SageMath is not solving this inequality

asked 2020-03-17 21:51:29 +0100

thethinker
107 ●3 ●6 ●12

updated 2020-03-17 21:52:02 +0100

I have the following inequality:

ineqal=T1Sol[0].rhs().numerator() > 0
ineqal

$$-\kappa m^{4} + 8 \pi m^{3} r - 4 \pi r^{2} > 0$$

So it's a quadratic, but I would imagine it's solveable. Find the zeros, check the sign on either side of them, and tell me where it's positive. If you need more info, yell at me about assumptions. But instead:

solve(ineqal,r)

$$\left[\left[-\kappa m^{4} + 8 \pi m^{3} r - 4 \pi r^{2} > 0\right]\right]$$

Sometimes I can trick it into behaving with some expand() or simplify_full(), but that seems not to be working here. Any ideas?

answered 2020-03-18 10:49:41 +0100

Sébastien
3271 ●7 ●42 ●88 http://www.slabbe.org/

updated 2020-03-18 10:51:43 +0100

At least SageMath solves the equality (you may then guess the solution from the sign of the coefficient for r^2):

sage: kappa = var('kappa')
sage: m = var('m')
sage: r = var('r')
sage: expr = -kappa*m^4+8*pi*m^3*r - 4*pi*r^2
sage: solve(expr == 0, r)
[r == 1/2*(2*pi*m^3 - sqrt(4*pi^2*m^2 - pi*kappa)*m^2)/pi, 
 r == 1/2*(2*pi*m^3 + sqrt(4*pi^2*m^2 - pi*kappa)*m^2)/pi]

Sympy gives a simplified solution for the equality, but it neither give you the intervals for when the expression is positive:

sage: solve(expr == 0, r, algorithm='sympy')
[r == m^3 - 1/2*sqrt(4*pi*m^2 - kappa)*m^2/sqrt(pi),
 r == m^3 + 1/2*sqrt(4*pi*m^2 - kappa)*m^2/sqrt(pi)]
sage: solve(expr > 0, r, algorithm='sympy')
ConditionSet(r, -kappa*m**4 + 8*pi*m**3*r - 4*pi*r**2 > 0, Reals)

edit flag offensive delete link

Comments

Right, so we can kind of do it ourselves (finding the zeros, if they exist, and then determining the sign of the function around them), but that seems "simple" enough that Sage should be able to do it. Is this a Sage thing, or algebra systems in general?

thethinker ( 2020-03-18 14:36:58 +0100 )edit

add a comment

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

SageMath is not solving this inequality

1 Answer

Comments

Your Answer

Question Tools

Stats

Related questions

SageMath is not solving this inequality edit

1 Answer

Comments

Your Answer

Question Tools

Stats

Related questions

SageMath is not solving this inequality