Francois Maltey wrote:
> I continue to try to plot in the complex plane the 4 solutions of the
> equation :
>
> z^4+2*a*z^2+1 = 0 when a is a real.
>
> I want to get a circle and 2 lines...
>
> Guru ckrisman explains that today this plot seems impossible and gives
> me a tip with lambda : .... calls in plot.
> I can make more parametric_plot with but I can't get this one.
>
> Guru harald proposes the use of list and list_plot... and I
> misunderstand an other sage property :
>
> var ("a,z")
> res = solve (z^4 + 2*a*z^2 + 1 == 0, z) # is right
> res1 = res[0].rhs() # - sqrt (-a+sqrt(a^2-1)), others have + or -...
> res2 = - sqrt (-a+sqrt(a^2-1)) # I type the same expression
>
> [res2 for a in sxrange (-5,5,0.8)] # is right
> [res1 for a in sxrange (-5,5,0.8)] # makes an error, even if the display
> of the inner formula is the same.
To substitute values into a symbolic expression, use either the .subs
function or just call the expression like it is a function, but
explicitly specify the values of the variables:
[res1.subs(a=i) for i in sxrange(-5,5,0.8)]
[res1(a=i) for i in sxrange(-5,5,0.8)]
>
> # I try this other case :
>
> b=a
> [sqrt(a) for a in sxrange(-2,2,0.8)] # is right
> [sqrt(b) for a in sxrange(-2,2,0.8)] # repeat the last value.
> # It seems that a remains a numerical variable outside the for loop.
These last two statements are assigning the python variable "a" to the
values -2, -1.2, ..., 2. When you finish the statement, "a" still
points to the last numeric value.
Think of it this way: when you do var('a'), an object, a symbolic
variable, is created. The python variable "a" is set to this symbolic
variable. However, they are two separate things. In a sense, you can
think of it as the name "a" is pointing to this symbolic variable, which
Sage prints as "a".
a --> (Sage symbolic variable, which is printed as "a")
When you do the above statements, you are reassigning what "a" points
to. After the above statements, you have:
a --> 2
but there is still a symbolic variable out there called "a"; it just
isn't accessed by typing "a" anymore.
I hope that helps.
Jason
--
Jason Grout
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