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2014-06-29 03:15:10 +0100 marked best answer Symbolic solve

Following the change of variable thread, I wanted to streamline the whole process.

Namely, using the same example in the above thread, I'd like to say

integral_def_change(x*cos(x^2+1), (x, 0, 2*pi), u == x^2 + 1, u)

The difference is, I wanted also Sage to automatically solve for x instead of providing x = sqrt(u - 1), say. But when I tried

solve(u == x^2 + 1, x)[0].rhs()

the output was r1.

1- What exactly is r1 ??

A way out (see this thread) seems to make of the solution a function of u

f(u) = solve(u == x^2 + 1, x)[0].rhs()

Now f is

u |--> -sqrt(u - 1)

2- What can I do to get +sqrt(u - 1) instead? Is this related to the positive function question there?

2014-06-29 03:15:09 +0100 marked best answer Getting help inside Sage

Sorry if it's a dumb question, folks.

What are all the ways of getting help inside Sage? I would like some table like this:

item?? | see code
help(item) | see help about item

I ask this question because I only know the ?? and help() ways. But they don't always work: I tried simplify_full?? and help(simplify_full) but ... got errors!

2014-06-29 03:15:08 +0100 marked best answer Change of variable in an integration

How to indicate a change of variable to Sage in an integration when Sage seems clueless?

2014-06-29 03:15:08 +0100 marked best answer Sympy integration algorithm towards -infinity

Following achrzesz hint about integral's algorithm option, I tried (Sage 4.7.2):

integral(1/x^2, x, -infinity, -1, algorithm='sympy')

Unfortunately, I got:

Traceback (click to the left of this block for traceback)
AttributeError: 'MinusInfinity' object has no attribute '_sympy_'

What's going wrong?

2014-06-29 03:15:08 +0100 marked best answer Keyboard layout in Sage appliance

Hi all,

I'm currently testing Sagemath on a Windows 7 box via sage appliance (4.7.2). I wanted to try the interactive shell out but it is not usable as my host keyboard layout is fr and the guest fedora box for sage uses en.

A quick search pointed me to the system-config-keyboard command but too bad, it is not shipped with sage appliance 4.7.2. Any other hint ?

Final solution (see below): change layout via sudo nano /etc/sysconfig/keyboard

2014-06-29 03:15:07 +0100 marked best answer Interactive question in notebooks

When trying to find some solution to the double integral problem and poking around with Sage (4.7.2), I stumbled upon this behavior:

integrate(x+y^k, y)

output (resembles maxima interaction):

Traceback (click to the left of this block for traceback)
Is  k+1  zero or nonzero?

How can I answer to this (with nonzero)?

Update: I accept solution below as there seems no way as for now to interactively answer those maxima questions.

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2013-08-28 09:13:38 +0100 marked best answer Symbolic solve
sage: var('u')
sage: solve(u==x^2+1, x)
[x == -sqrt(u - 1), x == sqrt(u - 1)]

So you could use [1] instead of [0] to get the "positive" one.

I don't know how you got the r1 from this example, but the documentation for solve says, among other things:

   If there is a parameter in the answer, that will show up as a new
   variable.  In the following example, "r1" is a real free variable
   (because of the "r"):

      sage: solve([x+y == 3, 2*x+2*y == 6],x,y)
      [[x == -r1 + 3, y == r1]]

Hope this helps!

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