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Greetings to all!

Recently I encouter the following issue:

Maple (version 17) coudn't recognize that 20.0 equals with 20 and with 20.00. Believe me, this is very annoying!

Do I miss something? Is there any command that do the trick?

 

Thank you!

Giorgos K.

 

 

To motivate some ideas in my research, I've been looking at the expected number of real roots of random polynomials (and their derivatives).  In doing so I have noticed an issue/bug with fsolve and RootFinding[Isolate].  One of the polynomials I came upon was

f(x) = -32829/50000-(9277/50000)*x-(37251/20000)*x^2-(6101/6250)*x^3-(47777/20000)*x^4+(291213/50000)*x^5.

We know that f(x) has at least 1 real root and, in fact, graphing shows that f(x) has exactly 1 real root (~1.018).  However, fsolve(f) and Isolate(f) both return no real roots.  On the other hand, Isolate(f,method=RC) correctly returns the root near 1.018.  I know that fsolve's details page says "It may not return all roots for exceptionally ill-conditioned polynomials", though this system does not seem especially ill-conditioned.  Moreover, Isolate's help page says confidently "All significant digits returned by the program are correct, and unlike purely numerical methods no roots are ever lost, although repeated roots are discarded" which is clearly not the case here.  It also seems interesting that the RealSolving package used by Isolate(f,method=RS) (default method) misses the root while the RegularChains package used by Isolate(f,method=RC) correctly finds the root.

 All-in-all, I am not sure what to make of this.  Is this an issue which has been fixed in more recent incarnations of fsolve or Isolate?  Is this a persistent problem?  Is there a theoretical reason why the root is being missed, particularly for Isolate?

Any help or insight would be greatly appreciated.

Hi everyone,

I have a maple program that generates a polynomial g(y)=(80y^8 + 68y^6 + 12y^4 -4y^2 -1). This polynomial has two real roots (irrational roots), call them +/- y*. My code does a sequential calculation, and often sI am left with a higher order polynomial in y that has the form h(y)= p(y)*g(y), where p(y) is also a polynomial in y. This polynomial h(y)=p(y)*g(y) is not in factored form (i.e. it would look like expand(p(y)*g(y)). Is there a way to instruct maple to recoginize that +/-y* is also a root h(y)=p(y)*g(y)? So far I've tried things like applyrule([g(y*)=0],h(y*)), but nothing seems to work (I suspect because Maple cannot recgonize that g(y) is a factor of h(y)). I am not interested in computing this numerically. I am just trying to find a way to instruct Maple to recognize symbolically that h(y*) =0.

Thanks a million for anyone who has any idea.

Best,

 

Justin

I am using Maple 15 to numerically solve a system of differential algebraic euqations (DAE) with given initial conditions, and I've tried rfk45_dae and rosenbrock_dae solver, but both solver responded in error like this

 

Error, (in dsolve/numeric) cannot numerically solve complex DAE initial value problems, the system must be converted to a real system

 

I don't understand what is a real system, and how could i convert it to a real system.

 

Hello,

• Is there a simple way to find the domain for the real solutions of f(x)?

• And is there a way to let maple get the part of f(x) with the sqrt?
   (not by typing it by hand as I dit below)

• Is there a way to write the summary of the found domains in one line?

Thanks for your help. 





restart:
# How to find the Domain for real solutions for x?
f(x):=(x-1+sqrt(x^2-3*x+2))/(x-1);
discont_for_x=discont(f(x),x);
# x<>+1 (because the de denom=0 is not allowed)
denom(f(x))=0;
x={solve(denom(f(x))=0,x)};
# x<=1 union  2<=x (because the part under the sqrt must be >=0 to give Real solutions)
sqrt(x^2-3*x+2);
0<=x^2-3*x+2;
x=solve(0<=x^2-3*x+2,x);




Hi, the title isn't great as I didn't know how to describe this really. I need to solve the following equation for b:

y = (1-exp(-x*b))/(1-exp(-50*b))

When I put a value for y in, this is fine and fsolve gives me a numeric real solution. However, even when using RealDomain, it does not give me a real solution if I leave y as it is, and instead gives a 'RootOf' solution, which I don't really understand. This is the same whether using solve or isolate:

b=-(1/50)RootOf(_Zx-50ln(-y+ye^(_Z)+1))

I have the values of x and y for multiple data points and can put them in an nx1 matrix. Is there a way to replace x and y with matrices (with real numbers in) and solve for each set of points for b (ie there would be n values of b)? Obviously I could go through and put in each value of x and y but this would take ages, so was just wondering if there's a quick way to do this.

I have tried by simply putting matrices instead of the letter but get the error:

Error, invalid input: exp expects its 1st argument, x, to be of type algebraic, but received Vector(50, {(1) = -50*b, (2) = -49*b,...

Thanks for your time

James

Real roots only...

January 17 2014 Syeda 25

I want to find real roots only.  Cannot we find a simplified formula for x in this case which gives only real roots? 

