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Solve fails

asked 2019-10-17 23:50:09 -0600

Cyrille gravatar image

updated 2019-10-17 23:52:26 -0600

I wonder why the Variable 'x_0' not found

 gr=Polyhedron(ieqs=[(10,-1,0),(-12,0,1)])
p1=gr.plot()
x_0, x_1 = var('x_0 x_1')
lin=solve([70==6*x_0+18*x_1],x_1)
p2=plot(lin, (x,8,14))
p1+p2
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because there is an infinity of solutions x_0,x_1 in R

eq=70==(6*x_0+18*x_1).subs(x_1=7/8)
lin=solve(eq,x_0)
show("lin : ",lin)
eq=70==(6*x_0+18*x_1).subs(x_0=3/5)
lin=solve(eq,x_1)
show("lin : ",lin)
ortollj gravatar imageortollj ( 2019-10-18 03:43:17 -0600 )edit

I was expecting thant $x_0$ will be taken as a parameter.

Cyrille gravatar imageCyrille ( 2019-10-18 03:58:50 -0600 )edit

2 answers

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answered 2019-10-18 06:34:51 -0600

tmonteil gravatar image

updated 2019-10-18 08:29:41 -0600

This is very unclear. For p2, if you want an implicit plot where x_0 is a parameter that belongs to the interval $[8,14]$, you can do:

sage: p2 = implicit_plot(70==6*x_0+18*x_1,(8,14),(-3,3))

You can also have a look to the parametric_plot function.

But without more details about your actual goal, there is not much to say.

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answered 2019-10-18 11:11:54 -0600

dsejas gravatar image

Hello, @Cyrille! Try the following:

gr = Polyhedron(ieqs=[(10,-1,0), (-12,0,1)])
p1 = gr.plot()
x_0, x_1 = var('x_0 x_1')
lin = solve([70==6*x_0+18*x_1], x_1, solution_dict=True)
p2 = plot(lin[0][x_1], (x_0,8,14))
p1 + p2

Notice I have added solution_dict=True, which makes lin a list of dictionaries of solutions:

[{x_1: -1/3*x_0 + 35/9}]

In order to plot it, first extract the dictionary from the list (that is done with lin[0]); we get

{x_1: -1/3*x_0 + 35/9}

Finally, we extract the equation you want to plot (that is done with lin[0][x_1]); we get

-1/3*x_0 + 35/9

That is what I used in the plot command.

Note: It is not necessary to use (x_0, 8, 14) in the plot command; you can use (x, 8, 14). I did that to be consistent with notation.

There are a couple of things that bother me:

  1. The polyhedron is too small in the plot, because the line is too far. Is this a problem for you?
  2. This won't work if x_1 has more than one solution.

Problem 2 is solved using tmontiel's suggestion.

There may be an alternative way to achieve the same thing. May I ask: what are you trying to achieve?

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Asked: 2019-10-17 23:50:09 -0600

Seen: 36 times

Last updated: Oct 18