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### How to Rationalize the Denominator of a Fraction ?

How to Rationalize the Denominator of a Fraction ?

Hi, experts.

Is there any way to rationalize the denomintor of a fraction ? For example, after difining a variable 'a' as follows: a = 1 / (2 * sqrt(2) + 3) I tried typing b=a.simplify_full(); b; c=a.simplify_factorial(); c; d=a.simplify_radical(); d; e=a.simplify_rational(); e;

As a result, all of the above commands return 1/(2sqrt(2) + 3), which is the same as a, though I expect any of them to return "3 - 2sqrt(2)" or "-2*sqrt(2) + 3".

I know Sage uses Maxima and Maxima can do this by typing ratsimp(a), algebraic: true;

Is there any way to rationalize the denominator with Sage ?

### How to Rationalize the Denominator of a Fraction ?

How to Rationalize the Denominator of a Fraction ??
Hi, experts.
Hi, experts. Is there any way to rationalize the denomintor of a fraction ?
For example, after difining a variable 'a' as follows:
a = 1 / (2 * sqrt(2) + 3)
I tried typing
b=a.simplify_full(); b;
c=a.simplify_factorial(); c;
e=a.simplify_rational(); e;e;
As a result, all of the above commands return 1/(2sqrt(2) 1/(2*sqrt(2) + 3),
which is the same as a, though I expect any of them
to return "3 - 2sqrt(2)" 2*sqrt(2)" or "-2*sqrt(2) + 3".  I know Sage uses Maxima and Maxima can do this by typing
ratsimp(a), algebraic: true;true;
Is there any way to rationalize the denominator with Sage ??
-Tatsuya-Tatsuya


### How to Rationalize the Denominator of a Fraction ?

How to Rationalize the Denominator of a Fraction ?

Hi, experts.

Is there any way to rationalize the denomintor of a fraction ?
For example, after difining a variable 'a' as follows:
a = 1 / (2 * sqrt(2) + 3)
I tried typing
b=a.simplify_full(); b;
c=a.simplify_factorial(); c;
e=a.simplify_rational(); e;

As a result, all of the above commands return 1/(2*sqrt(2) + 3),
which is the same as a, though I expect any of them
to return "3 - 2*sqrt(2)" or "-2*sqrt(2) + 3".

I know Sage uses Maxima and Maxima can do this by typing
ratsimp(a), algebraic: true;

Is there any way to rationalize the denominator with Sage ?

-Tatsuya


### How to Rationalize the Denominator of a Fraction ?

Hi, experts.
experts.
Is there any way to rationalize the denomintor of a fraction ?
? For example, after difining a variable 'a' as follows:
I tried a = 1 / (2 * sqrt(2) + 3)
I tried typing
b=a.simplify_full();
b = a.simplify_full(); b;
c=a.simplify_factorial(); c = a.simplify_factorial(); c;
e=a.simplify_rational(); e = a.simplify_rational(); e;
As a result,  expecting any of them to return "3 - 2*sqrt(2)" or "-2*sqrt(2) + 3".  However, all of the above commands return 1/(2*sqrt(2) + 3),
which 3),
whose denominator is the same as a, though I expect any of them not rational. to return "3 - 2*sqrt(2)" or "-2*sqrt(2) + 3".

I know Sage uses Maxima and Maxima can do this rationalize the denominator  by typing
typing  ratsimp(a), algebraic: true;

Is there any way to rationalize the denominator with Sage ?
?
-Tatsuya

-Tatsuya

### How to Rationalize the Denominator of a Fraction ?

Hi, experts.

Is there any way to rationalize the denomintor of a fraction ?

For example, I tried

a = 1 / (2 * sqrt(2) + 3)

b = a.simplify_full(); b;
c = a.simplify_factorial(); c;
e = a.simplify_rational(); e;


expecting any of them to return "3 - 2*sqrt(2)" or "-2*sqrt(2) + 3".

However, all of the above commands return 1/(2*sqrt(2) + 3),
whose denominator is not rational.

I know know
(1)
Sage uses Maxima and Maxima.
(2) Standalone version of
Maxima can rationalize the denominator
by typing

"ratsimp(a), algebraic: true;


true;".
(3) Sage accepts "maxima.ratsimp(a)", but I don't know how to pass the Maxima option "algebraic: true;" to Sage.

Is there any way to rationalize the denominator with Sage ?