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Hi,
Could someone please give me a 'yah' or 'nah' to the following please:
"The only situation where you will have more than one answer for a complex number is when you root the answer - i.e (a + ib)^1/2 means two answers, (a + ib)^1/3 means three answers"
Cheers,
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MarkBrock wrote: 'yah' or 'nah'
maybe, it depend on what the question is.
If you are asking about solutions to algebraic equations (polynomials like x^2=-1 but also more complex like 3x^4+2x^3+x+2) then the general rule is that an nth order equation has n roots. They may be real (x^2=1 has 2 roots +1 and -1).
There are lots of other equations e.g. log(x)=-1 and which can have an infinite number of solutions if there are no limits on x. You don't need complex numbers for this, the number of solutions to sin(x)=0 is also infinite.
So for a general function f(x), if you are solving for f(x)=a, then the graph of some functions pass the value of a for multiple values of x.
Peter
"Until the invention of the computer, the machine gun was the device that enabled humans to make the most mistakes in the smallest amount of time."
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I think we can safely say 'nah' then? 
Cheers mate.
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yah
Luc Pattyn [Forum Guidelines] [My Articles]
This month's tips:
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nah.
If the Lord God Almighty had consulted me before embarking upon the Creation, I would have recommended something simpler.
-- Alfonso the Wise, 13th Century King of Castile.
This is going on my arrogant assumptions. You may have a superb reason why I'm completely wrong.
-- Iain Clarke
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We're waiting for his revolutionary Data Hiding Algorithm [^].
If the Lord God Almighty had consulted me before embarking upon the Creation, I would have recommended something simpler.
-- Alfonso the Wise, 13th Century King of Castile.
This is going on my arrogant assumptions. You may have a superb reason why I'm completely wrong.
-- Iain Clarke
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Didn't you get it? All the details were hidden in his messages! Go back and take another look - make sure you read the entire thread - and check ALL the spaces.
Peter
"Until the invention of the computer, the machine gun was the device that enabled humans to make the most mistakes in the smallest amount of time."
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If the Lord God Almighty had consulted me before embarking upon the Creation, I would have recommended something simpler.
-- Alfonso the Wise, 13th Century King of Castile.
This is going on my arrogant assumptions. You may have a superb reason why I'm completely wrong.
-- Iain Clarke
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CPallini wrote: We're waiting for his revolutionary Data Hiding Algorithm
Although I too seriously doubt this, I am not one for deliberately calling out someone in a new thread. Certainly if they step on the pillory I'll flog a bit also, that's human nature. But I generally don't try to drag them back to the pillory for more ridicule.
I hope, that he has pulled up some of the hex editors, and other editors and realized that the idea is simple: it is too simple. Hiding data from the least qualified threat (the person who only knows how to use notepad), is not a very effective algorithm. Perhaps he has thrown out the algorithm and is trying for another. Who knows? Though he has given me some ideas, I may have to try it when I get the time. But mine would definitely change the text. Don't worry, no magic or infinite compression here, my wiccan skills are lacking, and outside of sitting on the data, I have only traditional ways of squashing bits down. 
_________________________
Asu no koto o ieba, tenjo de nezumi ga warau.
Talk about things of tomorrow and the mice in the ceiling laugh. (Japanese Proverb)
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Well, Probably you're right. My sarcasm is bad  . Anyway, you know, he promised me a sample text, done in a week. I'm not going to blame him if he'll not able to produce the sample. I'm just curious about.
BTW I've to admit I'm even more curous about your ideas, 'cause I cannot figure out a method for hiding info in a plain text file, but probably I'm lacking of imagination. Of course, I know, if someone will find a good trick then it probably will remain a secret. 
If the Lord God Almighty had consulted me before embarking upon the Creation, I would have recommended something simpler.
-- Alfonso the Wise, 13th Century King of Castile.
This is going on my arrogant assumptions. You may have a superb reason why I'm completely wrong.
-- Iain Clarke
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CPallini wrote: BTW I've to admit I'm even more curous about your ideas, 'cause I cannot figure out a method for hiding info in a plain text file, but probably I'm lacking of imagination. Of course, I know, if someone will find a good trick then it probably will remain a secret.
In my case I wasn't trying to "keep the same content" or "hide text" per se.... but I started wondering about text and public and private key systems and anagrams.... odd combination there. But what if you tried to take a sentance, and given the letters to hide and a given text, you created a new text which was a constrained anagram such that you could decode it later. It is still text, though now may not make much sense. But if you had the original text, which was the majority, could you then extract the remainder and retrieve the word anagram. Say one word per sentance, or one letter ever xx letters, or something like that. The net result is more like constrained anagram poetry/writing than encryption, but would certainly be a bugger to solve without knowing what was added or what the original text was.
See, I wasn't trying to keep the original text, I know that is too difficult, but keeping the original properties, i.e. an anagram of the original text and keep it as text. You could even do a letter substitution based on some formula, and then anagram. Knowing the original text you should be able to find out what letter was added Talk about a large key! 
for instance.... hiding "code project" within the text "four score and seven years ago our fathers brought forth a new"
would be
"A Decrescendo Nervous Of A Seafarer Yoghourt Pros Cab Fetter Wrought John"
Interleaved encryption. It is text, but a complete jibberish unless you knew what one of the halves was. You could even constrain it such that you chose an anagram that collapsed one space and added one letter. Though I think the latter would be too constrained and give itself away. The hard thing about interleaving text is fooling yourself into thinking that it is good because you WANT it to be good (self-bias).
