Items tagged with positive

I want to solve for the roots of a polynomial, such as a x^2+b x + c = 0, for which the output is only the positive root. All coefficients/variables in the polynomial are positive. 

Recently, someone posted an answer to a question where at some point they performed this task and their solution was really slick. But I can't find it. The answer used either solve, or eval or something like that. (Yes, I did perform a search via the MaplePrimes search before asking this question.) 

 

Hi guys.

           if an expression complicated as the following,  

sqrt(sqrt(9)*sqrt((1+(b+1)^2*c^2+((10/3)*b-2)*c)*(1+(b+1)^2*c^2+(2*b-2)*c))+3+(3*b^2+6*b+3)*c^2+(8*b-6)*c) , where b>0 c>0

is it possible to tell whether it could be positive? 

I used coulditbe command, however, it returned 'FAIL'.

Hi there,

            Recently, I encountered a problem. I have a function( omega as its variable)  (18)

 gamma*sqrt(4)*sqrt(omega^2*C2^2*R4^2/(C2^4*R4^4*beta^2*gamma^2*omega^4+C2^2*(1+gamma^2*(beta+1)^2-2*gamma)*R4^2*omega^2+1))

I tried to find a point where its first derivative equals 0. In this case, Maple returned four solutions. In my

question, both beta, gamma, R4 and C2 >0, I want it to return a real positive solution, the first term

in (19) (i.e. 1/(sqrt(beta *gamma) *1/R4 C2).

 

I know it is easy to find out the positive real roots in this case. This question seems to make no sense.

However, sometime I came across an expression complicated enough that I cannot tell whether it is real

positive.

Is there a approach to find a real positive solution of an symbolic eqution?

Thanks in advance!

 

                                                                     A University student in BeiHang University, Beijing

Hi,

how can I check in maple if my variable P is positive (always or only for some certain conditions)

P=(exp(a-1)-exp(g-1))*(b*d*(f-g)-b*g*(a-e)-g*(a-c)*(a-e)))/((a-g)*b*d) + exp(g-1)*(((a-c)*(a-e))/b*d + (a-e)/d + 1)

with assumptions

a>0,b>0,c>0,d>0,e>0,f>0,g>0 and a>c,e,g

I need to prove that P is always positive with that assumptions, how?


Dear all,

I wold like to find the solution of the next system of two equations with three unknowns but we assume that the unknows are positive integers. How the following code can work. Many thanks

 

 

 

> restart;
> assume(J, integer, J >= 0);
> assume(A, integer, A >= 0);
> assume(T, integer, T >= 0);
> eq1 := J+10*A+50*T=500;
   eq2 := J+A+T = 100;
  solve( {eq1,eq2},{J,A,T});

I want Positive values of Arcsin but maple give to me Negative values of Arcsin?

arcsin(-1);
-pi/2

but I want Positive values of Arcsin Namely:

arcsin(-1)=3 pi/2

hi.how i can chose a minimum and positive answer of different answer in solve rule...

my program attached below.for example at this , the second answer should be selected as 1.965392881*10^9 ,that is the minimum and posetive among other...

thanks alot

11.mw

Dear all:

hello everybody;

I need your help to solve the system f(x,y)=0, and g(x,y)=0, such that there some parameter in the system, also all the parameter are positive and also our unkowns  x and y are also positive.

I try to write this code. I feel that under some condition we can have four solution or three or two. I need your help. Many thinks.

 

Systemsolve.mw

Hi, i'm trying to solve the simultaneous equations,

a[1]:=2*x^2 + 3*x^2 + x*y - x^2 + x;

a[2]:=3*y^2 + 4*x^2 - y;

eval(y,fsolve({a[1],a[2]},{x,y}));
0.

Even though y can be 0 it can also be 1/3 and two other complex numbers.

How do you get fsolve to show all four y solutions.

Secondly, how would i get maple to just to show the positive y solution ie. 1/3 only.

Using the fsolve commmand how does one solve for just the positive solutions and remove the dublicate values?

