Thomas Madden

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15 years, 126 days

MaplePrimes Activity


These are replies submitted by Thomas Madden

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
Also, and perhaps better information at plab and "Randomness for crypto" from Berkeley
Also, and perhaps better information at plab and "Randomness for crypto" from Berkeley
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.
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.
I don't mean to quibble, but after reading the posts by Jacques and Dave I think it is an appropriately chosen term. Thomas
I don't mean to quibble, but after reading the posts by Jacques and Dave I think it is an appropriately chosen term. Thomas

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);

Maple Equation

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 Equation

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)];

Maple Equation

>

> allvalues(S);

Maple Equation

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;

Maple Equation

> diff(ex1,x);

Maple Equation

> allvalues(%);

Maple Equation

> int(ex1,x);

Maple Equation

> allvalues(%);

Maple Equation

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

Hope this helps,

Thomas

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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);

Maple Equation

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 Equation

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)];

Maple Equation

>

> allvalues(S);

Maple Equation

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;

Maple Equation

> diff(ex1,x);

Maple Equation

> allvalues(%);

Maple Equation

> int(ex1,x);

Maple Equation

> allvalues(%);

Maple Equation

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

Hope this helps,

Thomas

This post was generated using the MaplePrimes File Manager

View 162_RootOf.mw on MapleNet or Download 162_RootOf.mw
View file details

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
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
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
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
Prior to that other thread I pretty much only used 2D input whether in document or worksheet mode for the purposes of printing or presentation. After I started reconsider the idea of working in document mode. I also noticed that many new documents at the application center were done in document mode and the results were very impressive. Just like a textbook. Lately, I have been working in document mode more frequently and for all of the reasons you have stated above so eloquently I am really starting to love it. So for me the answer is yes. Thomas
Thanks Jacques. Although I am not sure I want to be on the first page in the ranking. It gives people the impression I might actually know something about Maple. My current user knowledge is only good for answering the most basic questions and even then I might not give the best method. Congrats on 600+ it looks like alec is not going to stay at the top for long. I do miss his post though. Maybe he is watching afar and this will give him incentive to start posting again. Thomas
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