 | 1 | initial version |
I'd like to plot one of the connected components of a plot. This is like
implicit_plot(x^2-y^2-1,(x,-2,2),(y,-2,2))
which one could solve and select the connected components. In my case, I deal with an equation that is inconvenient to plot directly from the solution. Is there a command to implicit plot, like saying "take this connected component of the curve" (e.g. in the example, passing through $(-1,0)$?)
I'd like to plot one of the connected components of a plot. This is like
implicit_plot(x^2-y^2-1,(x,-2,2),(y,-2,2))
which one could solve and select the connected components. In my case, I deal with an equation that is inconvenient to plot directly from the solution. Is there a command or a feature to implicit plot, like saying "take `implicit plot' which has the effect of "taking this connected component of the curve" solution" (e.g. in the example, passing through $(-1,0)$?)
I'd like to plot one of the connected components of a plot. This is like
implicit_plot(x^2-y^2-1,(x,-2,2),(y,-2,2))
which one could solve and manually select the connected components. In my case, I deal with an equation that is inconvenient to plot directly from the solution. Is there a command or a feature to `implicit plot' which has the effect of "taking this connected component of the solution" (e.g. in the example, passing through $(-1,0)$?)
I'd like to plot one of the connected components of a plot. This is like
implicit_plot(x^2-y^2-1,(x,-2,2),(y,-2,2))
which one could solve and manually select the connected components. In my case, I deal with an equation that is inconvenient to plot directly from the solution. Is there a command or a feature to `implicit plot' which has the effect of "taking this connected component of the solution" (e.g. in the example, passing through $(-1,0)$?)$(-1,0)$?)
Also I wouldn't like to restrict to either positive or negative $x$ (my curve is somehow more complicated and restricting to regions doesn't work).
I'd like to plot one of the connected components of a plot. This is like
implicit_plot(x^2-y^2-1,(x,-2,2),(y,-2,2))
which one could solve and manually select the connected components. In my case, I deal with an equation that is inconvenient to plot directly from the solution. Is there a command or a feature to `implicit plot' which has the effect of "taking this connected component of the solution" (e.g. in the example, passing through $(-1,0)$?) Also I wouldn't like to restrict to either positive or negative $x$ (my curve is somehow more complicated and restricting to regions doesn't work).