Thanks

``

-(-2*N__1*`ω__2`*`ω__1`^2*lambda-8*N__2*lambda^3*`ω__2`-sqrt(4*N__1^2*lambda^2*`ω__1`^2*`ω__2`^2+16*N__1*N__2*lambda^4*`ω__2`^2+N__1*N__2*`ω__1`^2*`ω__2`^4+4*N__2^2*lambda^2*`ω__2`^4)*`ω__1`)/(4*N__1*lambda*`ω__1`^2*`ω__2`+16*N__2*lambda^3*`ω__2`)

-(-2*N__1*`ω__2`*`ω__1`^2*lambda-8*N__2*lambda^3*`ω__2`-(4*N__1^2*lambda^2*`ω__1`^2*`ω__2`^2+16*N__1*N__2*lambda^4*`ω__2`^2+N__1*N__2*`ω__1`^2*`ω__2`^4+4*N__2^2*lambda^2*`ω__2`^4)^(1/2)*`ω__1`)/(4*N__1*lambda*`ω__1`^2*`ω__2`+16*N__2*lambda^3*`ω__2`)

(1)

`assuming`([simplify(-(-2*N__1*`ω__2`*`ω__1`^2*lambda-8*N__2*lambda^3*`ω__2`-(4*N__1^2*lambda^2*`ω__1`^2*`ω__2`^2+16*N__1*N__2*lambda^4*`ω__2`^2+N__1*N__2*`ω__1`^2*`ω__2`^4+4*N__2^2*lambda^2*`ω__2`^4)^(1/2)*`ω__1`)/(4*N__1*lambda*`ω__1`^2*`ω__2`+16*N__2*lambda^3*`ω__2`), 'size')], [all, positive])

(1/4)*(4^(1/2)*((N__1*lambda^2+(1/4)*N__2*`ω__2`^2)*`ω__2`^2*(N__1*`ω__1`^2+4*N__2*lambda^2))^(1/2)*`ω__1`+2*lambda*`ω__2`*(N__1*`ω__1`^2+4*N__2*lambda^2))/(lambda*`ω__2`*(N__1*`ω__1`^2+4*N__2*lambda^2))

(2)

`assuming`([combine((1/4)*(4^(1/2)*((N__1*lambda^2+(1/4)*N__2*`ω__2`^2)*`ω__2`^2*(N__1*`ω__1`^2+4*N__2*lambda^2))^(1/2)*`ω__1`+2*lambda*`ω__2`*(N__1*`ω__1`^2+4*N__2*lambda^2))/(lambda*`ω__2`*(N__1*`ω__1`^2+4*N__2*lambda^2)), 'size')], [N__1 > 0, N__2 > 0, `ω__1` > 0, `ω__2` > 0, lambda > 0])

(1/4)*(`ω__1`*`ω__2`*((4*N__1*lambda^2+N__2*`ω__2`^2)*(N__1*`ω__1`^2+4*N__2*lambda^2))^(1/2)+2*lambda*`ω__2`*(N__1*`ω__1`^2+4*N__2*lambda^2))/(lambda*`ω__2`*(N__1*`ω__1`^2+4*N__2*lambda^2))

(3)

 

``

``


Download question_13.12.06.mw

Hi, I have read the help files, and many posts in MaplePrime. However, I am struggling to understand how to properly extract a number from a list. I would like to extract only the positive, or the maximum solution of a quadratic expression.I have uploaded the .mw file. (1) (2) (3) (4) With no brackets around A it does no work, Error, incorrect number of extra arguments in select If I extract the positive value I get a list, (5...

I have to vary two variables A & B. For a fixed A, if I vary B such that l1 and l2 is positive, then I need the min value of B for which ((l1>0) and (l2>0)) 

. In such a way I need the list of A & B.

restart; printlevel := 0 

for A  from .1 by .01 to 3 do  
 for B  from .1 by .01 to 3 do
l1:=(exp(B)-A)-1
l2:=(exp(B)-A/2)-1.5

end do

if ((l1>0) and (l2>0)) then print(A,min(B)) end if

In an atomic physics calculation involving the quantum theory of angular momentum, there appear polynomials whose coefficients involve square roots of positive integers, for example

sqrt(6)-sqrt(2)*sqrt(3) 

Maple does not cancel such an expression to zero because the code allows for the possibility that a square root can be positive or negative.  In the physics context all these square roots are positive.  Is there some simple way to induce Maple...

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