 

 

``

eq1 := a^2*x^3+Typesetting:-delayDotProduct(2*a*b-Typesetting:-delayDotProduct(a^2, e), x^2)+(-2*a*b*c^2-a*c+b^2)*x-c*b-d-b^2*e = 0:

``

# Formula

eq2 := A*x^3+B*x^2+C*x+E = 0:

``

NULL

a := .7438:

b := 15.12*z[1]+10.85*z[1]^2:

c := 18.92-17.76*z[2]:

d := -.9224:

e := 2.106-5.317*z[2]+2.87*z[2]^2:NULL

NULL

A := a^2:

B := -a^2*e+2*a*b:

C := -2*a*b*e^2-a*c+b^2:

E := -b^2*e-b*c-d:

``

eq2

.55323844*x^3+(-1.165120155+2.941568785*z[2]-1.587794323*z[2]^2+22.492512*z[1]+16.140460*z[1]^2)*x^2+(-1.4876*(15.12*z[1]+10.85*z[1]^2)*(2.106-5.317*z[2]+2.87*z[2]^2)^2-14.072696+13.209888*z[2]+(15.12*z[1]+10.85*z[1]^2)^2)*x-(15.12*z[1]+10.85*z[1]^2)^2*(2.106-5.317*z[2]+2.87*z[2]^2)-(15.12*z[1]+10.85*z[1]^2)*(18.92-17.76*z[2])+.9224 = 0

(1)

``

``# Putting z1 and z2 value

"(->)"

.55323844*x^3+14.11629660*x^2+83.26002702*x-3.52866181 = 0

(2)

 

"(->)"

[[x = 0.4208050385e-1], [x = -9.354079555], [x = -16.20375615]]

(3)

``

``

 

Download cubic.mw

My attempt:

RealDomain[solve]({x^2+y^2+z^2 = 3, x+y+z = 3}, {x,y,z});

             {x = -RootOf(_Z^2+(z-3)*_Z+z^2-3*z+3)-z+3, y = RootOf(_Z^2+(z-3)*_Z+z^2-3*z+3), z = z}

 

In fact, the system in the real domain has a unique solution x = 1, y = 1, z = 1. It is easy to find by hand, noting that the plane  x + y + z = 3  is tangent to the sphere  

Hi, was wondering if any of you could help me, when I try and find the real part of a function to plot, I get a float(undefined) error, however by just using evalf if gives gives me the real and comlex parts.

zetaroots.mw

The function i want to find realy parts for is f(x).

 

Thanks,

Matt

I propose a different proof of this remarkable identity (see  http://www.mapleprimes.com/posts/144499-Stunningly-Beautiful-Identity-Proved ) in which  directly constructed a polynomial, whose root is the value of LHS, and this is expressed in radicals.

For the proof, we need three simple identities with cubic roots (a, b, c -any real numbers):

Hi,

I'm using Maple to carry out some calculations in Tropical algebra, which requires taking minima of real numbers and infinity.

I'm currently using symbols rather than real numbers, which is causing a problem, I have (for example) the following lines of Maple code:

> assume(0 < a)
> min(a+infinity, 2*a+infinity)
               min(a~ + infinity, 2a~ + infinity)

I am trying to determine if a particular system of 15 polynomial equations in 9 variables has a real solution using Maple's RegularChains library.  I am using the IsEmpty command which returns true if there are no solutions and false otherwise.  In Maple 16, this can be done using the command:

IsEmpty( sys, R ) ;

where "sys" is a list of equations and "R" is a polynomial ring, both of which I define in the worksheet.  But this syntax only works...

I'm very new to Maple and I'm just curious as to how Maple computes its summations with the MatrixPower command.

if A = a real square matrix

c = some real constant

x = c*A

then Why is it, that when I try to use...

sum(MatrixPower(x,k), k = 0..3);

I get a non-real / ridiculous result, but when I type it out...

MatrixPower(x,0) + MatrixPower(x,1) + MatrixPower(x,2) + MatrixPower(x,3);

x^0 + x^1 + x^2 + x^3;

Dear members,

I would like to generate a tree (the simplest "stage tree"that I have in mind is in the attached file) ad to work with it. For that I need to  "replicate" [the stage tree which starts in O (with some value R)] after the nodes x2, y2, z2. The nodes x1, y1, z1 are terminal (with values f(R), g(R), h(R) ).

I found soemthing on the posts on mapleprimes, but it is only bor "binarytrees".

How may I proceed?.

 

I really...

I use Maple 15 and I want to take the real and the imaginary part of a simple expression e.g. 5*Dirac(x)+3*I, having already assumed x a real value. However, Maple seems to have problem with the Dirac function. The output looks like this:

> assume(x, 'real');
> Re(5*Dirac(x)+3*I);
5 Re(Dirac(x))
> Im(5*Dirac(x)+3*I);
3 + 5 Im(Dirac(x))
 
Any thoughts on how to overcome this are welcomed.
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