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H-R

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These are questions asked by H-R

Simplifying Radicals: Part III...

H-R 155 Maple 2015
radical simplify assuming
February 06 2016
2 11

In this question, I asked for a way to simplify an expression containing radicals. The discussion led us to that as default field for simplicfication is the Complex number system we should use assume or assuming command to simplify the radicals. However, the mothod suggested there seems to not work in this new case that I have. For details please see the attached file. The terms sqrt{u} and sqrt{u-1} should cancel in denominator.

 What Maple Does

> 

restart
> 

`ϕ` := (1+sqrt(5))*(1/2)

1/2+(1/2)*5^(1/2)

 (1)
> 

f := (1/2)*sqrt(-(u-1)*(u+1)*(u^2-u-1))*u*(4*u-3)/sqrt(u*(u-1))

(1/2)*(-(u-1)*(u+1)*(u^2-u-1))^(1/2)*u*(4*u-3)/(u*(u-1))^(1/2)

 (2)
> 

`assuming`([combine(f)], [1 < u and u < `&varphi;`])

(1/2)*u*(4*u-3)*((u+1)*(-u^2+u+1)/u)^(1/2)

 (3)
> 

`assuming`([simplify(f)], [1 < u and u < `&varphi;`])

(1/2)*(-u^2+u+1)^(1/2)*(u^2-1)^(1/2)*u^(1/2)*(4*u-3)/(u-1)^(1/2)

 (4)
> 

`assuming`([combine(f, radical)], [1 < u and u < `&varphi;`])

(1/2)*u*(4*u-3)*((u+1)*(-u^2+u+1)/u)^(1/2)

 (5)
> 

`assuming`([simplify(f, radical)], [1 < u and u < `&varphi;`])

(1/2)*((u-1)*(u+1)*(-u^2+u+1))^(1/2)*u*(4*u-3)/(u*(u-1))^(1/2)

 (6)
> 

``

Radical.mw

 Remark by Markiyan Hirnyk. The below content is added by the questionner on 08.02.2016 .

What Mathematica Does

 

Simplifying Radicals: Part II...

H-R 155 Maple 2015
radical simplify sqrt
January 24 2016
1 10

I have the following expression

f=u/(sqrt(u*(u-1)))

and I want to simplify it. Eventhough that I tell Maple that u is real and greater than 1 but it does not simplify the expression. What is wrong? Please see the attached file.

Radical.mw

Simplifying Radicals: Part I...

H-R 155 Maple 2015
radical simplification quotient
January 21 2016
2 5

I want to cancel some expressions in numerator and denominator of a quotient. But Maple deos not cancel it!

Please see the attached file.


Simplifying_Radicals.mw

Problem with "atomic variables"...

H-R 155 Maple 18
view restart atomic-identifier
January 16 2016
0 7

I have some preferences for viewing. Specially, I prefer atomic variables to be showed with a different color. So I check mark the related option for this in the view menu. But every time I close and reopen the Maple, it just restore my setting for atomic variables. Suprisingly, this does not happen for other viewing options in the view menu! What should I do? Why is it like this?

Plot of Implicitly Defined 3D Curve...

H-R 155 Maple 18
plot implicit
January 10 2016
2 4

Suppose that we have the following curve on a unit sphere

r^2+z^2=1

phi=pi/3

-1<=z<=1

which is the implicit equation of a circle in "cylindrical coorinates" (r,phi,z) on the sphere.

How can I plot this curve without solving the implicit equation for r or z ?

Also, I don't want to make any parameterization.

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