods that they employ are often not familiar to the user. They rely on theory that is not typically seen by most undergraduate students any by many graduate students as well. Maple is actually much more user friendly in this regard than other CAS. They have student packages and tutors on the tools menu which assist you in using Maple in ways more closely related to textbook problems. It is a little difficult getting over the initial hurdle of sometimes having to do and see things differently than you are used to. My experience is that I have actually learned a great deal of mathematics as a result. The more I use Maple, the more I am impressed by what it can do, and what I can learn from the way it does it. You are taking the right approach, just keep posting questions as they come and the users here who helped me work through the same issues will help you as well. Thomas

## RootOf...

This is not unique to Maple. Mathematica does the same thing with Root Objects. My impression from reading post in both groups is that experienced users prefer this representation. Representation in terms of radicals often becomes to unwieldy. One of the hard things to get used to with a CAS is that the methods that they employ are often not familiar to the user. They rely on theory that is not typically seen by most undergraduate students any by many graduate students as well. Maple is actually much more user friendly in this regard than other CAS. They have student packages and tutors on the tools menu which assist you in using Maple in ways more closely related to textbook problems. It is a little difficult getting over the initial hurdle of sometimes having to do and see things differently than you are used to. My experience is that I have actually learned a great deal of mathematics as a result. The more I use Maple, the more I am impressed by what it can do, and what I can learn from the way it does it. You are taking the right approach, just keep posting questions as they come and the users here who helped me work through the same issues will help you as well. Thomas

## RootOf,indexed...

The roots are indexed, see ?RootOf,indexed. So _L2 is just indicating that RootOf(_Z^2 - 3, lable=_L2) can be either of the roots for _Z^2 - 3. So it is just a convenient notation for the whole set of roots. Note there is nothing special about the 2 in _L2, if you evaluate the line again you might get _L12 or _L(some Integer). However, if you use evalf: When evaluated numerically, the labeled RootOf returns the value of the principal branch, that is, evalf(RootOf(expr,label=...)) is equivalent to evalf(RootOf(expr,index=1)). (from the help ?RootOf) Thomas

## RootOf,indexed...

The roots are indexed, see ?RootOf,indexed. So _L2 is just indicating that RootOf(_Z^2 - 3, lable=_L2) can be either of the roots for _Z^2 - 3. So it is just a convenient notation for the whole set of roots. Note there is nothing special about the 2 in _L2, if you evaluate the line again you might get _L12 or _L(some Integer). However, if you use evalf: When evaluated numerically, the labeled RootOf returns the value of the principal branch, that is, evalf(RootOf(expr,label=...)) is equivalent to evalf(RootOf(expr,index=1)). (from the help ?RootOf) Thomas