integrating with unspecified constants

asked 2012-01-21 15:49:12 +0100

WVPhysicist
11 ●1 ●1 ●2

in the online sage I typed: var('x,a,b') integrate(1/sqrt(b+a/x), x)

And it answered: Traceback (click to the left of this block for traceback) ... Is b positive or negative?

Of course b is positive but there is no way to answer it's question or to predefine b as positive, so far as I know. so I used b^2 and got a question "Is b > 0?". Well yes b>0. So is a.

a and b are part of a physics problem. They change with the initial conditions. This is my first day with Sage. I have no idea what trace back is good for.

I don't know how to use this thing so send a copy of the answer to me at august04@frontier.com.

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answered 2012-01-21 16:09:14 +0100

god.one

395 ●7 ●15 ●26

Hi, see question Interactive question in notebooks. Sage does not know that b is positive and you have specify that. Insert

assume(b>0)

The Traceback gives you hints if sage needs further information or if there is an error in the code you want to compile.

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It works. The answer is simpler. Now all I have to do is check it. Thanks.

WVPhysicist ( 2012-01-21 17:36:24 +0100 )edit

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answered 2012-01-21 18:04:48 +0100

achrzesz
2803 ●5 ●25 ●61

sage: var('x,a,b')

sage: integrate(1/sqrt(b+a/x), x,algorithm='mathematica_free')

sqrt(b + a/x)x/b - 1/2alog(2sqrt(b + a/x)sqrt(b)x + 2bx + a)/b^(3/2)

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BTW, what is the difference between integrate and integral ?? Could you point us to the doc for this algorithm option?

Green diod ( 2012-01-21 18:30:20 +0100 )edit

They should be the same. One is an alias for the other, I believe, for convenience.

kcrisman ( 2012-01-23 13:14:44 +0100 )edit

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answered 2012-01-21 19:30:42 +0100

achrzesz
2803 ●5 ●25 ●61

sage: sage.symbolic.integration.integral.integral?

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Why doesn't "a = Constant('a')" work?

WVPhysicist ( 2012-01-27 20:54:26 +0100 )edit

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answered 2012-01-21 16:39:13 +0100

Green diod
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updated 2012-01-21 18:28:05 +0100

@WVPhysicist It seems there is no way to interactively answer the question. I just tried the integral I proposed in both notebook mode (via http) and at the console but same problem.

I must say the console output is more verbose.

I think the problem is with the way Sage is interfaced with Maxima.

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Or more precisely, the issue is that Maxima still adheres to a 1970s view of someone always being at the terminal ready to answer a prompt. This is a feature or a bug, depending on who you ask, but we really don't have any way to change how this interface is from that standpoint, as Python isn't really that sort of "interactive" language.

kcrisman ( 2012-01-21 16:43:35 +0100 )edit

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