I excluded the curve to make this a minimal example, but it's probably helpful to know that I don't know how to easily parametrize it. Is something like
-1/720*x^6*y*cos(sqrt(2)*pi) + 1/144*x^4*y^3*cos(sqrt(2)*pi) - 1/240*x^2*y^5*cos(sqrt(2)*pi) + 1/5040*y^7*cos(sqrt(2)*pi) - 1/5040*x^7*sin(sqrt(2)*pi) + 1/240*x^5*y^2*sin(sqrt(2)*pi) - 1/144*x^3*y^4*sin(sqrt(2)*pi) + 1/720*x*y^6*sin(sqrt(2)*pi) + 1/114688*720^(2/5)*abs(-2*sqrt(5) + 10)^(7/2)*cos(2/5*sqrt(2)*pi)*cos(7/2*arctan2(0, -2*sqrt(5) + 10)) + 1/114688*720^(2/5)*abs(-2*sqrt(5) + 10)^(7/2)*sin(2/5*sqrt(2)*pi)*sin(7/2*arctan2(0, -2*sqrt(5) + 10)) - 3/8192*720^(2/5)*sqrt(5)*abs(-2*sqrt(5) + 10)^(5/2)*cos(2/5*sqrt(2)*pi)*cos(5/2*arctan2(0, -2*sqrt(5) + 10)) - 3/8192*720^(2/5)*sqrt(5)*abs(-2*sqrt(5) + 10)^(5/2)*sin(2/5*sqrt(2)*pi)*sin(5/2*arctan2(0, -2*sqrt(5) + 10)) - 9/8192*720^(2/5)*abs(-2*sqrt(5) + 10)^(5/2)*cos(2/5*sqrt(2)*pi)*cos(5/2*arctan2(0, -2*sqrt(5) + 10)) - 9/8192*720^(2/5)*abs(-2*sqrt(5) + 10)^(5/2)*sin(2/5*sqrt(2)*pi)*sin(5/2*arctan2(0, -2*sqrt(5) + 10)) + 15/2048*720^(2/5)*sqrt(5)*abs(-2*sqrt(5) + 10)^(3/2)*cos(2/5*sqrt(2)*pi)*cos(3/2*arctan2(0, -2*sqrt(5) + 10)) + 15/2048*720^(2/5)*sqrt(5)*abs(-2*sqrt(5) + 10)^(3/2)*sin(2/5*sqrt(2)*pi)*sin(3/2*arctan2(0, -2*sqrt(5) + 10)) + 35/2048*720^(2/5)*abs(-2*sqrt(5) + 10)^(3/2)*cos(2/5*sqrt(2)*pi)*cos(3/2*arctan2(0, -2*sqrt(5) + 10)) + 35/2048*720^(2/5)*abs(-2*sqrt(5) + 10)^(3/2)*sin(2/5*sqrt(2)*pi)*sin(3/2*arctan2(0, -2*sqrt(5) + 10)) - 5/64*720^(2/5)*sqrt(5)*sqrt(abs(-2*sqrt(5) + 10))*cos(2/5*sqrt(2)*pi)*cos(1/2*arctan2(0, -2*sqrt(5) + 10)) - 5/64*720^(2/5)*sqrt(5)*sqrt(abs(-2*sqrt(5) + 10))*sin(2/5*sqrt(2)*pi)*sin(1/2*arctan2(0, -2*sqrt(5) + 10)) - 25/256*720^(2/5)*sqrt(abs(-2*sqrt(5) + 10))*cos(2/5*sqrt(2)*pi)*cos(1/2*arctan2(0, -2*sqrt(5) + 10)) - 25/256*720^(2/5)*sqrt(abs(-2*sqrt(5) + 10))*sin(2/5*sqrt(2)*pi)*sin(1/2*arctan2(0, -2*sqrt(5) + 10)) + x*y + 5/56*720^(2/5)*sqrt(5)*sin(2/5*sqrt(2)*pi) - 5/56*720^(2/5)*sin(2/5*sqrt(2)*pi)
I'd like to plot one of the connected components of a plot. This is like
implicit_plot(x^2-y^2-1,(x,-2,2),(y,-2,2))
which one could solve and manually select the connected components. In my case, I deal with an equation that is inconvenient to plot directly from the solution. Is there a command or a feature to `implicit plot' which has the effect of "taking this connected component of the solution" (e.g. in the example, passing through $(-1,0)$?) Also I wouldn't like to restrict to either positive or negative $x$ (my curve is somehow more complicated and restricting to regions doesn't work).
