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I have the system:

 

Update:

{-1/2 < 2*f*(1/53)+7*g*(1/53), 3/106 < 7*f*(1/53)-2*g*(1/53), 2*f*(1/53)+7*g*(1/53) < -37/106, 7*f*(1/53)-2*g*(1/53) < 1/2}

 

which I wish to solve over integers but isolve() gives me "Warning, solutions may have been lost and no solutions". The solutions exist and are {[f =0, g = -3] || [f = 1, g = -4], [f = 1, g = -3] || [f = 2, g = -4]}, but I cannot obtain them with Maple. Could you tell me what is wrong and how I should treat this kind of problems in the future, please.

Mathematica 10.0

Reduce[{-1/2 < 2*f*(1/53) + 7*g*(1/53), 3/106 < 7*f*(1/53) - 2*g*(1/53), 2*f*(1/53) + 7*g*(1/53) < -37/106, 7*f*(1/53) - 2*g*(1/53) < 1/2}, {f, g}, Integers]

(f == 0 && g == -3) || (f == 1 && g == -4) || (f == 1 &&
   g == -3) || (f == 2 && g == -4)

 

Maple

isolve({-1/2 < 2*f*(1/53)+7*g*(1/53), 3/106 < 7*f*(1/53)-2*g*(1/53), 2*f*(1/53)+7*g*(1/53) < -37/106, 7*f*(1/53)-2*g*(1/53) < 1/2});
Warning, solutions may have been lost

 

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

Dear friends,

I would like to know the agorithm of isovle for solving 2 order equations for more than 3 variables.

I see that not all the solutions are shown for example for:

x^2+y^2=z^2+t^2

 Could you please help me with this?

 

Hi all,

 

C:=2:

solve({K*(K-1)>6*C-2,K>0},K,useassumptions) assuming K::point;

It does not exacly give me 'integer'.

for C from 2 to 10 do

isolve({K*(K-1)>6*C-2,K>0},a);

end do;

gives me pretty much what I am expected to see. The positive smallest (ceiling) numbers, 4,5,6,6,7,7,8,8,9.

 

Is there a way to obtain a "neater" output?

Say I just want a sequence (list) of 4,5,6,6,7,7,8,8,9.

The equation 

solve(surd(-2*x+4,3)+surd(x+2,3)+surd(x -6> ,3)=0);

has three different integer solutions.

I want to choose the integer number a, b, c, d, e, f to the equation 

(a*x + b)^(1/3) + (c*x + d)^(1/3) + (e*x + f)^(1/3) =0 

has three different integer solutions.

I tried

restart:

L:=[]:

for a from -10 to -1  do

How to choose the integer parameters a, b, c, d, m to the following equation has two integer solutions?

sqrt(a* x + b) +  sqrt(c*x + d) = m. 

For example, the equation sqrt(x +5 ) + sqrt(8-x)=5 has two solution x = -1 and x = 4 

How many positive integer solutions (a,b,c) to 2a+3b+3c=2010

Dear friends, I encounter the following problem. Let k and i be two given positive integers such that k>=2i>=4. How to find all nonnegative integers tuples (x_1, x_2, ..., x_i) such that k-2i<=x_1+2x_2+...+ix_i<=k-i? The buildin command "isolve" seems not work. Thanks.

Why won't isolve show all the solutions here?

> a := 6*x+2*y >= 48:
> b := 6*x+2*y <= 60:
>
> with(plots):
> aa := implicitplot(a, x = 0 .. 10, y = 0 .. 5, filledregions = true, transparency = .5):
> bb := implicitplot(b, x = 0 .. 10, y = 0 .. 5, filledregions = true, transparency = .5):

display(aa,bb)

We can see the region of solutions.  But if we use isolve ...

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