## 250 Reputation

1 years, 172 days

## Can this formula be simplified?...

Maple

I tried to simplify it, but It didn't work that well.

simplify(%)

I always feel that this formula can be further simplified, but there is no way to start. Of course, My thoughts maybe incorrect. maybe this is the simplest form.

## Expression with products in both numerat...

Maple 2020

I have an expression

product(q^(n -2)- q^i, i = 0 .. r )/product(q^(n-2) - q^(i+1), i = 0 .. r)

Obviously, it can be further simplified.

But in maple I can't do that, I use simplify and expand , all failed.

simplify(expand(%))

What should I do to get the simplified result I want？

## convert every row of matrix to list...

I'd like to convert  every row of matrix to list, but failed.  I want to use batch operations map(~) not for-loop.

 > data:=Matrix(3, 5, [[2, -6, 3, 0, 0], [5, -2, 4, 1, 2], [17, -4, 10, 20, 99]])
 (2)
 > convert~(data,list)
 (3)
 > convert(data,list)
 (4)

The expected output is the following:

[2, -6, 3, 0, 0]
[5, -2, 4, 1, 2]
[17, -4, 10, 20, 99]

## How to find symbolic extreme values un...

Maple

Unfortunately,  Optimization:-Maximize command in following example returns a not precise result (I use Maple 2020).

```restart:
s1:= Optimization:-Maximize((x-2*y)/(5*x^2-2*x*y+2*y^2), {2*x^2 - y^2 + x*y=1})```

Maple is running the following results:

I read help of  Maximize, It seems to be using only numerical methods .

 The Minimize and Maximize commands use various methods implemented in a built-in library provided by the Numerical Algorithms Group (NAG).

Can't Maple find a symbolic solution for extreme values under such constrained inequality or equality conditions?

Ps:

For the correct  symbolic  solution, we can try to  use Mathematica 12.

```Maximize[{(x - 2*y)/(5*x^2 - 2*x*y + 2*y^2),
2*x^2 - y^2 + x*y == 1}, {x, y}]```

We can compare numerical sizes of Optimal solution between maple and mathematica.

```Digits:=20;
sqrt(2.)/4.```

Another Problem:

If I accept numerical solutions of maple ,how do I estimate errors without knowing the exact solution ?

## Find positive integer solutions of equat...

Maple

Hello,The system of equations is as follows：

I'd like to find all integer solutions in [1,20], when I use isolve ,the results are not good.  Since at least one variable is equal to 0 in evey solution.

{isolve}({a+b+c=a1+b1+c1, a^2+b^2+c^2=(a1)^2+(b1)^2+(c1)^2,a*b*c=2*a1*b1*c1})

In maple I did not  want to use less efficient for-loop like C programing as following.

#include <math.h>
#include <stdio.h>
void main()
{
long int a,b,c,d,e,f;
for(a=1;a<20;a++)
{
for(b=1;b<20;b++)
{
for(c=1;c<20;c++)
{
for(d=1;d<20;d++)
{
for(e=1;e<20;e++)
{
for(f=1;f<20;f++)
{
if(a+b+c==d+e+f&&a*a+b*b+c*c==d*d+e*e+f*f&&a*b*c==2*d*e*f)                                             printf("a=%d,b=%d,c=%d,d=%d,e=%d,f=%d\n",a,b,c,d,e,f);
}
}
}
}
}
}
}
a=3,b=5,c=16,d=1,e=8,f=15
a=3,b=5,c=16,d=1,e=15,f=8
a=3,b=5,c=16,d=8,e=1,f=15
a=3,b=5,c=16,d=8,e=15,f=1
a=3,b=5,c=16,d=15,e=1,f=8
a=3,b=5,c=16,d=15,e=8,f=1
a=3,b=16,c=5,d=1,e=8,f=15
a=3,b=16,c=5,d=1,e=15,f=8
a=3,b=16,c=5,d=8,e=1,f=15
a=3,b=16,c=5,d=8,e=15,f=1
a=3,b=16,c=5,d=15,e=1,f=8
a=3,b=16,c=5,d=15,e=8,f=1
a=5,b=3,c=16,d=1,e=8,f=15
a=5,b=3,c=16,d=1,e=15,f=8
a=5,b=3,c=16,d=8,e=1,f=15
a=5,b=3,c=16,d=8,e=15,f=1
a=5,b=3,c=16,d=15,e=1,f=8
a=5,b=3,c=16,d=15,e=8,f=1
a=5,b=16,c=3,d=1,e=8,f=15
a=5,b=16,c=3,d=1,e=15,f=8
a=5,b=16,c=3,d=8,e=1,f=15
a=5,b=16,c=3,d=8,e=15,f=1
a=5,b=16,c=3,d=15,e=1,f=8
a=5,b=16,c=3,d=15,e=8,f=1
a=16,b=3,c=5,d=1,e=8,f=15
a=16,b=3,c=5,d=1,e=15,f=8
a=16,b=3,c=5,d=8,e=1,f=15
a=16,b=3,c=5,d=8,e=15,f=1
a=16,b=3,c=5,d=15,e=1,f=8
a=16,b=3,c=5,d=15,e=8,f=1
a=16,b=5,c=3,d=1,e=8,f=15
a=16,b=5,c=3,d=1,e=15,f=8
a=16,b=5,c=3,d=8,e=1,f=15
a=16,b=5,c=3,d=8,e=15,f=1
a=16,b=5,c=3,d=15,e=1,f=8
a=16,b=5,c=3,d=15,e=8,f=1

Does Maple have more good ways to solve that?

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