I excluded the curve to make this a minimal example, but it's probably helpful to know that I don't know how to easily parametrize it. Is something like
-1/720*x^6*y*cos(sqrt(2)*pi) implicit_plot(-1/720*x^6*y*cos(sqrt(2)*pi) + 1/144*x^4*y^3*cos(sqrt(2)*pi) - 1/240*x^2*y^5*cos(sqrt(2)*pi) + 1/240*x^2*y^5*cos(sqrt(2)*pi)+ 1/5040*y^7*cos(sqrt(2)*pi) - 1/5040*x^7*sin(sqrt(2)*pi) + 1/240*x^5*y^2*sin(sqrt(2)*pi) - 1/144*x^3*y^4*sin(sqrt(2)*pi) -1/144*x^3*y^4*sin(sqrt(2)*pi) + 1/720*x*y^6*sin(sqrt(2)*pi) +1/114688*720^(2/5)*abs(-2*sqrt(5) + 10)^(7/2)*cos(2/5*sqrt(2)*pi)*cos(7/2*arctan2(0, -2*sqrt(5) + 10)) + 1/114688*720^(2/5)*abs(-2*sqrt(5) + 10)^(7/2)*cos(2/5*sqrt(2)*pi)*cos(7/2*arctan2(0, -2*sqrt(5) + 10)) + 1/114688*720^(2/5)*abs(-2*sqrt(5) + 10)^(7/2)*sin(2/5*sqrt(2)*pi)*sin(7/2*arctan2(0, -2*sqrt(5) + 10)) - 10))- 3/8192*720^(2/5)*sqrt(5)*abs(-2*sqrt(5) + 10)^(5/2)*cos(2/5*sqrt(2)*pi)*cos(5/2*arctan2(0, -2*sqrt(5) + 10)) - 3/8192*720^(2/5)*sqrt(5)*abs(-2*sqrt(5) + 10)^(5/2)*sin(2/5*sqrt(2)*pi) *sin(5/2*arctan2(0, -2*sqrt(5) + 10)) - 9/8192*720^(2/5)*abs(-2*sqrt(5) + 10)^(5/2) *cos(2/5*sqrt(2)*pi)*cos(5/2*arctan2(0, -2*sqrt(5) + 10)) - 9/8192*720^(2/5)*abs(-2*sqrt(5) + 10)^(5/2)*sin(2/5*sqrt(2)*pi)*sin(5/2*arctan2(0, -2*sqrt(5) + 10)) - 9/8192*720^(2/5)*abs(-2*sqrt(5) + 10)^(5/2)*cos(2/5*sqrt(2)*pi)*cos(5/2*arctan2(0, -2*sqrt(5) + 10)) - 9/8192*720^(2/5)*abs(-2*sqrt(5) + 10)^(5/2)*sin(2/5*sqrt(2)*pi)*sin(5/2*arctan2(0, -2*sqrt(5) + 10)) + 10))+ 15/2048*720^(2/5)*sqrt(5)*abs(-2*sqrt(5) + 10)^(3/2)*cos(2/5*sqrt(2)*pi)*cos(3/2*arctan2(0, -2*sqrt(5) + 10)) + 15/2048*720^(2/5)*sqrt(5)*abs(-2*sqrt(5) + 10)^(3/2)*sin(2/5*sqrt(2)*pi)*sin(3/2*arctan2(0, -2*sqrt(5) + 10)) + 35/2048*720^(2/5)*abs(-2*sqrt(5) + 10)^(3/2)*cos(2/5*sqrt(2)*pi)*cos(3/2*arctan2(0, -2*sqrt(5) + 10)) + 35/2048*720^(2/5)*abs(-2*sqrt(5) + 10)^(3/2)*sin(2/5*sqrt(2)*pi)*sin(3/2*arctan2(0, -2*sqrt(5) + 10)) - 5/64*720^(2/5)*sqrt(5)*sqrt(abs(-2*sqrt(5) + 10))*cos(2/5*sqrt(2)*pi)*cos(1/2*arctan2(0, -2*sqrt(5) + 10)) - 5/64*720^(2/5)*sqrt(5)*sqrt(abs(-2*sqrt(5) + 10))*sin(2/5*sqrt(2)*pi)*sin(1/2*arctan2(0, -2*sqrt(5) + 10)) - 25/256*720^(2/5)*sqrt(abs(-2*sqrt(5) + 10))*cos(2/5*sqrt(2)*pi)*cos(1/2*arctan2(0, -2*sqrt(5) + 10)) - 25/256*720^(2/5)*sqrt(abs(-2*sqrt(5) + 10))*sin(2/5*sqrt(2)*pi)*sin(1/2*arctan2(0, -2*sqrt(5) + 10)) + x*y + 5/56*720^(2/5)*sqrt(5)*sin(2/5*sqrt(2)*pi) - 5/56*720^(2/5)*sin(2/5*sqrt(2)*pi)
5/56*720^(2/5)*sin(2/5*sqrt(2)*pi), (x,-10,10), (y,-10,10))
This has many connected components (on the finite plane). Cannot upload the plot yet.
