Items tagged with inequality inequality Tagged Items Feed

Hi I'm not really sure how to phrase this but I'm doing projectile motion and I'm try to graph the solutions for v_0 by theta_0.

 

How to prove the inequality 12*sqrt((a^2+b^2+c^2+d^2)*a*b*c*d) <= (a+b+c+d)*(a*b+a*c+a*d+b*c+b*d+c*d) , assuming that the  variables are nonnegative? That hard question  was asked by arqady in dxdy and answered  by himself  in a complicated way. Maple proves the inequality by the LagrangeMultipliers command which is strong. I think these calculations cannot be done by hand at all. Without loss of generality one may assume a+b+c+d = 1. Then

 restart:with(Student[MultivariateCalculus]):

ans := [LagrangeMultipliers((a+b+c+d)*(a*b+a*c+a*d+b*c+b*d+c*d)-12*sqrt((a^2+b^2+c^2+d^2)*a*b*c*d), [a+b+c+d-1], [a, b, c, d], output = detailed)]:

We have to remove complex solutions by
ans1:=remove(c -> has(evalf(c), I),ans):

The next big output is  only partly seen in the post (look in the attached file for the whole one).

ans2:=simplify(ans1,radical);

[[a = 1/6, b = 1/2, c = 1/6, d = 1/6, lambda[1] = 0, -12*sqrt((a^2+b^2+c^2+d^2)*a*b*c*d)+(b+c+d)*a^2+(b^2+(3*c+3*d)*b+c^2+3*c*d+d^2)*a+(d+c)*b^2+(c^2+3*c*d+d^2)*b+c^2*d+c*d^2 = 0],[a = 1/4, b = 1/4, c = 1/4, d = 1/4, lambda[1] = 0, -12*sqrt((a^2+b^2+c^2+d^2)*a*b*c*d)+(b+c+d)*a^2+(b^2+(3*c+3*d)*b+c^2+3*c*d+d^2)*a+(d+c)*b^2+(c^2+3*c*d+d^2)*b+c^2*d+c*d^2 = 0],[a = 13/72-(1/216)*sqrt(3)*sqrt((2*(11548+108*sqrt(13397))^(2/3)+11*(11548+108*sqrt(13397))^(1/3)-568)/(11548+108*sqrt(13397))^(1/3))+(1/216)*sqrt(3)*sqrt(2)*sqrt((11*(11548+108*sqrt(13397))^(1/3)-(11548+108*sqrt(13397))^(2/3)+284)/(11548+108*sqrt(13397))^(1/3)+273*sqrt(3)/sqrt((2*(11548+108*sqrt(13397))^(2/3)+11*(11548+108*sqrt(13397))^(1/3)-568)/(11548+108*sqrt(13397))^(1/3))), b = 11/24+(1/72)*sqrt(3)*sqrt((2*(11548+108*sqrt(13397))^(2/3)+11*(11548+108*sqrt(13397))^(1/3)-568)/(11548+108*sqrt(13397))^(1/3))-(1/72)*sqrt(3)*sqrt(2)*sqrt((11*(11548+108*sqrt(13397))^(1/3)-(11548+108*sqrt(13397))^(2/3)+284)/(11548+108*sqrt(13397))^(1/3)+273*sqrt(3)/sqrt((2*(11548+108*sqrt(13397))^(2/3)+11*(11548+108*sqrt(13397))^(1/3)-568)/(11548+108*sqrt(13397))^(1/3))), c = 13/72-(1/216)*sqrt(3)*sqrt((2*(11548+108*sqrt(13397))^(2/3)+11*(11548+108*sqrt(13397))^(1/3)-568)/(11548+108*sqrt(13397))^(1/3))+(1/216)*sqrt(3)*sqrt(2)*sqrt((11*(11548+108*sqrt(13397))^(1/3)-(11548+108*sqrt(13397))^(2/3)+284)/(11548+108*sqrt(13397))^(1/3)+273*sqrt(3)/sqrt((2*(11548+108*sqrt(13397))^(2/3)+11*(11548+108*sqrt(13397))^(1/3)-568)/(11548+108*sqrt(13397))^(1/3))), d = 13/72-(1/216)*sqrt(3)*sqrt((2*(11548+108*sqrt(13397))^(2/3)+11*(11548+108*sqrt(13397))^(1/3)-568)/(11548+108*sqrt(13397))^(1/3))+(1/216)*sqrt(3)*sqrt(2)*sqrt((11*(11548+108*sqrt(13397))^(1/3)-(11548+108*sqrt(13397))^(2/3)+284)/(11548+108*sqrt(13397))^(1/3)+273*sqrt(3)/sqrt((2*(11548+108*sqrt(13397))^(2/3)+11*(11548+108*sqrt(13397))^(1/3)-568)/(11548+108*sqrt(13397))^(1/3))), lambda[1] = -(5/36)*(sqrt(2)*(sqrt(3)*(sqrt(13397)-(71/27)*(11548+108*sqrt(13397))^(1/3)-(103/540)*(11548+108*sqrt(13397))^(2/3)+2887/27)*sqrt((2*(11548+108*sqrt(13397))^(2/3)+11*(11548+108*sqrt(13397))^(1/3)-568)/(11548+108*sqrt(13397))^(1/3))-15*sqrt(13397)+(355/9)*(11548+108*sqrt(13397))^(1/3)+(109/36)*(11548+108*sqrt(13397))^(2/3)-14435/9)*sqrt((11*(11548+108*sqrt(13397))^(1/3)-(11548+108*sqrt(13397))^(2/3)+284)/(11548+108*sqrt(13397))^(1/3)+273*sqrt(3)/sqrt((2*(11548+108*sqrt(13397))^(2/3)+11*(11548+108*sqrt(13397))^(1/3)-568)/(11548+108*sqrt(13397))^(1/3)))-(133/15)*(11548+108*sqrt(13397))^(2/3)*sqrt((2*(11548+108*sqrt(13397))^(2/3)+11*(11548+108*sqrt(13397))^(1/3)-568)/(11548+108*sqrt(13397))^(1/3))+(2*((sqrt(13397)+2374/45)*(11548+108*sqrt(13397))^(1/3)+(103/5)*sqrt(13397)+(449/90)*(11548+108*sqrt(13397))^(2/3)+132727/45))*sqrt(3))/((11548+108*sqrt(13397))^(2/3)*sqrt((2*(11548+108*sqrt(13397))^(2/3)+11*(11548+108*sqrt(13397))^(1/3)-568)/(11548+108*sqrt(13397))^(1/3))), -12*sqrt((a^2+b^2+c^2+d^2)*a*b*c*d)+(b+c+d)*a^2+(b^2+(3*c+3*d)*b+c^2+3*c*d+d^2)*a+(d+c)*b^2+(c^2+3*c*d+d^2)*b+c^2*d+c*d^2 = -(13/46656)*(((2/13)*sqrt((11*(11548+108*sqrt(13397))^(1/3)-(11548+108*sqrt(13397))^(2/3)+284)/(11548+108*sqrt(13397))^(1/3)+273*sqrt(3)/sqrt((2*(11548+108*sqrt(13397))^(2/3)+11*(11548+108*sqrt(13397))^(1/3)-568)/(11548+108*sqrt(13397))^(1/3)))*(11548+108*sqrt(13397))^(1/3)*sqrt((2*(11548+108*sqrt(13397))^(2/3)+11*(11548+108*sqrt(13397))^(1/3)-568)/(11548+108*sqrt(13397))^(1/3))+sqrt(2)*(sqrt(3)*(11548+108*sqrt(13397))^(1/3)*sqrt((2*(11548+108*sqrt(13397))^(2/3)+11*(11548+108*sqrt(13397))^(1/3)-568)/(11548+108*sqrt(13397))^(1/3))-(11/13)*(11548+108*sqrt(13397))^(1/3)-(2/13)*(11548+108*sqrt(13397))^(2/3)+568/13))*sqrt(5)*sqrt((sqrt(3)*sqrt(2)*sqrt((11*(11548+108*sqrt(13397