Disclaimer: I do not know the SAGE code here, just general theory.
As BFJ pointed out, there is no 'canonical' form for such expressions,
where 'canonical' means (see 2.3.1, p.79 of Davenport, Siret
Tournier) that there is a unique representation for every expression.
But there may well be a 'normal' form, in the sense that zero only has
one representation, so you could try full_simplify(A-B)==0 rather than
full_simplify(A)==full_simplify(B).
On Nov 20, 3:57 pm, pevzi pevz...@gmail.com wrote:
Thank you for your reply.
But so is there any way to check if the expressions are equivalent?
On 20 ноя, 05:05, BFJ benjaminfjo...@gmail.com wrote:
The two expressions you give may be algebraically equivalent, but
they're not identical. There is no canonical fully simplified form
for a general algebraic expression, so you can't expect
full_simplify() to output this non-existant form. If the expressions
are simple enough, like polynomials, you might, but not in general.
On Nov 19, 3:31 pm, pevzi pevz...@gmail.com wrote:
I have two expressions:
(x/(2*sqrt(x+1)) + 1/(2*sqrt(x+1)*(sqrt(x+1)+1)))
((x*(sqrt(x+1)+1)+1)/(2*sqrt(x+1)*(sqrt(x+1)+1)))
As you see, they are identical, so full_simplify() method should
return the same result for both expressions. But:
sage: (x/(2*sqrt(x+1)) + 1/(2*sqrt(x+1)*(sqrt(x
+1)+1))).full_simplify()
1/2*(x + sqrt(x + 1))/(sqrt(x + 1) + 1)
sage: ((x*(sqrt(x+1)+1)+1)/(2*sqrt(x+1)*(sqrt(x
+1)+1))).full_simplify()
1/2*(sqrt(x + 1)*x + x + 1)/(x + sqrt(x + 1) + 1)
Although
sage: ((1/2*(x + sqrt(x + 1))/(sqrt(x + 1) + 1))/(1/2*(sqrt(x + 1)*x +
x + 1)/(x + sqrt(x + 1) + 1))).full_simplify()
1
Is this really a bug or I misunderstand something?
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