On Nov 27, 10:03 am, Yotam Avital <yota...@gmail.com> wrote:
> Hello.
>
> In the tutorials there is an example for numerical approximation:
>
> var('x y p q')
> (x, y, p, q)
> eq1 = p+q==9
> eq2 = q*y+p*x==-6
> eq3 = q*y^2+p*x^2==24
> solns = solve([eq1,eq2,eq3,p==1],p,q,x,y, solution_dict=True)
> [[s[p].n(30), s[q].n(30), s[x].n(30), s[y].n(30)] for s in solns]
> [[1.0000000, 8.0000000, -4.8830369, -0.13962039],
> [1.0000000, 8.0000000, 3.5497035, -1.1937129]]
>
> As I far as I can understand, solution_dict tells sage that I want the
> output to be in dictionary form(that is, {x:1, y:8 ...})
> I also know that the .n(30) tell sage I want the answer to have 30
> digits accuracy. I can't understand though the logic of the last
> command. Can any of you explain it to me?
If you're asking about the command
[[s[p].n(30), s[q].n(30), s[x].n(30), s[y].n(30)] for s in solns]
then note first that "solns" is a list, and a construction like [blah
for s in solns] evaluates "blah" for each entry s in solns. If you
just print solns at this point, you should get
[{q: 8, x: -4/3*sqrt(10) - 2/3, p: 1, y: 1/6*sqrt(2)*sqrt(5) - 2/3},
{q: 8, x: 4/3*sqrt(10) - 2/3, p: 1, y: -1/6*sqrt(2)*sqrt(5) - 2/3}]
Each entry s in solns is a dictionary with keys the variables p, q, x,
y. For the first entry, s[p] is 1, s[q] is 8, etc. So the command
that I think you were asking about prints s[p], s[q], s[x], and s[y],
each with 30 bits of precision, for each of the two solutions.
--
John
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