))^(1/3)-(11548+108*sqrt(13397))^(2/3)+284)/(11548+108*sqrt(13397))^(1/3)+273*sqrt(3)/sqrt((2*(11548+108*sqrt(13397))^(2/3)+11*(11548+108*sqrt(13397))^(1/3)-568)/(11548+108*sqrt(13397))^(1/3)))-sqrt(3)*sqrt((2*(11548+108*sqrt(13397))^(2/3)+11*(11548+108*sqrt(13397))^(1/3)-568)/(11548+108*sqrt(13397))^(1/3))-33)*(sqrt(3)*sqrt(2)*sqrt((11*(11548+108*sqrt(13397))^(1/3)-(11548+108*sqrt(13397))^(2/3)+284)/(11548+108*sqrt(13397))^(1/3)+273*sqrt(3)/sqrt((2*(11548+108*sqrt(13397))^(2/3)+11*(11548+108*sqrt(13397))^(1/3)-568)/(11548+108*sqrt(13397))^(1/3)))-sqrt(3)*sqrt((2*(11548+108*sqrt(13397))^(2/3)+11*(11548+108*sqrt(13397))^(1/3)-568)/(11548+108*sqrt(13397))^(1/3))+39)*(sqrt(2)*(sqrt(3)*(11548+108*sqrt(13397))^(1/3)*sqrt((2*(11548+108*sqrt(13397))^(2/3)+11*(11548+108*sqrt(13397))^(1/3)-568)/(11548+108*sqrt(13397))^(1/3))+(11/5)*(11548+108*sqrt(13397))^(1/3)+(2/5)*(11548+108*sqrt(13397))^(2/3)-568/5)*sqrt((11*(11548+108*sqrt(13397))^(1/3)-(11548+108*sqrt(13397))^(2/3)+284)/(11548+108*sqrt(13397))^(1/3)+273*sqrt(3)/sqrt((2*(11548+108*sqrt(13397))^(2/3)+11*(11548+108*sqrt(13397))^(1/3)-568)/(11548+108*sqrt(13397))^(1/3)))-(216/5)*(11548+108*sqrt(13397))^(1/3)*sqrt((2*(11548+108*sqrt(13397))^(2/3)+11*(11548+108*sqrt(13397))^(1/3)-568)/(11548+108*sqrt(13397))^(1/3))-(328/5*((11548+108*sqrt(13397))^(1/3)+(5/164)*(11548+108*sqrt(13397))^(2/3)-355/41))*sqrt(3))/((11548+108*sqrt(13397))^(1/3)*sqrt((2*(11548+108*sqrt(13397))^(2/3)+11*(11548+108*sqrt(13397))^(1/3)-568)/(11548+108*sqrt(13397))^(1/3))))-(180/13)*sqrt(2)*(sqrt(3)*(11548+108*sqrt(13397))^(1/3)*sqrt((2*(11548+108*sqrt(13397))^(2/3)+11*(11548+108*sqrt(13397))^(1/3)-568)/(11548+108*sqrt(13397))^(1/3))+(11/5)*(11548+108*sqrt(13397))^(1/3)+(2/5)*(11548+108*sqrt(13397))^(2/3)-568/5)*sqrt((11*(11548+108*sqrt(13397))^(1/3)-(11548+108*sqrt(13397))^(2/3)+284)/(11548+108*sqrt(13397))^(1/3)+273*sqrt(3)/sqrt((2*(11548+108*sqrt(13397))^(2/3)+11*(11548+108*sqrt(13397))^(1/3)-568)/(11548+108*sqrt(13397))^(1/3)))-(15552/13)*(11548+108*sqrt(13397))^(1/3)*sqrt((2*(11548+108*sqrt(13397))^(2/3)+11*(11548+108*sqrt(13397))^(1/3)-568)/(11548+108*sqrt(13397))^(1/3))+(11808/13*((11548+108*sqrt(13397))^(1/3)+(5/164)*(11548+108*sqrt(13397))^(2/3)-355/41))*sqrt(3))/((11548+108*sqrt(13397))^(1/3)*sqrt((2*(11548+108*sqrt(13397))^(2/3)+11*(11548+108*sqrt(13397))^(1/3)-568)/(11548+108*sqrt(13397))^(1/3)))]

