radsimp -- simplify radicals in
arithmetical expressions
Introductionradsimp simplifies arithmetical expressions containing
radicals.
Call(s)radsimp(z)
Parametersz |
- | an arithmetical expression |
Returnsan arithmetical expression.
Further
DocumentationChapter ``Manipulating Expressions'' of the Tutorial.
Related
Functionscombine, ifactor, normal, rectform, simplify
Detailsradsimp(z) tries to simplify the radicals
in the expression z. The result is mathematically
equivalent to z.radsimp(z) is equivalent to
simplify(z,
sqrt).
Example
1We demonstrate the simplification of constant expressions with square roots and higher order radicals:
>> radsimp(2*2^(1/4) + 2^(3/4) - (6*2^(1/2) + 8)^(1/2))
0
>> radsimp(
sqrt(14 + 3*sqrt(3 + 2*sqrt(5 - 12*sqrt(3 - 2*sqrt(2)))))
)
1/2
2 + 3
>> radsimp(3*sqrt(7)/(sqrt(7) - 2))
1/2
2 7 + 7
>> radsimp(sqrt(1 + sqrt(3)) + sqrt(3 + 3*sqrt(3))
- sqrt(10 + 6*sqrt(3)))
0
>> x := sqrt(3)*I/2 + 1/2: y := x^(1/3) + x^(-1/3): z := y^3 - 3*y
/ 1 1/2 1/3 \3
| --------------------- + (1/2 I 3 + 1/2) | -
| 1/2 1/3 |
\ (1/2 I 3 + 1/2) /
1/2 1/3 3
3 (1/2 I 3 + 1/2) - ---------------------
1/2 1/3
(1/2 I 3 + 1/2)
>> radsimp(z)
1
>> delete x, y, z:
Example
2radsimp also works on arithmetical
expressions containing variables:
>> z := x/(sqrt(3) - 1) - x/2
x x
-------- - -
1/2 2
3 - 1
>> radsimp(z) = expand(radsimp(z))
/ 1/2 \ 1/2
| 3 | x x 3
x | ---- + 1/2 | - - = ------
\ 2 / 2 2
>> delete z:
Backgroundradsimp constructs
a tower of algebraic extensions of Q using
the domain Dom::AlgebraicExtension. It
tries to return the simplest possible form.