# Items tagged with inequalityinequality Tagged Items Feed

### Plotting inequality over complexes...

February 01 2016
0 5

How can I plot this one?

### How to solve hard inequality?...

February 01 2016
0 15

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.

### Problem with isolve...

December 01 2015
0 1

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?

David

### Solve inequalities assuming positive...

November 13 2015
1 3

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.

### How to check input in Maple TA?...

October 20 2015
1 3

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?

3. expression type: Maple syntax?!
4. Text/Symbolic entry: Symbolic entry only

### How do you check that the correct inequality was p...

October 19 2015
1 1

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 !?

### Solving a big system of inequalities ...

September 09 2015
3 18

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:

Best regards,

Lucas

### How do I plot a polyhedron in 3D ?...

August 26 2015
3 5

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;

### Equivalent of Mathematica's FindInstance ...

June 17 2015
1 1

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.

### proving or negating an inequality...

April 01 2015
0 2

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:

### Solving inequality with one variable and one param...

March 20 2015
1 3

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?

### Find a group of parameters from contstraint equati...

February 17 2015
1 4

Hi all,

I have lots of contstraint equations group and I want to fund a group of parameters which can fit them.

For example, these are a simple constraint eqqations group:
eqs:{x1>0, x2>0 x1<1000, x2<1000, x1+x2>300,x1+x2<700}

Through SolveTools library, I can determine whether there is a group of parameters.

with(SolveTools[Inequality]);

LinearMultivariateSystem({x1 > 0, x1+x2 > 300, x2 < 1000, x1+x2 < 700, x2 > 0*x1 and 0*x1 < 1000}, [x1, x2]);

{[{x1 <= 300, 0 < x1}, {x2 < -x1 + 700, 300 - x1 < x2}],[{300 < x1, x1 < 700}, {0 < x2, x2 < -x1 + 700}]}

Then, if I want to find a group of parameter a group of parameters (ex, x1=300, x2=200 in this case), how should I do?

### How to solve this inequality with Maple?...

November 04 2014
0 11

How to solve the inequality

with Maple?

My attempts were the following.

Warning, solutions may have been lost

Of course, this works

f(1);
,

but one wishes to describe the solutions in the dependence on the parameter a. Unfortunately, both

and

produce wrong outputs(An SCR has been submitted by me.).

### System of multivariable linear inequalities (12 va...

September 26 2014
4 30

Hi there.

I'm kind of new to Maple and i'm trying to solve a Linear Algebra problem for my class of Linear Algebra of the course of Physics. Also, my first language is portuguese so forgive for my not-so-perfect english.

I have a (solved) linear system of 7 equations and 12 variables (A, B, C, D, E, F, G, H, I, J, K, L) that is the following:

• A = 33 - K - L
• B = 1 + F - J
• C = -15 - F + J + K + L
• D = 15 + H - K
• E = 16 - F - H + J + K
• G = 34 - H - J - L
• I = 18 - J - K

Note: I'm using letters (A, B, ..., L) instead of X1X2, ..., X12 because it's easier to write it like this here and because I don't know if the Xn notation is allowed on Maple (i don't think so).

So, the system is possible but undetermined (with 5 degrees of freedom), being F, H, J, K and L the free variables.

Until here, everything's fine. The problem arises when the professor asks us for every solution of the system that satisfies the condition that all the variables (form A to L) are positive integers (A, B, C, D, E, F, G, H, I, J, K, L ϵ IN → natural numbers).

From my understanding, that gives rise to a system of linear inequalities with 12 variables and the following inequalities:

• A = 33 - K - L > 0
• B = 1 + F - J > 0
• C = -15 - F + J + K + L > 0
• D = 15 + H - K > 0
• E = 16 - F - H + J + K > 0
• G = 34 - H - J - L > 0
• I = 18 - J - K > 0
• > 0
• > 0
• > 0
• > 0
• > 0                            (and A,B,C,D,E,F,G,H,I,J,K,L ϵ IN)

After some research, i found that a possible way to solve this type of system of linear inequalities is trough a method of elimination (analog to Gauss-Jordan's elimination method for systems of linear equations) named Fourier-Motzkin. But it's hardwork and i wanted to do it on the computer. After some research, i came across with the following Maple command:

SolveTools[Inequality][LinearMultivariateSystem]

http://www.maplesoft.com/support/help/Maple/view.aspx?path=SolveTools%2fInequality%2fLinearMultivariateSystem

So, I tried to use that command to solve my system, with the following result (or non-result):

with(SolveTools[Inequality]);
LinearMultivariateSystem({F > 0, H > 0, J > 0, K > 0, L > 0, 1+F-J > 0, 15+H-K > 0, 18-J-K > 0, 33-K-L > 0, 34-H-J-L > 0, -15-F+J+K+L > 0, 16-F-H+J+K > 0}, [F, H, J, K, L]);

Error, (in SolveTools:-Inequality:-Piecewise) piecewise takes at least 2 parameters

So, i really need help solving this as the professor told us that the first one to solve would win a book, eheh. I don't know what I'm doing wrong. Maybe this Maple command is not made for 12 variables? Or maybe i'm just writing something on a wrong form. I've never used Maple before so i can be doing something really stupid without knowing it.

I would really apreciate an answer, as my only goal as a future physicist is to unveil the secrets of the Cosmos to us all.

Thank you again.

Miguel Jesus

### Plotting an equation given inequalities...

September 24 2014
0 1

Hi, I have an equation and I want to plot it for a set of inequalities, is this possible or will i need to insert values for the constant?

So if i have the equation;

y=(X_0-aX)/a+(X_0-bX)/b, can I plot y given that: X_0>bX and <aX

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