I khow it is possible for a TI to solve it!

But what about a CP?

I entered equations as below:
solve({x+x*y=5,x^2+y=2},{x,y})
Thanks for your kind attention.

Posted 22 May 2006 - 05:29 PM
Posted 22 May 2006 - 08:42 PM
Posted 23 May 2006 - 05:27 PM
Posted 23 May 2006 - 06:00 PM
Posted 23 May 2006 - 06:18 PM
Posted 23 May 2006 - 06:57 PM
How?
It's not clear for me!
Do u mean it needs programming?
solve(x^2+y=2,y) {y=-x^2+2} solve(x+x*y=5,x)|ans[1] {x=-5/(x^2-3)} solve(x=-5/(x^2-3),x) // CP can't solve this. We must edit the expression. solve(x(x^2-3)=-5,x) {x=-2.279018786}I'll find same problem even if I start with second equation.
Posted 23 May 2006 - 10:28 PM
Posted 25 May 2006 - 08:05 AM
A quick solution:How can I solve a non-linear Equation system?
I khow it is possible for a TI to solve it!![]()
But what about a CP?![]()
I entered equations as below:
solve({x+x*y=5,x^2+y=2},{x,y})
Thanks for your kind attention.
require("table","LuaNumAn/Broyden") local function F(x) return {x[1]+x[1]*x[2]-5,x[1]^2+x[2]-2} end local function J(x) return{{1+x[2],x[1]},{2*x[1],1}} end root=Broyden({-1,0},F,J,5E-16) table.foreach(root,print)You get {-2.27901878616659,-3.19392662770025}, accurate to at least 15 decimal digits. See LuaNumAn's documentation for details
Posted 25 May 2006 - 01:03 PM
My HP49 couldn't solve it and mathematica gave a really long solution,are you sure the TIs can solve this particular one?
Posted 25 May 2006 - 03:33 PM
I don't remember having said that require() now accepts several arguments. But since you use it, that means you know it.A quick solution:
require("table","LuaNumAn/Broyden") local function F(x) return {x[1]+x[1]*x[2]-5,x[1]^2+x[2]-2} end local function J(x) return{{1+x[2],x[1]},{2*x[1],1}} end root=Broyden({-1,0},F,J,5E-16) table.foreach(root,print)You get {-2.27901878616659,-3.19392662770025}, accurate to at least 15 decimal digits. See LuaNumAn's documentation for details.
for key,value in pairs(root) do print(key,value) endThe pairs() function does not require any extra package
Posted 25 May 2006 - 05:35 PM
Posted 25 May 2006 - 07:26 PM
Posted 25 May 2006 - 10:12 PM
My HP49 couldn't solve it and mathematica gave a really long solution,are you sure the TIs can solve this particular one?
Posted 26 May 2006 - 08:25 AM
Posted 26 May 2006 - 11:41 PM
Oh, yes, you didI don't remember having said that require() now accepts several arguments. But since you use it, that means you know it.
Glad to see it's useful.
I know this solution, but it doesn't make the program shorter, and I usually want to print a table more than once in a program. But if the "table" package uses a lot of memory, your solution is definitely better.Btw, I noticed that you often use the "table" package only for the foreach() function. You could have the same result with
for key,value in pairs(root) do print(key,value) endThe pairs() function does not require any extra package
Posted 26 May 2006 - 11:59 PM
First, I want to ask something: What do you mean by "i use the same method used to solve it on the classpad"? As far as I know the only way to solve nonlinear systems in ClassPad is to use the "Broyden" function, included in my LuaNumAn package. Don't tell me that you have translated it for the HPi was looking for an EXACT solution not an aproximation, the HP can't solve it as a system directly because it can't factor the expression, but if i use the same method used to solve it on the classpad i get not one but three solutions
{x=1.14+.946i , x=1.14-.946i , x=-2.279} and {y=1.597-2.157i , y=1.597+2.157i , y=-3.194}, these are the rounded results (obviously).
Incorrect. In most cases, nonlinear systems cannot be solved "exactly" by any CAS system, simply because there is no exact solution, or because there is an exact solution, but it is very complicated and useless. This is when Numerical Analysis is involved. Nonlinear systems can be solved "exactly" only in very special (simple) cases. Their numerical solution is not an easy task as well: numerical methods for nonlinear systems are not easy.anyway, this system gives a third order system, that can still be solved exactly but calcs don't have it implemented.
Posted 29 May 2006 - 05:11 PM
Posted 30 May 2006 - 01:13 PM
Ok. I guessed that you used some method, but you didn't specified which one.When i said "i use the same method used to solve it on the classpad" i meant i used the same method "Daniel (CZE)" used.
No offence, but this is not correct. The web page you mentioned does not describe a way to solve third order nonlinear systems. It describes a way to solve general cubic equations, which is a completely different thing. Cardano's method involves some nonlinear systems, but they are only special cases, not an arbitrarily complex nonlinear system. I insist: there is no general method to solve nonlinear systems analytically, including third order systems; only special nonlinear systems can be solved exactly, and this is the exception, not the rule.i guess you should take a look at the cardano method to solve third order systems at http://mathworld.wol...bicFormula.html
I know that, it was obvious that you didn't wanted to be offensive.also i wasn't trying in any way to say anything bad about LuaNumAn.
I absolutely agree. We use calculators to perform addition, but we should know how to add numbers anyway. We use numerical methods to solve a complicated problem, but we should at least know what exactly we solve, and how. I never said that one must use numerical methods blindly.my point is, you should have a math background even when solving linear or nonlinear problems with a calculator or pc, so you can at least see if the result is coherent.
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