2

I'm a maple newbie and I would like to simplify this expression as much as i can:

$$g(q) = -8 \cdot 2^q + 8 \cdot 2^{\frac{3}{2}q} + 1$$

In such case i would like to write the expression like:

$$g(q) = -2^{q+3} + 2^{\frac{3}{2}q + 3} + 1 \;\;\;\; (1)$$

and then factorize $2^q$ in order to have:

$$g(q) = 2^{q+3}(2^{\frac{q}{2}} - 1) + 1 \;\;\;\; (2)$$

Is it possible to have at least the expression (1)? What about the (2)? assume the original one is given, $q$ is an integer positive variable, even (i don't think such detail is particularly useful).

I tried, factor, collect, simplify etc...

Kaster
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user8469759
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  • Is it $82$ or $8 \cdot 2$? – Kaster Feb 17 '16 at 13:50
  • It is $8 \times 2$ – user8469759 Feb 17 '16 at 13:50
  • Too short for a comment.

    $8=2^3$

     – Chinny84 Feb 17 '16 at 14:08
  • Is the question how do you reduce by hand or is it how do you use maple to reduce? – Chinny84 Feb 17 '16 at 14:16
  • How to use maple to reduce the expression, specifically i just to want to pass from the original expression to the (1), assuming is possible. I would also like to be able to pass from the original one to the (2), otherwise I want just to know how to reduce it as much as i can. – user8469759 Feb 17 '16 at 14:18
  • I think you need to be more explicit in the post since using "I am newbie in maple" does not immediately lead to asking for help with maple. IMHO – Chinny84 Feb 17 '16 at 14:23
  • The question is simple... IMHO... do you know which sequence of maple statements could let me transform my original expression into (1)? I was thinking something like a sequence of simplify, factor etc... I tried but i don't reach the expression I'm looking for. So i don't get if maple is "smart enough" to provide me the (1). The "newbie" means "maybe there's some special command that I don't know or i can't come up which sequence of maple statements could help me". – user8469759 Feb 17 '16 at 14:29

2 Answers2

1

HINT:

Use the following factorization:
$$8=2^3$$

Mary Star
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0

Maple has trouble recognizing a number as anything but exactly that: $2^3$ is just the number $8$ to Maple, not the other way around. You can work around this, however, with the following substitutions,

g:=q->-8*2^(q)+8*2^(3/2*q)+1;

subs(8=2^x, -8=-2^x, g(q));
simplify(%);
subs(x = 3, %);

This gives you (1), however this is one of those cases where the computer program does not recognize things as well as you do. I think you need to motivate why you wish to get something like (2) - if you are looking to check your own solution for root finding, you could use the is command

is(g(q) = 2^(q+3)*(2^(q/2)-1)+1); # is g(q) equal to (2)

otherwise, for root finding, solve should work just fine.

Therkel
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