I'd like to plot one of the connected components of a plot. This is like
implicit_plot(x^2-y^2-1,(x,-2,2),(y,-2,2))
which one could solve and manually select the connected components. In my case, I deal with an equation that is inconvenient to plot directly from the solution. Is there a command or a feature to `implicit plot' which has the effect of "taking this connected component of the solution" (e.g. in the example, passing through $(-1,0)$?) Also I wouldn't like to restrict to either positive or negative $x$ (my curve is somehow more complicated and restricting to regions doesn't work).
I excluded the curve to make this a minimal example, but it's probably helpful to know that I don't know how to easily parametrize it. Is something like
implicit_plot(-1/720*x^6*y*cos(sqrt(2)*pi) + 1/144*x^4*y^3*cos(sqrt(2)*pi) - 1/240*x^2*y^5*cos(sqrt(2)*pi)+ 1/5040*y^7*cos(sqrt(2)*pi) - 1/5040*x^7*sin(sqrt(2)*pi) + 1/240*x^5*y^2*sin(sqrt(2)*pi) -1/144*x^3*y^4*sin(sqrt(2)*pi) + 1/720*x*y^6*sin(sqrt(2)*pi) +1/114688*720^(2/5)*abs(-2*sqrt(5) + 10)^(7/2)*cos(2/5*sqrt(2)*pi)*cos(7/2*arctan2(0, -2*sqrt(5) + 10)) + 1/114688*720^(2/5)*abs(-2*sqrt(5) + 10)^(7/2)*sin(2/5*sqrt(2)*pi)*sin(7/2*arctan2(0, -2*sqrt(5) + 10))- 3/8192*720^(2/5)*sqrt(5)*abs(-2*sqrt(5) + 10)^(5/2)*cos(2/5*sqrt(2)*pi)*cos(5/2*arctan2(0, -2*sqrt(5) + 10)) - 3/8192*720^(2/5)*sqrt(5)*abs(-2*sqrt(5) + 10)^(5/2)*sin(2/5*sqrt(2)*pi) *sin(5/2*arctan2(0, -2*sqrt(5) + 10)) - 9/8192*720^(2/5)*abs(-2*sqrt(5) + 10)^(5/2) *cos(2/5*sqrt(2)*pi)*cos(5/2*arctan2(0, -2*sqrt(5) + 10)) - 9/8192*720^(2/5)*abs(-2*sqrt(5) + 10)^(5/2)*sin(2/5*sqrt(2)*pi)*sin(5/2*arctan2(0, -2*sqrt(5) + 10))+ 15/2048*720^(2/5)*sqrt(5)*abs(-2*sqrt(5) + 10)^(3/2)*cos(2/5*sqrt(2)*pi)*cos(3/2*arctan2(0, -2*sqrt(5) + 10)) + 15/2048*720^(2/5)*sqrt(5)*abs(-2*sqrt(5) + 10)^(3/2)*sin(2/5*sqrt(2)*pi)*sin(3/2*arctan2(0, -2*sqrt(5) + 10)) + 35/2048*720^(2/5)*abs(-2*sqrt(5) + 10)^(3/2)*cos(2/5*sqrt(2)*pi)*cos(3/2*arctan2(0, -2*sqrt(5) + 10)) + 35/2048*720^(2/5)*abs(-2*sqrt(5) + 10)^(3/2)*sin(2/5*sqrt(2)*pi)*sin(3/2*arctan2(0, -2*sqrt(5) + 10)) - 5/64*720^(2/5)*sqrt(5)*sqrt(abs(-2*sqrt(5) + 10))*cos(2/5*sqrt(2)*pi)*cos(1/2*arctan2(0, -2*sqrt(5) + 10)) - 5/64*720^(2/5)*sqrt(5)*sqrt(abs(-2*sqrt(5) + 10))*sin(2/5*sqrt(2)*pi)*sin(1/2*arctan2(0, -2*sqrt(5) + 10)) - 25/256*720^(2/5)*sqrt(abs(-2*sqrt(5) + 10))*cos(2/5*sqrt(2)*pi)*cos(1/2*arctan2(0, -2*sqrt(5) + 10)) - 25/256*720^(2/5)*sqrt(abs(-2*sqrt(5) + 10))*sin(2/5*sqrt(2)*pi)*sin(1/2*arctan2(0, -2*sqrt(5) + 10)) + x*y + 5/56*720^(2/5)*sqrt(5)*sin(2/5*sqrt(2)*pi) - 5/56*720^(2/5)*sin(2/5*sqrt(2)*pi), (x,-10,10), (y,-10,10))
This has many connected components (on the finite plane). plane), the square root of two is just to match another conventions, you could ignore it. Cannot upload the plot yet.