(1)

evalf(ans2);

[[a = .1666666667, b = .5000000000, c = .1666666667, d = .1666666667, lambda[1] = 0., -12.*((a^2+b^2+c^2+d^2)*a*b*c*d)^(1/2)+(b+c+d)*a^2+(b^2+(3.*c+3.*d)*b+c^2+3.*c*d+d^2)*a+(d+c)*b^2+(c^2+3.*c*d+d^2)*b+c^2*d+c*d^2 = 0.], [a = .2500000000, b = .2500000000, c = .2500000000, d = .2500000000, lambda[1] = 0., -12.*((a^2+b^2+c^2+d^2)*a*b*c*d)^(1/2)+(b+c+d)*a^2+(b^2+(3.*c+3.*d)*b+c^2+3.*c*d+d^2)*a+(d+c)*b^2+(c^2+3.*c*d+d^2)*b+c^2*d+c*d^2 = 0.], [a = .1666666667, b = .1666666667, c = .5000000000, d = .1666666667, lambda[1] = 0., -12.*((a^2+b^2+c^2+d^2)*a*b*c*d)^(1/2)+(b+c+d)*a^2+(b^2+(3.*c+3.*d)*b+c^2+3.*c*d+d^2)*a+(d+c)*b^2+(c^2+3.*c*d+d^2)*b+c^2*d+c*d^2 = 0.], [a = .1666666667, b = .1666666667, c = .1666666667, d = .5000000000, lambda[1] = 0., -12.*((a^2+b^2+c^2+d^2)*a*b*c*d)^(1/2)+(b+c+d)*a^2+(b^2+(3.*c+3.*d)*b+c^2+3.*c*d+d^2)*a+(d+c)*b^2+(c^2+3.*c*d+d^2)*b+c^2*d+c*d^2 = 0.], [a = .5000000000, b = .1666666667, c = .1666666667, d = .1666666667, lambda[1] = 0., -12.*((a^2+b^2+c^2+d^2)*a*b*c*d)^(1/2)+(b+c+d)*a^2+(b^2+(3.*c+3.*d)*b+c^2+3.*c*d+d^2)*a+(d+c)*b^2+(c^2+3.*c*d+d^2)*b+c^2*d+c*d^2 = 0.], [a = .2118620934, b = .3644137199, c = .2118620934, d = .2118620934, lambda[1] = 0.2834790478e-2, -12.*((a^2+b^2+c^2+d^2)*a*b*c*d)^(1/2)+(b+c+d)*a^2+(b^2+(3.*c+3.*d)*b+c^2+3.*c*d+d^2)*a+(d+c)*b^2+(c^2+3.*c*d+d^2)*b+c^2*d+c*d^2 = 0.9449303017e-3], [a = 0.3692850681e-1, b = .8892144797, c = 0.3692850681e-1, d = 0.3692850681e-1, lambda[1] = 0.9303874297e-1, -12.*((a^2+b^2+c^2+d^2)*a*b*c*d)^(1/2)+(b+c+d)*a^2+(b^2+(3.*c+3.*d)*b+c^2+3.*c*d+d^2)*a+(d+c)*b^2+(c^2+3.*c*d+d^2)*b+c^2*d+c*d^2 = 0.3101291407e-1], [a = .8892144797, b = 0.3692850681e-1, c = 0.3692850681e-1, d = 0.3692850681e-1, lambda[1] = 0.9303874297e-1, -12.*((a^2+b^2+c^2+d^2)*a*b*c*d)^(1/2)+(b+c+d)*a^2+(b^2+(3.*c+3.*d)*b+c^2+3.*c*d+d^2)*a+(d+c)*b^2+(c^2+3.*c*d+d^2)*b+c^2*d+c*d^2 = 0.3101291407e-1], [a = .3644137199, b = .2118620934, c = .2118620934, d = .2118620934, lambda[1] = 0.2834790478e-2, -12.*((a^2+b^2+c^2+d^2)*a*b*c*d)^(1/2)+(b+c+d)*a^2+(b^2+(3.*c+3.*d)*b+c^2+3.*c*d+d^2)*a+(d+c)*b^2+(c^2+3.*c*d+d^2)*b+c^2*d+c*d^2 = 0.9449303017e-3], [a = 0.3692850681e-1, b = 0.3692850681e-1, c = 0.3692850681e-1, d = .8892144797, lambda[1] = 0.9303874297e-1, -12.*((a^2+b^2+c^2+d^2)*a*b*c*d)^(1/2)+(b+c+d)*a^2+(b^2+(3.*c+3.*d)*b+c^2+3.*c*d+d^2)*a+(d+c)*b^2+(c^2+3.*c*d+d^2)*b+c^2*d+c*d^2 = 0.3101291407e-1], [a = .2118620934, b = .2118620934, c = .2118620934, d = .3644137199, lambda[1] = 0.2834790478e-2, -12.*((a^2+b^2+c^2+d^2)*a*b*c*d)^(1/2)+(b+c+d)*a^2+(b^2+(3.*c+3.*d)*b+c^2+3.*c*d+d^2)*a+(d+c)*b^2+(c^2+3.*c*d+d^2)*b+c^2*d+c*d^2 = 0.9449303017e-3], [a = 0.3692850681e-1, b = 0.3692850681e-1, c = .8892144797, d = 0.3692850681e-1, lambda[1] = 0.9303874297e-1, -12.*((a^2+b^2+c^2+d^2)*a*b*c*d)^(1/2)+(b+c+d)*a^2+(b^2+(3.*c+3.*d)*b+c^2+3.*c*d+d^2)*a+(d+c)*b^2+(c^2+3.*c*d+d^2)*b+c^2*d+c*d^2 = 0.3101291407e-1], [a = .2118620934, b = .2118620934, c = .3644137199, d = .2118620934, lambda[1] = 0.2834790478e-2, -12.*((a^2+b^2+c^2+d^2)*a*b*c*d)^(1/2)+(b+c+d)*a^2+(b^2+(3.*c+3.*d)*b+c^2+3.*c*d+d^2)*a+(d+c)*b^2+(c^2+3.*c*d+d^2)*b+c^2*d+c*d^2 = 0.9449303017e-3]]

