integral command fails: copy, paste and run. Then exchange m(x,y) and n(x,y) and rerun. I get Maxima error
show("G.2.a singularity across sinks and swirls from Mathematica Text")
show("second try to enter workable code that can be copied, pasted and run")
var('y a b q t r')
m(x,y)=q*(x-a)/((x-a)^2+(y-b)^2)
n(x,y)=q*(y-b)/((x-a)^2+(y-b)^2)
"""
replacments get Maxima error in integrate command
m(x,y)=5*(x-a)/sqrt((x-a)^2+(y-b)^2)
n(x,y)=5*(y-b)/sqrt((x-a)^2+(y-b)^2)
I have other examples of m(x,y) and n(x,y) that fail
"""
show("n(x,y)=",n(x,y))
show("Field(x,y)=(m(x,y),n(x,y))")
Field=(m(x,y),n(x,y))
show("Field=",Field)
singularity=(a,b)
show("singularity=(a,b), when a==x and b==y")
show("----------------")
show("constructing small circle centered at singularity (a,b) with radius 'r'")
show("aiming to determine if the singularity is a source of flow, sink or neither")
xr(t)=singularity[0]+r*cos(t)
yr(t)=singularity[1]+r*sin(t)
show("xr(t)=",xr(t))
show("yr(t)=",yr(t))
xrprime(t)=diff(xr(t),t)
yrprime(t)=diff(yr(t),t)
show("xrprime(t)=",xrprime(t)," = derivative(xr(t),t)")
show("yrprime(t)=",yrprime(t)," = derivative(yr(t),t)")
show("----------------")
show("measure flow across the circle surrounding the singularity")
show("integral=integral(-n(xr(t),yr(t)) * xrprime(t)+m(xr(t),yr(t)) * yrprime(t),(t,0,2*pi))")
integral=integral(-n(xr(t),yr(t)) * xrprime(t)+m(xr(t),yr(t)) * yrprime(t),(t,0,2*pi))
show("integral=",integral)
show("q>0 then singularity at (a,b) is a source of flow ")
show("q<0 then singularity at (a,b) is a sink for flow")
show("q=0 then no net flow at singularity (a,b)")
show("----------------")
show("now try to run the above with the replacement m(x,y), n(x,y) :")
show("I get an error in Maxima, see below")
show("these m(x,y) and n(x,y) do not work for me")
show("m(x,y)=5*(x-a)/sqrt((x-a)^2+(y-b)^2)")
show("n(x,y)=5*(y-b)/sqrt((x-a)^2+(y-b)^2)")
show("In sage I get RuntimeError: ECL says: Error executing code in Maxima: atanh: argument 1 isn't in the")
show("domain of atanh.")
show("Mathematica's correct answer is: integral=flow=10pisqrt(r^2)")
show("thank you")
This the same as
https://ask.sagemath.org/question/39316/integration/
isn't it?
sageas many other computer algebra systems is not the solution to all mathematical problems, at least i do not expect so. A good ratio of human interaction is always welcome. So why not help help the machine?integral. (Except you know what you are doing...)dan; I do not know how to write the integral that is not evaluated, that is; how to plug in (what is plugged in) into the mix,m(x,y) and n(x,y) terms in the integral command. Mathematica handles the problem and sage does not in the way I wrote the code. I assume my code is at fault ;but do not know where. I lost my Mathematica when I went to a 64 bit machine and too expensive to buy again on SS pension; hence I am learning sage. I am not a mathematician. I am nearly 80 and math is a hobby. So, perhaps I don't know what I am doing. If I did I maybe I would not need 'ask.sagemath
I did not know about reposting. I used no other name. I did not know how to write sage code for predator/model and I came to ask.sagemath and now I know.