I'd like to plot one of the connected components of a plot. This is like
implicit_plot(x^2-y^2-1,(x,-2,2),(y,-2,2))
which one could solve and manually select the connected components. In my case, I deal with an equation that is inconvenient to plot directly from the solution. Is there a command or a feature to `implicit plot' which has the effect of "taking this connected component of the solution" (e.g. in the example, passing through $(-1,0)$?) Also I wouldn't like to restrict to either positive or negative $x$ (my curve is somehow more complicated and restricting to regions doesn't work).
I excluded the curve to make this a minimal example, but it's probably helpful to know that I don't know how to easily parametrize it. Is something like
implicit_plot(-1/720*x^6*y*cos(sqrt(2)*pi) + 1/144*x^4*y^3*cos(sqrt(2)*pi) - 1/240*x^2*y^5*cos(sqrt(2)*pi)+ 1/5040*y^7*cos(sqrt(2)*pi) - 1/5040*x^7*sin(sqrt(2)*pi) + 1/240*x^5*y^2*sin(sqrt(2)*pi) -1/144*x^3*y^4*sin(sqrt(2)*pi) + 1/720*x*y^6*sin(sqrt(2)*pi) +1/114688*720^(2/5)*abs(-2*sqrt(5) + 10)^(7/2)*cos(2/5*sqrt(2)*pi)*cos(7/2*arctan2(0, -2*sqrt(5) + 10)) + 1/114688*720^(2/5)*abs(-2*sqrt(5) + 10)^(7/2)*sin(2/5*sqrt(2)*pi)*sin(7/2*arctan2(0, -2*sqrt(5) + 10))- 3/8192*720^(2/5)*sqrt(5)*abs(-2*sqrt(5) + 10)^(5/2)*cos(2/5*sqrt(2)*pi)*cos(5/2*arctan2(0, -2*sqrt(5) + 10)) - 3/8192*720^(2/5)*sqrt(5)*abs(-2*sqrt(5) + 10)^(5/2)*sin(2/5*sqrt(2)*pi) *sin(5/2*arctan2(0, -2*sqrt(5) + 10)) - 9/8192*720^(2/5)*abs(-2*sqrt(5) + 10)^(5/2) *cos(2/5*sqrt(2)*pi)*cos(5/2*arctan2(0, -2*sqrt(5) + 10)) - 9/8192*720^(2/5)*abs(-2*sqrt(5) + 10)^(5/2)*sin(2/5*sqrt(2)*pi)*sin(5/2*arctan2(0, -2*sqrt(5) + 10))+ 15/2048*720^(2/5)*sqrt(5)*abs(-2*sqrt(5) + 10)^(3/2)*cos(2/5*sqrt(2)*pi)*cos(3/2*arctan2(0, -2*sqrt(5) + 10)) + 15/2048*720^(2/5)*sqrt(5)*abs(-2*sqrt(5) + 10)^(3/2)*sin(2/5*sqrt(2)*pi)*sin(3/2*arctan2(0, -2*sqrt(5) + 10)) + 35/2048*720^(2/5)*abs(-2*sqrt(5) + 10)^(3/2)*cos(2/5*sqrt(2)*pi)*cos(3/2*arctan2(0, -2*sqrt(5) + 10)) + 35/2048*720^(2/5)*abs(-2*sqrt(5) + 10)^(3/2)*sin(2/5*sqrt(2)*pi)*sin(3/2*arctan2(0, -2*sqrt(5) + 10)) - 5/64*720^(2/5)*sqrt(5)*sqrt(abs(-2*sqrt(5) + 10))*cos(2/5*sqrt(2)*pi)*cos(1/2*arctan2(0, -2*sqrt(5) + 10)) - 5/64*720^(2/5)*sqrt(5)*sqrt(abs(-2*sqrt(5) + 10))*sin(2/5*sqrt(2)*pi)*sin(1/2*arctan2(0, -2*sqrt(5) + 10)) - 25/256*720^(2/5)*sqrt(abs(-2*sqrt(5) + 10))*cos(2/5*sqrt(2)*pi)*cos(1/2*arctan2(0, -2*sqrt(5) + 10)) - 25/256*720^(2/5)*sqrt(abs(-2*sqrt(5) + 10))*sin(2/5*sqrt(2)*pi)*sin(1/2*arctan2(0, -2*sqrt(5) + 10)) + x*y + 5/56*720^(2/5)*sqrt(5)*sin(2/5*sqrt(2)*pi) - 5/56*720^(2/5)*sin(2/5*sqrt(2)*pi), (x,-10,10), (y,-10,10))