(2)

Indeed, the minimum value of the target function is exactly 0. Quod erat demonstrantum.

NULL

 inequality.mw

 

 

How to prove the inequality x^(4*y)+y^(4*x) <= 2 provided x^2+y^2 = 2, 0 <= x, 0 <= y? That problem was posed  by Israeli mathematician nicked by himself as arqady in Russian math forum and was not answered there.I know how to prove that with Maple and don't know how to prove that without Maple. Neither LagrangeMultipliers nor extrema work here. The difficulty consists in the nonlinearity both the target function and the main constraint. The first step is to linearize the main constraint and the second step is to reduce the number of variables to one.

restart; A := eval(x^(4*y)+y^(4*x), [x = sqrt(u), y = sqrt(v)]);

(u^(1/2))^(4*v^(1/2))+(v^(1/2))^(4*u^(1/2))

(1)

 

B := expand(A);

u^(2*v^(1/2))+v^(2*u^(1/2))

(2)

C := eval(B, u = 2-v);

(2-v)^(2*v^(1/2))+v^(2*(2-v)^(1/2))

(3)

It is more or less clear that the plot of F is symmetric wrt  the straight line v=1. This motivates the following change of variable  to obtain an even function.

F := simplify(expand(eval(C, v = z+1)), symbolic, power);

(1-z)^(2*(z+1)^(1/2))+(z+1)^(2*(1-z)^(1/2))

(4)

NULL

The plots suggest the only maximim of F at z=0 and its concavity.

Student[Calculus1]:-FunctionPlot(F, z = -1 .. 1);

 

Student[Calculus1]:-FunctionPlot(diff(F, z, z), z = -1 .. 1);

 

As usually, numeric global solvers cannot prove certain inequalities. However, the GlobalSearch command of the DirectSearch package indicates the only local maximum of  F and F''.NULL

Digits := 25; DirectSearch:-GlobalSearch(F, {z = -1 .. 1}, maximize, solutions = 3, tolerances = 10^(-15)); DirectSearch:-GlobalSearch(diff(F, z, z), {z = -1 .. 1}, maximize, solutions = 3, tolerances = 10^(-15));

Array([[0.8e-23, [z = -0.1980181305884928531875965e-12], 36]])

(5)

The series command confirms a local maximum of F at z=0.

series(F, z, 6);

series(2-(2/3)*z^4+O(z^6),z,6)

(6)

The extrema command indicates only the value of F at a critical point, not outputting its position.

extrema(F, z); extrema(F, z, 's');

{2}

(7)

solve(F = 2);

RootOf((1-_Z)^(2*(_Z+1)^(1/2))+(_Z+1)^(2*(1-_Z)^(1/2))-2)

(8)

DirectSearch:-SolveEquations(F = 2, {z = -1 .. 1}, AllSolutions, solutions = 3);