_________________________
Asu no koto o ieba, tenjo de nezumi ga warau.
Talk about things of tomorrow and the mice in the ceiling laugh. (Japanese Proverb)
modified on Monday, March 31, 2008 5:04 PM
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OK. That makes sense. Probably you can also avoid to anagram, but then I suppose you'll need a bit of AI (for instance, you may add to the original text redundant sentences or unnecessary details - as novelists already do - most of them full of salt-bits but also containing the hidden message letters).
Uhm...Maybe the above resembles steganography...
If the Lord God Almighty had consulted me before embarking upon the Creation, I would have recommended something simpler.
-- Alfonso the Wise, 13th Century King of Castile.
This is going on my arrogant assumptions. You may have a superb reason why I'm completely wrong.
-- Iain Clarke
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CPallini wrote: you may add to the original text redundant sentences or unnecessary details
yeah... my problem with that is that if the text is not already completely unknown, or original (pretty hard writing a completely original piece of text every time you want to hide another set of text), then if you constrain it too much you can give clues to the original text and thus the hidden text (inserted items) as well. No, I would rather it be complete jibberish than leave any of the original text. But again, as I just added above, that could easily be self-bias.
_________________________
Asu no koto o ieba, tenjo de nezumi ga warau.
Talk about things of tomorrow and the mice in the ceiling laugh. (Japanese Proverb)
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If you mix this thread with the recent one in the lounge about the stuff circulating the web on permuting the letters within a word whilst retaining the human readability, here is another (new?) method of hiding messages within human readable text. The information is actually in the permutation used. Damn, now I've told everyone so I can't apply for the patent...
Then again, maybe those messages circulating the web demonstrating the readability of permuted words actually contain hidden messages....
Peter
"Until the invention of the computer, the machine gun was the device that enabled humans to make the most mistakes in the smallest amount of time."
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Hey Peter, do you hear voices whispering in your ears?
If the Lord God Almighty had consulted me before embarking upon the Creation, I would have recommended something simpler.
-- Alfonso the Wise, 13th Century King of Castile.
This is going on my arrogant assumptions. You may have a superb reason why I'm completely wrong.
-- Iain Clarke
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CPallini wrote: Hey Peter, do you hear voices whispering in your ears?
The spaces in your message are SO RUDE!! Can't you see it?
Peter
"Until the invention of the computer, the machine gun was the device that enabled humans to make the most mistakes in the smallest amount of time."
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If the Lord God Almighty had consulted me before embarking upon the Creation, I would have recommended something simpler.
-- Alfonso the Wise, 13th Century King of Castile.
This is going on my arrogant assumptions. You may have a superb reason why I'm completely wrong.
-- Iain Clarke
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I'm glad this new thread was started, otherwise I would have missed the original having been away for a few weeks - what a laugh!! That guy was certainly persistent.
The only way I can think of hiding data in text is to use a key/index of some sort - take the first letter of the third word, fourth letter of the thirteenth word etc but this would require either the key to decode it or for the text to be specifically arranged so that certain letters are in certain positions, neither of which is practical or secure. If that is the method then it certainly isn't new - didn't Napoleon or some such character use the same method?
Apathy Rules - I suppose...
Its not the things you fear that come to get you but all the things that you don't expect
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I never claimed it to be revolutionary and its very very simple.Give ur email and i will send u the files.Sorry for being late.My net was down for the last two days.I told u guys...i am just a novice in compared to you.But what excited me was...all the steganography softwares available on net changes the file size and appends the data.
As i know u guys are far more superior than me so i just came here to learn not to prove anything...Anyway...give me ur email i will send u the files.
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Oh don't worry. Indeed, as El Corazon pointed out, my sarcasm was bad. I must apologize to you.
However, if you want to send me the files, I'm going to sent my address to you soon.
If the Lord God Almighty had consulted me before embarking upon the Creation, I would have recommended something simpler.
-- Alfonso the Wise, 13th Century King of Castile.
This is going on my arrogant assumptions. You may have a superb reason why I'm completely wrong.
-- Iain Clarke
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Definitely wanna send u the files.Plse get me ur email.
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Hi,
I sent you my e-mail address, but I've received no file yet.
If the Lord God Almighty had consulted me before embarking upon the Creation, I would have recommended something simpler.
-- Alfonso the Wise, 13th Century King of Castile.
This is going on my arrogant assumptions. You may have a superb reason why I'm completely wrong.
-- Iain Clarke
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The file has been sent to you; however it got hidden perfectly between the previous
and next messages, so you can't notice it unless you apply the newest decoding
algorithm to it first.
Luc Pattyn [Forum Guidelines] [My Articles]
This month's tips:
- before you ask a question here, search CodeProject, then Google;
- the quality and detail of your question reflects on the effectiveness of the help you are likely to get;
- use PRE tags to preserve formatting when showing multi-line code snippets.
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