This has many connected components (on the finite plane), the square root of two is just to match another conventions, you could ignore it. this and any numbertheoretical stuff, just think about the sort of not low degree polynomial in two variables. Cannot upload the plot yet.
I'd like to plot one of the connected components of a plot. This is like
implicit_plot(x^2-y^2-1,(x,-2,2),(y,-2,2))
sage: x, y = SR.var('x, y', domain='real')
sage: F0 = x^2 - y^2 - 1
sage: B0 = 3.5
sage: G0 = implicit_plot(F0, (x, -B0, B0), (y, -B0, B0), gridlines=True)
sage: G0.show(figsize=5)
Launched png viewer for Graphics object consisting of 1 graphics primitive
which one could solve and manually select the connected components. In my case, I deal with an equation that is inconvenient to plot directly from the solution. Is there a command or a feature to `implicit plot' which has the effect of "taking this connected component of the solution" (e.g. in the example, passing through $(-1,0)$?) Also I wouldn't like to restrict to either positive or negative $x$ (my curve is somehow more complicated and restricting to regions doesn't work).
I excluded the curve to make this a minimal example, but it's probably helpful to know that I don't know how to easily parametrize it. Is something like
implicit_plot(-1/720*x^6*y*cos(sqrt(2)*pi) sage: F = -1/720*x^6*y*cos(sqrt(2)*pi) + 1/144*x^4*y^3*cos(sqrt(2)*pi) - 1/240*x^2*y^5*cos(sqrt(2)*pi)+ 1/5040*y^7*cos(sqrt(2)*pi) - 1/5040*x^7*sin(sqrt(2)*pi) + 1/240*x^5*y^2*sin(sqrt(2)*pi) -1/144*x^3*y^4*sin(sqrt(2)*pi) + 1/720*x*y^6*sin(sqrt(2)*pi) +1/114688*720^(2/5)*abs(-2*sqrt(5) + 10)^(7/2)*cos(2/5*sqrt(2)*pi)*cos(7/2*arctan2(0, -2*sqrt(5) + 10)) + 1/114688*720^(2/5)*abs(-2*sqrt(5) + 10)^(7/2)*sin(2/5*sqrt(2)*pi)*sin(7/2*arctan2(0, -2*sqrt(5) + 10))- 3/8192*720^(2/5)*sqrt(5)*abs(-2*sqrt(5) + 10)^(5/2)*cos(2/5*sqrt(2)*pi)*cos(5/2*arctan2(0, -2*sqrt(5) + 10)) - 3/8192*720^(2/5)*sqrt(5)*abs(-2*sqrt(5) + 10)^(5/2)*sin(2/5*sqrt(2)*pi) *sin(5/2*arctan2(0, -2*sqrt(5) + 10)) - 9/8192*720^(2/5)*abs(-2*sqrt(5) + 10)^(5/2) *cos(2/5*sqrt(2)*pi)*cos(5/2*arctan2(0, -2*sqrt(5) + 