Matrix(1, 4, {(1, 1) = 0., (1, 2) = Vector(1, {(1) = 0.}), (1, 3) = [z = -0.5463886313e-6], (1, 4) = 27})

(9)

DirectSearch:-SolveEquations(F = 2, {z = -1 .. 1}, AllSolutions, solutions = 3, assume = integer);

Matrix(1, 4, {(1, 1) = 0., (1, 2) = Vector(1, {(1) = 0.}), (1, 3) = [z = 0], (1, 4) = 30})

(10)

NULL

 PS. I see my proof needs an additional explanation. The DirectSearch command establishes the only both local and global  maximum of F is located at z= -1.98*10^(-13) up to default error 10^(-9). After that  the series command confirms a local maximum at z=0. Combining these, one draws the conclusion that the global maximum is placed exactly at z=0 and equals 2. In order to confirm that the only real root of F=2 at z=0  is found approximately and exactly by the DirectSearch.

Download maxi.mw

For my task I have to solve inequalities in the form

abs(z) < 1

With z being an expression yielding a complex number, but taking a real number as argument. Maple does not give any results when I pass such an expression to the function solve. It just immediately returns without any output.

 

What can I do to get the solution?

How to solve the inequality

,

assuming a::real ?

Of course, with Maple. I'd like to demonstrate the difficulties, solving

>solve(log[2*abs(x-a)](abs(x+a)+abs(x-a)) < 1, x) assuming a > 0, a < 1/2

.

The correct answer under the above restrictions is

{x  > 0, x  <  a} union {a  <  x, x <  a + 1/2} union { -infinity < x, x < a - 1/2}.

This is a problem from Lviv math school olympiad '2016.

 

 

Hello everyone, 

I have some problems with the "isolve" command on Maple. I am trying to solve for integer a very easy system of equations. When I type the commands

 

restart; 

n := 2;
isolve({sum(a[k], k = 1 .. n)-1 = 1}, d)


I get the expected {a[1] = 2-d, a[2] = d}. However, if I add conditions a[1],a[2] >= 0, that is the commands



restart;
n := 2;
isolve({ge(a[1], 0), ge(a[2], 0), sum(a[k], k = 1 .. n)-1 = 1}, d)


I get the warning "Warning, solutions may have been lost". What am I doing wrong? Is there a way to get Maple to give me the possible values?

 

Thank you in advance,

David

Hi all,

I'm new to Maple. Probably this is trivial, but how can I solve an inequality as e.g., the following

-2 <=  a/x <= 0

knowing that x > 0?

Thanks

S.

Assume the inequality xA,2+xB,2+xC,2 ≤ 110 has to be entered as "symbolic entry only".

How can I check that in Maple T.A.?

It seems that there are type conversions necessary. I attempted to use the MathML package without any luck.

  1. Tried to transform $ANSWER within the answer field using MathML[ExportPresentation]( x[A,2]+x[B,2]+x[C,2] <= 110) and compare it with evalb(($ANSWER)=($RESPONSE)) in the grading code field
  2. Tried to transform $RESPONSE in the grading code: evalb(($ANSWER)=( MathML[ImportContent] ($RESPONSE)))

What’s the format of a symbolic entry? Is it really MathML!?

What is the correct way to do it?

  1. answer: ?
  2. grading code: ?
  3. expression type: Maple syntax?!
  4. Text/Symbolic entry: Symbolic entry only

Assume you want to check that the following inequality was correctly derived:

xA2+xB2+xC2 ≤ 110

How can I check that in Maple T.A.?

If I use a Maple-Graded questions, what must be in the answer field? x[A,2]+x[B,2]+x[C,2] <= 110 !?

What is the grading code?

