Maple 2024 Questions and Posts

These are Posts and Questions associated with the product, Maple 2024

Is there a way to disable Maples AI Formula Assistant? This could be relevant when using Maple for a test.

I found that sometimes Maple gives

               Error, (in Typesetting:-Parse) too many levels of recursion

When using the Latex command on the output of Student:-ODEs:-ODESteps

Below is worksheet showing it works for some and gives error for others. Is there a workaround for this? I'd like to convert the steps to Latex.

This happens in worksheet using either Display->Typesetting level as EXTENDED or STANDARD

restart;

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1722 and is the same as the version installed in this computer, created 2024, April 12, 17:58 hours Pacific Time.`

ode:=diff(y(x),x)=0;
the_output:=Student:-ODEs:-ODESteps(ode,y(x)):
latex(the_output)

diff(y(x), x) = 0

\begin{array}{ccc}
 & {} & \textrm{Let's solve}
\\
 {} & {} & \frac{d}{d x}y \! \left(x \right)=0
\\
 \textrm{•} & {} & \textrm{Highest derivative means the order of the ODE is}1
\\
 {} & {} & \frac{d}{d x}y \! \left(x \right)
\\
 \textrm{•} & {} & \textrm{Integrate both sides with respect to}x  
\\
 {} & {} & \int \left(\frac{d}{d x}y \! \left(x \right)\right)d x =\int 0d x +\mathit{C1}  
\\
 \textrm{•} & {} & \textrm{Evaluate integral}
\\
 {} & {} & y \! \left(x \right)=\mathit{C1}  
\\
 \textrm{•} & {} & \textrm{Solve for}y \! \left(x \right)
\\
 {} & {} & y \! \left(x \right)=\mathit{C1}  
\end{array}

ode := diff(y(x), x, x, x ) + 3*diff(y(x), x, x) + 4*diff(y(x), x) + 2*y(x) = 0;
the_output:=Student:-ODEs:-ODESteps(ode,y(x)):
latex(the_output)

diff(diff(diff(y(x), x), x), x)+3*(diff(diff(y(x), x), x))+4*(diff(y(x), x))+2*y(x) = 0

Error, (in Typesetting:-Parse) too many levels of recursion

 

 

Download latex_error_ODE_steps_maple_2024_april_13_2024.mw

update: Reported to Maplesoft support.

I have a proceure that returns 7 values. I cac get it to return ang single specific value ousing e.g [2] to get the second.
Or a range[3..6] for the third to sixth.

Is there a way to get specific seperated values e.g [1] and[[6]. The procedure is burried in a package so it is difficult to post.

This second order (Euler type) ode has no solution for the given two initial conditions. but Maple gives solution with one unresolved constant of integration.

ode:=x^2*diff(y(x),x$2)-2*y(x)=0;
ic:=y(0)=4,D(y)(0)=-1;

sol_no_IC:=dsolve(ode)

The IC's are given at x=0 as a trick to see what Maple will do. We see that at x=0 there is division by zero. So no solution exist for these IC's. But see what happens

sol_with_IC:=dsolve([ode,ic])

It seems Maple simply threw away the part of the solution it could not handle due to the x=0 and just returned the rest.

odetest(sol_with_IC,[ode,ic])

The correct answer should have been the NULL solution (i.e. no solution). 

What Am I missing here? Why does Maple do this? Should Maple have returned such a solution?

Maple 2024 on windows 10.

update:

Reported to Maplesoft support.

update:

Here is another example ode. This is first order ode. Maple gives a solution that does not satisfy the initial condition also. I wish I can understand how Maple comes up with these solutions since when I solve these by hand I see it is not possible to satisfy the IC, hence no solution exist.

14876

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1722 and is the same as the version installed in this computer, created 2024, April 12, 17:58 hours Pacific Time.`

restart;

14876

ode:=diff(y(x),x)+y(x)/x=x^2;
ic:=y(0)=a;

diff(y(x), x)+y(x)/x = x^2

y(0) = a

dsolve(ode)

y(x) = ((1/4)*x^4+c__1)/x

sol:=dsolve([ode,ic])

y(x) = (1/4)*x^3

odetest(sol,[ode,ic])

[0, a]

Student:-ODEs:-ODESteps([ode,ic])

Error, (in Student:-ODEs:-applyICO1) numeric exception: division by zero

 

 

Download another_strange_solution_ode_maple_2024.mw

I have a simple tank design worksheet that calculates dimensions of a tank that I need to build to hold a given amount of liquid.  My question is this - when I include a "with(Units);" statement, the volume function gets rendered in operator prefix notation.  Why is this?  Is there a setting to prevent this from happening?  Thanks.