10)) - 9/8192*720^(2/5)*abs(-2*sqrt(5) + 10)^(5/2)*sin(2/5*sqrt(2)*pi)*sin(5/2*arctan2(0, -2*sqrt(5) + 10))+ 15/2048*720^(2/5)*sqrt(5)*abs(-2*sqrt(5) + 10)^(3/2)*cos(2/5*sqrt(2)*pi)*cos(3/2*arctan2(0, -2*sqrt(5) + 10)) + 15/2048*720^(2/5)*sqrt(5)*abs(-2*sqrt(5) + 10)^(3/2)*sin(2/5*sqrt(2)*pi)*sin(3/2*arctan2(0, -2*sqrt(5) + 10)) + 35/2048*720^(2/5)*abs(-2*sqrt(5) + 10)^(3/2)*cos(2/5*sqrt(2)*pi)*cos(3/2*arctan2(0, -2*sqrt(5) + 10)) + 35/2048*720^(2/5)*abs(-2*sqrt(5) + 10)^(3/2)*sin(2/5*sqrt(2)*pi)*sin(3/2*arctan2(0, -2*sqrt(5) + 10)) - 5/64*720^(2/5)*sqrt(5)*sqrt(abs(-2*sqrt(5) + 10))*cos(2/5*sqrt(2)*pi)*cos(1/2*arctan2(0, -2*sqrt(5) + 10)) - 5/64*720^(2/5)*sqrt(5)*sqrt(abs(-2*sqrt(5) + 10))*sin(2/5*sqrt(2)*pi)*sin(1/2*arctan2(0, -2*sqrt(5) + 10)) - 25/256*720^(2/5)*sqrt(abs(-2*sqrt(5) + 10))*cos(2/5*sqrt(2)*pi)*cos(1/2*arctan2(0, -2*sqrt(5) + 10)) - 25/256*720^(2/5)*sqrt(abs(-2*sqrt(5) + 10))*sin(2/5*sqrt(2)*pi)*sin(1/2*arctan2(0, -2*sqrt(5) + 10)) + x*y + 5/56*720^(2/5)*sqrt(5)*sin(2/5*sqrt(2)*pi) - 5/56*720^(2/5)*sin(2/5*sqrt(2)*pi), (x,-10,10), (y,-10,10))
5/56*720^(2/5)*sin(2/5*sqrt(2)*pi)
sage: B = 7.5
sage: G = implicit_plot(F, (x, -B, B), (y, -B, B), gridlines=True)
sage: G.show(figsize=5)
This has many connected components (on the finite plane), the square root of two is just to match another conventions, you could ignore this and any numbertheoretical number-theoretical stuff, just think about the sort of not low degree polynomial in two variables. Cannot upload the plot yet.
I'd like to plot one of the connected components of a plot. This is like
sage: x, y = SR.var('x, y', domain='real')
sage: F0 = x^2 - y^2 - 1
sage: B0 = 3.5
sage: G0 = implicit_plot(F0, (x, -B0, B0), (y, -B0, B0), gridlines=True)
sage: G0.show(figsize=5)
Launched png viewer for Graphics object consisting of 1 graphics primitive
which one could solve and manually select the connected components. In my case, I deal with an equation that is inconvenient to plot directly from the solution. Is there a command or a feature to `implicit plot' which has the effect of "taking this connected component of the solution" (e.g. in the example, passing through $(-1,0)$?) Also I wouldn't like to restrict to either positive or negative $x$ (my curve is somehow more complicated and restricting to regions doesn't work).
