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2016-04-14 10:15:34 -0500 commented answer Extract coefficients of polynomials

that works, thank you!

2016-04-13 22:59:50 -0500 asked a question Extract coefficients of polynomials

I have the following code:

var('a')
_.<k> = PolynomialRing(ZZ)
f = k^3+2*k^2+1
g = k^3 + a*k^2 + 1
f.coefficients()
g.coefficients()

the coefficients of f that i get are perfect:

[1, 2, 1]

the coefficients of g should be [1,a,1], but instead i get:

 [[k^3 + 1, 0], [k^2, 1]]

I've tried the solution suggested here:

but it doesn't always produce the coefficients in a logical order.

As always, any help figuring out how to get the correct coefficients of g would be greatly appreciated.

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2016-04-12 11:50:37 -0500 commented answer formatting pdf of sage worksheet on smc

Thank you!

2016-04-11 01:38:46 -0500 asked a question formatting pdf of sage worksheet on smc

I have a formatting query about the background colors on sagemath cloud. I regularly generate and print pdf of the sage worksheets on a black and white printer. On the printed page, its hard to distinguish between the cell that contains the code and the output of the cell (both have the same background color).

Is there any way to clearly demarcate the cell that contains the code and the output of the cell? Would it be possible to get the output of any cell with a shaded background or with a border around it, so that on a printed paper, the output of the cell appears clearly different from the contents of the cell.

I've tried some of the Editor color scheme options, but I don't see an option where the cell appears with a different background color.

Thank you.

2016-04-05 16:12:05 -0500 commented answer solve irrational inequality

Thank you, I am able to access the latest version of sympy now. My original question was on solving the irrational inequality above. Is that not possible in sagemath? Thanks.

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2016-04-03 14:52:36 -0500 asked a question solve irrational inequality

Is there any way to solve the following inequality for a in Sage?

(It's pretty easy to do in Maple.)

abs(-1/4*a - 1/4*sqrt(a^2 - 30*a + 17) + 1/4) < 1

Using solve doesn't work. I tried using the QEPCAD package, but on SageMathCloud, i get an error: "unable to start QEPCAD".

I tried using sympy-solve and sympy-solveset, and that didn't work either. I plan to raise questions regarding sympy on stackexchange, but if anyone has helpful guidelines on using sagemath's solve vs sympy-solve, that'd be greatly appreciated. My general experience has been that sympy-solve is a lot more capable than sagemath's solve.

Any help would be greatly appreciated. Thank you.

EDIT

Thank you for replying. I am able to use qepcad now, but the problem I'm trying to solve takes a very long time. Here is the code:

var('a')
dnf = solve(abs(-1/4*a - 1/4*sqrt(a^2 - 30*a + 17) + 1/4) <= 1, a)
qf = apply(qepcad_formula.or_, map(qepcad_formula.and_, dnf)) # reformat the solution
qf
qepcad(qf, vars='(a)') # simplify

Any help solving this would be greatly appreciated. Also, would it be possible to update the version of sympy on sagemathcloud? Thank you.

2016-03-29 21:38:43 -0500 commented answer finding the derivative of a functional w.r.t a function

that works great, thank you!

2016-03-29 15:12:33 -0500 commented answer finding the derivative of a functional w.r.t a function

your example is correct. I'm trying to accomplish something like this:

the rhs of de1 is just y(t). lets call the rhs of de1 F, so F = y(t). now dF/dy = 1. but dF/dx = 0, and that's what i'm trying to calculate - the derivative of the rhs of de1 w.r.t y and w.r.t x.

2016-03-29 12:19:51 -0500 commented answer finding the derivative of a functional w.r.t a function

Thanks a lot for replying. I tried what you suggested with de1 first, and it works when the rhs is only a function of y(t). so to compute dF/dx, i calculated it as (dF/dt)/(dx/dt) as follows:

sage: de1 = diff(x(t),t) == y(t) sage: F = de1.rhs() sage: (diff(F,t)/diff(x(t),t)).subs(de1)

the result is : D0(t)/y(t), whereas it should just be Zero.

any further suggestions would be greatly appreciated. Thank you.