Without "with(Units);"...

With "with(Units);"...

I've included a worksheet that shows the function both with and without the inclusion of "with(Units);".

Tank_Design_Calculation_-_Units_Question_(v00).mw

I have two expressions, wo_theta and with_theta, which depend on multiple variables.

I would need your help to:

  1. Verify, as formally as possible, that wo_theta > with_theta always, i.e., for any value of theta different from zero (and regardless of the values taken up by the other variables)
  2. Show the above in a way that is easy and immediate to interpret (perhaps using some type of plot?)

In other words, I want to verify that as soon as I introduce any theta in my expression such expression becomes smaller:

restart;

local gamma;

gamma

(1)

assume(0 < gamma, 0 < nu__02, 0 < nu__01, 0 <= sigma__v, delta__1::real, delta__2::real, delta__3::real, theta::real);
interface(showassumed=0);

1

(2)

wo_theta := X__3*(-X__3*lambda__3 - delta__3*lambda__3 + DEV) + X__2*(-X__2*lambda__2 - delta__2*lambda__2 - nu__02) + X__1*(-X__1*lambda__1 - delta__1*lambda__1 - nu__01) + X__2*(nu__02 + DEV/2) + X__1*(nu__01 + DEV/2) - gamma*X__2^2*sigma__v^2/4 - gamma*X__1^2*sigma__v^2/4 + gamma*X__2*X__1*sigma__v^2/2;

X__3*(-X__3*lambda__3-delta__3*lambda__3+DEV)+X__2*(-X__2*lambda__2-delta__2*lambda__2-nu__02)+X__1*(-X__1*lambda__1-delta__1*lambda__1-nu__01)+X__2*(nu__02+(1/2)*DEV)+X__1*(nu__01+(1/2)*DEV)-(1/4)*gamma*X__2^2*sigma__v^2-(1/4)*gamma*X__1^2*sigma__v^2+(1/2)*gamma*X__2*X__1*sigma__v^2

(3)

with_theta := X__3*(-X__3*lambda__3 - theta*lambda__3 - delta__3*lambda__3 + DEV) + X__2*(-X__2*lambda__2 + theta*lambda__2 - delta__2*lambda__2 - nu__02) + X__1*(-X__1*lambda__1 + theta*lambda__1 - delta__1*lambda__1 - nu__01) + X__2*(nu__02 + DEV/2) + X__1*(nu__01 + DEV/2) - gamma*X__2^2*sigma__v^2/4 - gamma*X__1^2*sigma__v^2/4 + gamma*X__2*X__1*sigma__v^2/2 + theta*(lambda__1*(X__1 + delta__1 - theta) + lambda__2*(X__2 + delta__2 - theta) - lambda__3*(X__3 + delta__3 + theta));

X__3*(-X__3*lambda__3-theta*lambda__3-delta__3*lambda__3+DEV)+X__2*(-X__2*lambda__2+theta*lambda__2-delta__2*lambda__2-nu__02)+X__1*(-X__1*lambda__1+theta*lambda__1-delta__1*lambda__1-nu__01)+X__2*(nu__02+(1/2)*DEV)+X__1*(nu__01+(1/2)*DEV)-(1/4)*gamma*X__2^2*sigma__v^2-(1/4)*gamma*X__1^2*sigma__v^2+(1/2)*gamma*X__2*X__1*sigma__v^2+theta*(lambda__1*(X__1+delta__1-theta)+lambda__2*(X__2+delta__2-theta)-lambda__3*(X__3+delta__3+theta))

(4)

collect(with_theta, theta);

(-lambda__1-lambda__2-lambda__3)*theta^2+(-X__3*lambda__3+X__2*lambda__2+X__1*lambda__1+lambda__1*(X__1+delta__1)+lambda__2*(X__2+delta__2)-lambda__3*(X__3+delta__3))*theta+X__3*(-X__3*lambda__3-delta__3*lambda__3+DEV)+X__2*(-X__2*lambda__2-delta__2*lambda__2-nu__02)+X__1*(-X__1*lambda__1-delta__1*lambda__1-nu__01)+X__2*(nu__02+(1/2)*DEV)+X__1*(nu__01+(1/2)*DEV)-(1/4)*gamma*X__2^2*sigma__v^2-(1/4)*gamma*X__1^2*sigma__v^2+(1/2)*gamma*X__2*X__1*sigma__v^2

