H-R

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These are questions asked by H-R

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

 

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

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

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?

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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