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Which of Maple commands is better for computing the radical of a polynomial f (less time of computation and less complexity)?

For example if f=x^3+3x^2y+3xy^2+y^3 then rad(f)=x+y.

is there a built in function which calculates the radical of a number?

e.g. 54=2*3^3


Hello all. I have a probably simple problem, that is drinving me totally crazy. I have a expression having:



and it refuses to simplify. I told maple assume(m>0, M>0), etc. But it doesn't want to simplify. Anyone has any ideas?





Edit: uploaded the mw file, so it can be seen what the problem

[I added Physics to the tags.--Carl Love as moderator]

The simplification of 1/sqrt(2) is always simplified or unsimplified as the case may be to sqrt(2)/2.  It is a matter of opinion which is simpler I suppose, but throughout mathematics teachings I've always learned cos(45) as 1/sqrt(2) as I'm sure the rest of you all have as well. Yes it is merely aesthetic, but a quirk to see it as sqrt(2)/2

Is the simplification process to get radicals in the numerator rather than the denominator?  I think yes if the answer...


with great interest and surprise I read the post
"Converting Half-Angle Trig Formulas to Radicals".
Isnt it possible to evaluate cos(arccos(13/14)/3) also
to an exact expression in radicals ?
I simply do not succeed with my humble knowledge of
the Maple commands/internal workings...
Would be great if someone finds a solution ( of an 
unsolvable problem ??? ).

[Edit: Excess white space deleted.---Carl Love]


I am experiencing wrong results using the PolynomialIdeals package in Maple 16 (see Creating the same ideal with different generators, the radicals computed differ which of course is wrong:

J := <t*(a+A), A*(b+B+t), b*(a+A), B*a-A*(b+t), (variables = {A, B, a, b, t})>:
J2 := <t*(a+A), A*(b+B+t), b*(a+A), B*(a+A...

Maybe many questions on forum because method is not universal. What about this one:

JA1S := (2*sqrt(2*y+3)*y+3*sqrt(2*y+3)-3*sqrt(3))/((2*y+3)^(3/2)*y);


simplify(JA1S, power, radical, symbolic); - nothing

combine(JA1S, power, radical, symbolic); - nothing


Moreover, can i somehow also reduce by y?

GAL := 3*sqrt(6)/((2*x^2+3)*sqrt(4*x^2+6));

simplify(GAL) and combine(GAL,power)

have same result.

How to make them return

3*sqrt(3)/(2*x^2+3)^(3/2) ?

Let a:= (2x-1)/sqrt(1-4x2)  , b:=sqrt(1-2x)/sqrt(1+2x)

then c:=combine(a/b,radical,symbolic) is 1, it should be -1 !

(Multiply b top and bottom by sqrt(1-2x) to see this).


Am I misunderstanding combine?


How can I sort a list with radicals?


sort(a) returns the same list in the same order. 

Is there a way in Maple to compute a radical ideal?


For example, how to compute radical ideal of "a+b" with a,b in any field?


Thanks in advance.


In this previous post, an example is shown that demonstrates the potential problems that can arise following symbolic conversions such as from sqrt(x^2)  to x^(1/2).

Here x is an unknown symbol. The difficulties include the fact that, while `sqrt` can be smart about simplifying numeric values (eg. integers, rationals) the `^` operator has no such opportunity. Once the conversion from `sqrt`...

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