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# integral not simplifying

hello, can anyone please explain why the first integral works but the second doesnt? even thought that they are both the same (only minus in different places):

sage: x = var('x')
sage: f = -(x - 1)*((x - 1)^2/((x - 1)^2 + 1)^2 + 1/((x - 1)^2 + 1)^2)/sqrt((x - 1)^2 + 1)
sage: integrate(f, x)
-integrate((x - 1)*((x - 1)^2/((x - 1)^2 + 1)^2 + 1/((x - 1)^2 + 1)^2)/sqrt((x - 1)^2 + 1), x)
sage: f = (x - 1)*((x - 1)^2/((x - 1)^2 + 1)^2 + 1/((x - 1)^2 + 1)^2)/sqrt((x - 1)^2 + 1)
sage: -integrate(f, x)
1/sqrt((x - 1)^2 + 1)


only full simplify somehow helps:

sage: f = -(x - 1)*((x - 1)^2/((x - 1)^2 + 1)^2 + 1/((x - 1)^2 + 1)^2)/sqrt((x - 1)^2 + 1)
sage: f.simplify()
-(x - 1)*((x - 1)^2/((x - 1)^2 + 1)^2 + 1/((x - 1)^2 + 1)^2)/sqrt((x - 1)^2 + 1)
sage: f.full_simplify()
-(x - 1)/(x^2 - 2*x + 2)^(3/2)
sage: integrate(f.full_simplify(), x)
1/sqrt(x^2 - 2*x + 2)


so basically the answer is to do full simplify, but i cant do full simplify on a vector (my original problem is to do this integral on vector):

sage: v = vector([x , 1 , 2])
sage: v.full_simplify()
... 'FreeModule_ambient_field_with_category.element_class' object has no attribute 'full_simplify'


so how can i avoid sagemath from returning me the "integrate(...)" thing and just do the integral?

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## Comments

Both works fine for me in sage 9.5.beta4. Which version of sage do you use ?

( 2021-10-24 21:16:23 +0100 )edit

SageMath version 9.2, Release Date: 2020-10-24 Using Python 3.7.7

( 2021-10-25 07:35:15 +0100 )edit
1

You should use a more recent version of sage. For the second point :

sage: v = vector(SR,[x,cos(x)**2+sin(x)**2,(x**3-1)/(x-1)]); v
(x, cos(x)^2 + sin(x)^2, (x^3 - 1)/(x - 1))
sage: v.apply_map(lambda c:c.simplify_full())
(x, 1, x^2 + x + 1)

( 2021-10-25 13:06:12 +0100 )edit

thank you for the simplifying method! i upgraded to sage 9.4 (latest that i found for linux), and now i dont have that problem anymore! my first issue is solved and everything works, but now i have a new problem which is very familiar:

sage: a,b = var('a,b')
sage: integrate((((a - b)^2/(abs(-a + b)^2 + 1) - 1)^2 + (a - b)^2/(abs(-a + b)^2 + 1)^2)/(abs(-a + b)^2 + 1)^(3/2), b)
integrate((a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4 - 2*a^2*abs(a - b)^2 + 4*a*b*abs(a - b)^2 - 2*b^2*abs(a - b)^2 + abs(a - b)^4 - a^2 + 2*a*b - b^2 + 2*abs(a - b)^2 + 1)/(abs(a - b)^2 + 1)^(7/2), b)
sage: (previous output)
(some long good ...
(more)
( 2021-10-25 20:40:16 +0100 )edit

In sage 9.5.beta4, this works fine. But you would need to compile from source. Or wait for the release of sage 9.5.

sage: sage: a,b = var('a,b')
sage: integrate((((a - b)^2/(abs(-a + b)^2 + 1) - 1)^2 + (a - b)^2/(abs(-a + b)^2 + 1)^2)/(abs(-a + b)^2 + 1)^(3/2), b)
-1/3*(2*a^3 - (6*a^2 - 2*(3*a - b)*b + 3)*b + 3*a)/((a - b)^2 + 1)^(3/2)

( 2021-10-25 20:52:50 +0100 )edit

## 1 Answer

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upgrading to SageMath version 9.5.beta5 really solved the problems. thank very much to FrédéricC for the help !

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## Comments

Thanks for flagging your answer to your own question for future users !

( 2021-11-03 10:27:56 +0100 )edit

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Asked: 2021-10-24 20:46:45 +0100

Seen: 467 times

Last updated: Nov 02 '21