I excluded the curve to make this a minimal example, but it's probably helpful to know that I don't know how to easily parametrize it. Is something like
sage: F = -1/720*x^6*y*cos(sqrt(2)*pi) + 1/144*x^4*y^3*cos(sqrt(2)*pi) - 1/240*x^2*y^5*cos(sqrt(2)*pi)+ 1/5040*y^7*cos(sqrt(2)*pi) - 1/5040*x^7*sin(sqrt(2)*pi) + 1/240*x^5*y^2*sin(sqrt(2)*pi) -1/144*x^3*y^4*sin(sqrt(2)*pi) + 1/720*x*y^6*sin(sqrt(2)*pi) +1/114688*720^(2/5)*abs(-2*sqrt(5) + 10)^(7/2)*cos(2/5*sqrt(2)*pi)*cos(7/2*arctan2(0, -2*sqrt(5) + 10)) + 1/114688*720^(2/5)*abs(-2*sqrt(5) + 10)^(7/2)*sin(2/5*sqrt(2)*pi)*sin(7/2*arctan2(0, -2*sqrt(5) + 10))- 3/8192*720^(2/5)*sqrt(5)*abs(-2*sqrt(5) + 10)^(5/2)*cos(2/5*sqrt(2)*pi)*cos(5/2*arctan2(0, -2*sqrt(5) + 10)) - 3/8192*720^(2/5)*sqrt(5)*abs(-2*sqrt(5) + 10)^(5/2)*sin(2/5*sqrt(2)*pi) *sin(5/2*arctan2(0, -2*sqrt(5) + 10)) - 9/8192*720^(2/5)*abs(-2*sqrt(5) + 10)^(5/2) *cos(2/5*sqrt(2)*pi)*cos(5/2*arctan2(0, -2*sqrt(5) + 10)) - 9/8192*720^(2/5)*abs(-2*sqrt(5) + 10)^(5/2)*sin(2/5*sqrt(2)*pi)*sin(5/2*arctan2(0, -2*sqrt(5) + 10))+ 15/2048*720^(2/5)*sqrt(5)*abs(-2*sqrt(5) + 10)^(3/2)*cos(2/5*sqrt(2)*pi)*cos(3/2*arctan2(0, -2*sqrt(5) + 10)) + 15/2048*720^(2/5)*sqrt(5)*abs(-2*sqrt(5) + 10)^(3/2)*sin(2/5*sqrt(2)*pi)*sin(3/2*arctan2(0, -2*sqrt(5) + 10)) + 35/2048*720^(2/5)*abs(-2*sqrt(5) + 10)^(3/2)*cos(2/5*sqrt(2)*pi)*cos(3/2*arctan2(0, -2*sqrt(5) + 10)) + 35/2048*720^(2/5)*abs(-2*sqrt(5) + 10)^(3/2)*sin(2/5*sqrt(2)*pi)*sin(3/2*arctan2(0, -2*sqrt(5) + 10)) - 5/64*720^(2/5)*sqrt(5)*sqrt(abs(-2*sqrt(5) + 10))*cos(2/5*sqrt(2)*pi)*cos(1/2*arctan2(0, -2*sqrt(5) + 10)) - 5/64*720^(2/5)*sqrt(5)*sqrt(abs(-2*sqrt(5) + 10))*sin(2/5*sqrt(2)*pi)*sin(1/2*arctan2(0, -2*sqrt(5) + 10)) - 25/256*720^(2/5)*sqrt(abs(-2*sqrt(5) + 10))*cos(2/5*sqrt(2)*pi)*cos(1/2*arctan2(0, -2*sqrt(5) + 10)) - 25/256*720^(2/5)*sqrt(abs(-2*sqrt(5) + 10))*sin(2/5*sqrt(2)*pi)*sin(1/2*arctan2(0, -2*sqrt(5) + 10)) + x*y + 5/56*720^(2/5)*sqrt(5)*sin(2/5*sqrt(2)*pi) - 5/56*720^(2/5)*sin(2/5*sqrt(2)*pi)
sage: B = 7.5
sage: G = implicit_plot(F, (x, -B, B), (y, -B, B), gridlines=True)
sage: G.show(figsize=5)
This has many connected components (on the finite plane), the square root of two is just to match another conventions, you could ignore this and any number-theoretical stuff, just think about the sort of not low degree polynomial in two variables. Cannot upload the plot yet.
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