(5)

solve(wo_theta > with_theta, theta) assuming 0 < gamma, 0 < nu__02, 0 < nu__01, 0 < sigma__v, delta__1::real, delta__2::real, delta__3::real, theta::real;

solve(with_theta < wo_theta, theta);

Warning, solve may be ignoring assumptions on the input variables.

 

Warning, solutions may have been lost

 

difference_term := (-lambda__1 - lambda__2 - lambda__3)*theta^2 + (X__1*lambda__1 + X__2*lambda__2 - X__3*lambda__3 + lambda__1*(X__1 + delta__1) + lambda__2*(X__2 + delta__2) - lambda__3*(X__3 + delta__3))*theta;

(-lambda__1-lambda__2-lambda__3)*theta^2+(-X__3*lambda__3+X__2*lambda__2+X__1*lambda__1+lambda__1*(X__1+delta__1)+lambda__2*(X__2+delta__2)-lambda__3*(X__3+delta__3))*theta

(6)

# I would expect such difference_term in theta to be always < 0, i.e., for any theta different from 0)
# (Note that lambda_1, lambda_2, and lambda_3 are always > 0, while theta, the three X and the three delta can be positive or negative. In other words, it suffices to show that the linear term in theta is always negative...)
solve(difference_term<0);

Warning, solve may be ignoring assumptions on the input variables.

 

