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- bobbym
- 2011-04-11 21:49:23
Hi gAr;
- gAr
- 2011-04-11 21:43:26
Hi bobbym,
- bobbym
- 2011-04-11 21:22:45
What did you get, do not forget to hide it?
- gAr
- 2011-04-11 21:21:28
Aha, now both the expressions work fine.
I increased the precision to 100 digits.
- bobbym
- 2011-04-11 21:07:31
Hi gAr;
That expression is extremely difficult for a package to evaluate. We say it is ill conditioned. Adjust your digit command to get higher precision and try again.
- gAr
- 2011-04-11 21:03:31
Hi bobbym,
Ok.
For that expression I get:
-1.18059162071741e21
and 1.18059162071741e21 for those two numbers as integers.
I evaluated this expression and got
-4.38605752237005e29 for a = 77617.0 , b = 33096.0 ; and
-4.38605749875822e29 for a = 77617 , b = 33096
- bobbym
- 2011-04-11 20:45:31
Hi gAr;
With that identity as well as lots of others the best way is to plot (a+b)(a-b) - (a^2 - b^2 ). Instead of getting a flat line on the x axis ( y = 0 ) you should get a crazy graph of undulating spikes.
I meant the expression in post #1.
- gAr
- 2011-04-11 20:39:42
Hi bobbym,
Did you try that expression? What did you get?
Is it the identity you are asking about?
For numbers like a=1.1 and b=2.2, it displays correctly. When digits after decimal places are increased, it fails.
- bobbym
- 2011-04-11 20:19:48
You also do not use the quadratic formula to get roots.
Did you try that expression? What did you get?
- gAr
- 2011-04-11 20:15:26
I agree.
For that identity, yes, real numbers are always a problem!
- bobbym
- 2011-04-11 20:06:54
You should always mistrust an answer a CAS gives. Same way you should mistrust anything a human says. There are basic guidelines and I will be posing them in the future.
There is a big difference between the way human mathematicians do math and the way a CAS does it. One of the funniest examples is
Human math: This is an identity:
Computer math: This is not!
- gAr
- 2011-04-11 19:58:39
So we do not know when to trust the answers and when not to!
- bobbym
- 2011-04-11 19:37:23
That is the point. Sometimes you can tell that an equation is going to give a CAS ( or a calculator ) a lot of problems. But sometimes you cannot. That one came as a surprise to me too.
- gAr
- 2011-04-11 19:32:42
Oh, does he tell what kind of equations suffer like that?
- bobbym
- 2011-04-11 19:15:46
Hi gAr;
That is one of its problems. The guy who designed it wanted to prove there was a big hole in the way numerical people verify digits.