2016-03-28 18:48:20 -0500 commented answer FEniCS on sagemath

Thanks for replying. Please do let me know if you find a solution to this.

2016-03-27 13:57:42 -0500 asked a question FEniCS on sagemath

Dr. Stein explains in the link below that FEniCS can be accessed on sagemath cloud. I followed the instructions in his post but i get an error that says: "No module named dolfin".

http://ask.sagemath.org/question/1100...

I'd appreciate any help figuring out how to import dolfin in sagemath.

Thanks,

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2016-03-24 01:51:23 -0500 commented answer solve a system of two equations for a derivative

that helps me solve what i wanted to, thank you!

i had simplified the problem that i wanted to solve considerably. finding the Jacobian will require solving for the derivative of a functional w.r.t a function. Instead of crowding this post, i've asked a new question here:

http://ask.sagemath.org/question/32876/finding-the-derivative-of-a-functional-wrt-a-function/ (http://ask.sagemath.org/question/3287...)

thank you again for your help.

2016-03-24 01:50:20 -0500 asked a question finding the derivative of a functional w.r.t a function

I've defined a system as:

var('a, t'); function('x, y');

de1 = diff(x(t),t) == y(t); de2 = diff(y(t),t) == -ax(t) - (a-4)/ay(t) - y(t)^3;

I'd like to compute the derivatives of the rhs of de1 and de2 w.r.t to x(t) and y(t) (to eventually form a Jacobian matrix), i.e. the derivative of the rhs of de1 w.r.t to x(t) is Zero and w.r.t y(t) is 1. I've tried the following:

diff(de1.rhs(),y); diff(de1.rhs(),y(t)); derivative(de1.rhs(),y(t));

I get errors on all three. I'd appreciate any help. thank you.

2016-03-23 20:28:57 -0500 commented answer solve a system of two equations for a derivative

thanks for replying. i don't want to use desolve yet. all i'd like to do is to solve the equations algebraically (explicitly) for the derivatives. thank you,

2016-03-23 20:27:30 -0500 commented answer solve a system of two equations for a derivative

thanks for replying. i'd like to automate the solution process. i tried substituting x1 for diff(x(t),t), but got an error ( i don't want to manually type in the x1 and y1 part). i tried both:

sage: de1.substitute_function(diff(x(t),t),x1) and sage: de1.subs(diff(x(t),t)=x1)

any suggestions as to how i can sub x1 for diff(x(t),t) directly in de1?

thank you,

2016-03-23 15:45:55 -0500 commented question solve a system of two equations for a derivative

I'm not trying to solve the differential equations just yet. i only want to solve the equations algebraically (explicitly) for the derivatives, so I can compute the Jacobian matrix of the right hand sides for further bifurcation analysis. the equations in my actual problem have parameters.

(this is pretty easy to do in Maple)

2016-03-23 05:18:26 -0500 asked a question solve a system of two equations for a derivative

I have the following defined:

sage: var('a, t');

sage: function('x, y, v, u')

sage: de1 = diff(x(t),t) - diff(y(t),t) == x(t)

sage: de2 = diff(y(t),t) == y(t)

I'd like to solve these two equations algebraically for diff(x(t),t) and diff(y(t),t).

sage: sol = solve(de1, diff(x(t),t)); works, and i get an explicit solution for diff(x(t),t), but when i try solving both equations using:

sage: sol = solve([de1, de2],diff(x(t),t),diff(y(t),t));

i get the following error:

Traceback (most recent call last): File "/projects/sage/sage-6.10/local/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 905, in execute exec compile(block+'\n', '', 'single') in namespace, locals File "", line 1, in <module> File "/projects/sage/sage-6.10/local/lib/python2.7/site-packages/sage/symbolic/relation.py", line 822, in solve variables = tuple(args[0]) TypeError: 'sage.symbolic.expression.Expression' object is not iterable

=============================

I'd appreciate any help with this. thank you.