{X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, X__1 < -(1/2)*(2*X__2*lambda__2-2*X__3*lambda__3-lambda__1*theta-lambda__2*theta-lambda__3*theta+delta__1*lambda__1+delta__2*lambda__2-delta__3*lambda__3)/lambda__1, theta < 0, lambda__1 < 0, lambda__2 < 0, lambda__3 < 0}, {X__1 = X__1, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__1 = 0, X__2 < (1/2)*(2*X__3*lambda__3+lambda__2*theta+lambda__3*theta-delta__2*lambda__2+delta__3*lambda__3)/lambda__2, theta < 0, lambda__2 < 0, lambda__3 < 0}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, 0 < lambda__1, theta < 0, lambda__2 < 0, lambda__3 < 0, -(1/2)*(2*X__2*lambda__2-2*X__3*lambda__3-lambda__1*theta-lambda__2*theta-lambda__3*theta+delta__1*lambda__1+delta__2*lambda__2-delta__3*lambda__3)/lambda__1 < X__1}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__2 = 0, X__1 < (1/2)*(2*X__3*lambda__3+lambda__1*theta+lambda__3*theta-delta__1*lambda__1+delta__3*lambda__3)/lambda__1, theta < 0, lambda__1 < 0, lambda__3 < 0}, {X__1 = X__1, X__2 = X__2, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__1 = 0, lambda__2 = 0, theta < 0, lambda__3 < 0, -(1/2)*delta__3-(1/2)*theta < X__3}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__2 = 0, 0 < lambda__1, theta < 0, lambda__3 < 0, (1/2)*(2*X__3*lambda__3+lambda__1*theta+lambda__3*theta-delta__1*lambda__1+delta__3*lambda__3)/lambda__1 < X__1}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, 0 < lambda__2, X__1 < -(1/2)*(2*X__2*lambda__2-2*X__3*lambda__3-lambda__1*theta-lambda__2*theta-lambda__3*theta+delta__1*lambda__1+delta__2*lambda__2-delta__3*lambda__3)/lambda__1, theta < 0, lambda__1 < 0, lambda__3 < 0}, {X__1 = X__1, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__1 = 0, 0 < lambda__2, theta < 0, lambda__3 < 0, (1/2)*(2*X__3*lambda__3+lambda__2*theta+lambda__3*theta-delta__2*lambda__2+delta__3*lambda__3)/lambda__2 < X__2}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, 0 < lambda__1, 0 < lambda__2, theta < 0, lambda__3 < 0, -(1/2)*(2*X__2*lambda__2-2*X__3*lambda__3-lambda__1*theta-lambda__2*theta-lambda__3*theta+delta__1*lambda__1+delta__2*lambda__2-delta__3*lambda__3)/lambda__1 < X__1}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__3 = 0, X__1 < -(1/2)*(2*X__2*lambda__2-lambda__1*theta-lambda__2*theta+delta__1*lambda__1+delta__2*lambda__2)/lambda__1, theta < 0, lambda__1 < 0, lambda__2 < 0}, {X__1 = X__1, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__1 = 0, lambda__3 = 0, X__2 < -(1/2)*delta__2+(1/2)*theta, theta < 0, lambda__2 < 0}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__3 = 0, 0 < lambda__1, theta < 0, lambda__2 < 0, -(1/2)*(2*X__2*lambda__2-lambda__1*theta-lambda__2*theta+delta__1*lambda__1+delta__2*lambda__2)/lambda__1 < X__1}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__2 = 0, lambda__3 = 0, X__1 < -(1/2)*delta__1+(1/2)*theta, theta < 0, lambda__1 < 0}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__2 = 0, lambda__3 = 0, 0 < lambda__1, theta < 0, -(1/2)*delta__1+(1/2)*theta < X__1}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__3 = 0, 0 < lambda__2, X__1 < -(1/2)*(2*X__2*lambda__2-lambda__1*theta-lambda__2*theta+delta__1*lambda__1+delta__2*lambda__2)/lambda__1, theta < 0, lambda__1 < 0}, {X__1 = X__1, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__1 = 0, lambda__3 = 0, 0 < lambda__2, theta < 0, -(1/2)*delta__2+(1/2)*theta < X__2}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__3 = 0, 0 < lambda__1, 0 < lambda__2, theta < 0, -(1/2)*(2*X__2*lambda__2-lambda__1*theta-lambda__2*theta+delta__1*lambda__1+delta__2*lambda__2)/lambda__1 < X__1}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, 0 < lambda__3, X__1 < -(1/2)*(2*X__2*lambda__2-2*X__3*lambda__3-lambda__1*theta-lambda__2*theta-lambda__3*theta+delta__1*lambda__1+delta__2*lambda__2-delta__3*lambda__3)/lambda__1, theta < 0, lambda__1 < 0, lambda__2 < 0}, {X__1 = X__1, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__1 = 0, 0 < lambda__3, X__2 < (1/2)*(2*X__3*lambda__3+lambda__2*theta+lambda__3*theta-delta__2*lambda__2+delta__3*lambda__3)/lambda__2, theta < 0, lambda__2 < 