Hello,

I have a problem with MAPLE. I would like to solve a system of 18 inequalities with 4 variables. The variables shall be rational numbers. I should also mention that I am not sure if the system has a solution. Here is my MAPLE code: 

LinearMultivariateSystem({0 < (1/20)*b11, 0 < (1/20)*b1818, 0 < (1/20)*b22, 0 < (1/20)*b33, 0 < -653385574770525739/313841848320000+(1001/20)*b33+(3003/5)*b22+4004*b11-(91/5)*b1818, 0 < -476383516463665673/69742632960000+(3003/20)*b33-(1001/10)*b1818+(27027/2)*b11+(3861/2)*b22, 0 < -372810037848242383/52306974720000+(72072/5)*b11+(3003/20)*b33-(858/5)*b1818+2002*b22, 0 < -302968656462848461/125536739328000+(1001/20)*b33-(1001/10)*b1818+5005*b11+(1365/2)*b22, 0 < -94060277895192911/627683696640000+(91/20)*b33+273*b11-(7/10)*b1818+(91/2)*b22, 0 < -3219528868317343/14944849920000+468*b11+(91/20)*b33-(91/5)*b1818+63*b22, 0 < -1167616840098623/627683696640000+(7/10)*b22+(1/20)*b33+(21/4)*b11-(7/10)*b1818, 0 < 6620337745005653/9510359040000+(91/20)*b1818-(91/5)*b33-(6552/5)*b11-(819/4)*b22, 0 < 10321214321183681/627683696640000-(21/4)*b22-(7/10)*b33-28*b11+(1/20)*b1818, 0 < 19939504442621873/627683696640000-(7/10)*b33-(39/4)*b22-(364/5)*b11+(91/20)*b1818, 0 < 21128314477665001/24141680640000-(91/5)*b33-1848*b11+(1001/20)*b1818-(1001/4)*b22, 0 < 30458564958023749/6340239360000-(1001/10)*b33+(3003/20)*b1818-9828*b11-(27027/20)*b22, 0 < 78768022311702133/17933819904000-(1001/10)*b33-8580*b11+(1001/20)*b1818-(5005/4)*b22, 0 < 418747163878248241/52306974720000-(858/5)*b33+(3003/20)*b1818-16016*b11-(9009/4)*b22}, [b11, b22, b33, b1818])

I am sorry for the writing style but I do not know how to write the command in MAPLE-style in this forum:-)

The first 4 inequalities shall ensure that all four variables b11, b22, b33, b1818 are positive. When entering the command i get the following error:

Can anybody help me please?:-)

Best regards,

Lucas

I have a linear problem with 4 variables (p0, p1,p2, p3) and a list of inequality constraints (shown below).  I would like to plot a polyhedral in 3 dimensions (p1,p2, p3 and omitting p0) showing the region that satisfies the inequalities.  That is, something similar to plots[inequal] but in 3d.  Any pointers would be appreciated.

/* Constraints */
+p0 <= 60;
-p0 +p1 >= 4;
-p0 +p2 >= 5;
-p0 +p3 >= -12;
+p0 -p2 >= -33;
+p1 -p2 >= -36;
+p2 <= 67;
-p2 +p3 >= -35;
+p0 -p3 >= 2;
+p1 -p3 >= 0;
+p2 -p3 >= 11;
+p3 <= 57;
+p0 -p1 >= -7;
+p1 <= 43;
-p1 +p2 >= 0;
-p1 +p3 >= -9;

 

Hi,

I just started to use Maple and I have a question if there exists in it an equivalent function to Mathematica's FindInstance? In general, I have an inequality and I would like to find few first solutions to it.

Hello. I have an inequality and I need to prove or negate if it is true or false. This inequality has 8 variables. I simplify it and try to see if it is ture or false. I tried "test relation" in maple and it seems I can't say it is always true or false. For some values of the variables it is true and for some others its false. Is there a method I can show if this inequlity is hold under some assumptions? I mean I want to keep some variables as constant and prove it up to a point. My inequlity is below. Thank you for the help in advance.


(P[A]*(p-w)/(1-P[A])-c)*H[A]+(w-P[A]*(p-w)/(1-P[A]))*P[A]*H[A]+w[u]*P[B]*(1-P[A])*H[B] < (P[B]*(p-w)/(1-P[B])-c)*H[B]+(w-P[B]*(p-w)/(1-P[B]))*P[B]*H[B]+w[u]*P[A]*(1-P[B])*H[B]

And this is how it looks on maple:

Hello to everyone,

I want to solve the following inequality:

solve(b^4-(2-d)*b^2-2*d*b+1+d > 0, [b]), where b is my variable and d is a pamater in (0,1]. 

When I try to sovle this I get a message "Warning, solutions may have been lost" and from the official maple website they suggest to reformulate the problem.

Is there anything I can do to solve the above inequality?

 

Thanks in advance!

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