0}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, 0 < lambda__1, 0 < lambda__3, theta < 0, lambda__2 < 0, -(1/2)*(2*X__2*lambda__2-2*X__3*lambda__3-lambda__1*theta-lambda__2*theta-lambda__3*theta+delta__1*lambda__1+delta__2*lambda__2-delta__3*lambda__3)/lambda__1 < X__1}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__2 = 0, 0 < lambda__3, X__1 < (1/2)*(2*X__3*lambda__3+lambda__1*theta+lambda__3*theta-delta__1*lambda__1+delta__3*lambda__3)/lambda__1, theta < 0, lambda__1 < 0}, {X__1 = X__1, X__2 = X__2, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__1 = 0, lambda__2 = 0, 0 < lambda__3, X__3 < -(1/2)*delta__3-(1/2)*theta, theta < 0}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__2 = 0, 0 < lambda__1, 0 < lambda__3, theta < 0, (1/2)*(2*X__3*lambda__3+lambda__1*theta+lambda__3*theta-delta__1*lambda__1+delta__3*lambda__3)/lambda__1 < X__1}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, 0 < lambda__2, 0 < lambda__3, X__1 < -(1/2)*(2*X__2*lambda__2-2*X__3*lambda__3-lambda__1*theta-lambda__2*theta-lambda__3*theta+delta__1*lambda__1+delta__2*lambda__2-delta__3*lambda__3)/lambda__1, theta < 0, lambda__1 < 0}, {X__1 = X__1, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__1 = 0, 0 < lambda__2, 0 < lambda__3, theta < 0, (1/2)*(2*X__3*lambda__3+lambda__2*theta+lambda__3*theta-delta__2*lambda__2+delta__3*lambda__3)/lambda__2 < X__2}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, 0 < lambda__1, 0 < lambda__2, 0 < lambda__3, theta < 0, -(1/2)*(2*X__2*lambda__2-2*X__3*lambda__3-lambda__1*theta-lambda__2*theta-lambda__3*theta+delta__1*lambda__1+delta__2*lambda__2-delta__3*lambda__3)/lambda__1 < X__1}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, 0 < theta, lambda__1 < 0, lambda__2 < 0, lambda__3 < 0, -(1/2)*(2*X__2*lambda__2-2*X__3*lambda__3-lambda__1*theta-lambda__2*theta-lambda__3*theta+delta__1*lambda__1+delta__2*lambda__2-delta__3*lambda__3)/lambda__1 < X__1}, {X__1 = X__1, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__1 = 0, 0 < theta, lambda__2 < 0, lambda__3 < 0, (1/2)*(2*X__3*lambda__3+lambda__2*theta+lambda__3*theta-delta__2*lambda__2+delta__3*lambda__3)/lambda__2 < X__2}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, 0 < theta, 0 < lambda__1, X__1 < -(1/2)*(2*X__2*lambda__2-2*X__3*lambda__3-lambda__1*theta-lambda__2*theta-lambda__3*theta+delta__1*lambda__1+delta__2*lambda__2-delta__3*lambda__3)/lambda__1, lambda__2 < 0, lambda__3 < 0}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__2 = 0, 0 < theta, lambda__1 < 0, lambda__3 < 0, (1/2)*(2*X__3*lambda__3+lambda__1*theta+lambda__3*theta-delta__1*lambda__1+delta__3*lambda__3)/lambda__1 < X__1}, {X__1 = X__1, X__2 = X__2, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__1 = 0, lambda__2 = 0, 0 < theta, X__3 < -(1/2)*delta__3-(1/2)*theta, lambda__3 < 0}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__2 = 0, 0 < theta, 0 < lambda__1, X__1 < (1/2)*(2*X__3*lambda__3+lambda__1*theta+lambda__3*theta-delta__1*lambda__1+delta__3*lambda__3)/lambda__1, lambda__3 < 0}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, 0 < theta, 0 < lambda__2, lambda__1 < 0, lambda__3 < 0, -(1/2)*(2*X__2*lambda__2-2*X__3*lambda__3-lambda__1*theta-lambda__2*theta-lambda__3*theta+delta__1*lambda__1+delta__2*lambda__2-delta__3*lambda__3)/lambda__1 < X__1}, {X__1 = X__1, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__1 = 0, 0 < theta, 0 < lambda__2, X__2 < (1/2)*(2*X__3*lambda__3+lambda__2*theta+lambda__3*theta-delta__2*lambda__2+delta__3*lambda__3)/lambda__2, lambda__3 < 0}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, 0 < theta, 0 < lambda__1, 0 < lambda__2, X__1 < -(1/2)*(2*X__2*lambda__2-2*X__3*lambda__3-lambda__1*theta-lambda__2*theta-lambda__3*theta+delta__1*lambda__1+delta__2*lambda__2-delta__3*lambda__3)/lambda__1, lambda__3 < 0}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__3 = 0, 0 < theta, lambda__1 < 0, lambda__2 < 0, -(1/2)*(2*X__2*lambda__2-lambda__1*theta-lambda__2*theta+delta__1*lambda__1+delta__2*lambda__2)/lambda__1 < X__1}, {X__1 = X__1, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__1 = 0, lambda__3 = 0, 0 < theta, lambda__2 < 0, -(1/2)*delta__2+(1/2)*theta < X__2}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__3 = 0, 0 < theta, 0 < lambda__1, X__1 < -(1/2)*(2*X__2*lambda__2-lambda__1*theta-lambda__2*theta+delta__1*lambda__1+delta__2*lambda__2)/lambda__1, lambda__2 < 0}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__2 = 0, lambda__3 = 0, 0 < theta, lambda__1 < 0, -(1/2)*delta__1+(1/2)*theta < X__1}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__2 = 0, lambda__3 = 0, 0 < theta, 0 < lambda__1, X__1 < -(1/2)*delta__1+(1/2)*theta}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__3 = 0, 0 < theta, 0 < lambda__2, lambda__1 < 0, -(1/2)*(2*X__2*lambda__2-lambda__1*theta-lambda__2*theta+delta__1*lambda__1+delta__2*lambda__2)/lambda__1 < X__1}, {X__1 = X__1, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__1 = 0, lambda__3 = 0, 0 < theta, 0 < lambda__2, X__2 < -(1/2)*delta__2+(1/2)*theta}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__3 = 0, 0 < theta, 0 < lambda__1, 0 < lambda__2, X__1 < -(1/2)*(2*X__2*lambda__2-lambda__1*theta-lambda__2*theta+delta__1*lambda__1+delta__2*lambda__2)/lambda__1}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, 0 < theta, 0 < lambda__3, lambda__1 < 0, lambda__2 < 0, -(1/2)*(2*X__2*lambda__2-2*X__3*lambda__3-lambda__1*theta-lambda__2*theta-lambda__3*theta+delta__1*lambda__1+delta__2*lambda__2-delta__3*lambda__3)/lambda__1 < X__1}, {X__1 = X__1, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__1 = 0, 0 < theta, 0 < lambda__3, lambda__2 < 0, (1/2)*(2*X__3*lambda__3+lambda__2*theta+lambda__3*theta-delta__2*lambda__2+delta__3*lambda__3)/lambda__2 < X__2}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, 0 < theta, 0 < lambda__1, 0 < lambda__3, X__1 < -(1/2)*(2*X__2*lambda__2-2*X__3*lambda__3-lambda__1*theta-lambda__2*theta-lambda__3*theta+delta__1*lambda__1+delta__2*lambda__2-delta__3*lambda__3)/lambda__1, lambda__2 < 0}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__2 = 0, 0 < theta, 0 < lambda__3, lambda__1 < 0, (1/2)*(2*X__3*lambda__3+lambda__1*theta+lambda__3*theta-delta__1*lambda__1+delta__3*lambda__3)/lambda__1 < X__1}, {X__1 = X__1, X__2 = X__2, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__1 = 0, lambda__2 = 0, 0 < theta, 0 < lambda__3, -(1/2)*delta__3-(1/2)*theta < X__3}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__2 = 0, 0 < theta, 0 < lambda__1, 0 < lambda__3, X__1 < (1/2)*(2*X__3*lambda__3+lambda__1*theta+lambda__3*theta-delta__1*lambda__1+delta__3*lambda__3)/lambda__1}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, 0 < theta, 0 < lambda__2, 0 < lambda__3, lambda__1 < 0, -(1/2)*(2*X__2*lambda__2-2*X__3*lambda__3-lambda__1*theta-lambda__2*theta-lambda__3*theta+delta__1*lambda__1+delta__2*lambda__2-delta__3*lambda__3)/lambda__1 < X__1}, {X__1 = X__1, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, lambda__1 = 0, 0 < theta, 0 < lambda__2, 0 < lambda__3, X__2 < (1/2)*(2*X__3*lambda__3+lambda__2*theta+lambda__3*theta-delta__2*lambda__2+delta__3*lambda__3)/lambda__2}, {X__2 = X__2, X__3 = X__3, delta__1 = delta__1, delta__2 = delta__2, delta__3 = delta__3, 0 < theta, 0 < lambda__1, 0 < lambda__2, 0 < lambda__3, X__1 < -(1/2)*(2*X__2*lambda__2-2*X__3*lambda__3-lambda__1*theta-lambda__2*theta-lambda__3*theta+delta__1*lambda__1+delta__2*lambda__2-delta__3*lambda__3)/lambda__1}

(7)
 

NULL

Download inequality.mw

I have a problem with the order  of the Eigenvalues and Vectors flipping. It is a bit random. I only found it trying to understand why a procedure sometimes rotated a conic one way and  then the other. This a really causing a quite a problem, I have only tried this in Maple 2024 so far. I have included screen shots to prove the effect.

restart

 

with(LinearAlgebra):

 

M:=Matrix([[0,1],[1,0]]);

a,b:=Eigenvectors(M)  ;#click here and press enter again possible a 4 times, output can filp

 

Matrix(2, 2, {(1, 1) = 0, (1, 2) = 1, (2, 1) = 1, (2, 2) = 0})

 

Vector[column](%id = 36893491125752073860), Matrix(%id = 36893491125752073980)

(1)

a

Vector(2, {(1) = 1, (2) = -1})

(2)

b

Matrix(2, 2, {(1, 1) = 1, (1, 2) = -1, (2, 1) = 1, (2, 2) = 1})

(3)