如何求解功能方程?
我有
B(2z^4 + 4z^6 + 9z^8 + 20z^{10} + 44z^{12} + 96z^{14}) = (B(z))^4
”
(%i2) e: B(2*z^4 + 4*z^6 + 9*z^8 + 20*z^10 + 44*z^12 + 96*z^14) = (B(z))^4;
14 12 10 8 6 4 4
(%o2) B(96 z + 44 z + 20 z + 9 z + 4 z + 2 z ) = B (z)
(%i3) funcsolve (e,B(z));
expt: undefined: 0 to a negative exponent.
#0: rform(%r=[0,0])
#1: funcsol(%a=B(96*z^14+44*z^12+20*z^10+9*z^8+4*z^6+2*z^4) = B(z)^4,%f=B(z),l%=[])
#2: funcsolve(%a=B(96*z^14+44*z^12+20*z^10+9*z^8+4*z^6+2*z^4) = B(z)^4,%f=B(z))
#3: funcsolve(_l=[B(96*z^14+44*z^12+20*z^10+9*z^8+4*z^6+2*z^4) = B(z)^4,B(z)])
-- an error. To debug this try: debugmode(true);
https://en.wikibooks.org/wiki/wiki/fractals/iterations_in_the_complex_plane/boettcher#the_bubble_bath_bath_julia_set 简单的示例
define(f(z),z^2-1)
(%o3) f(z):=z^2-1
(%i4) f2:factor(f(f(z)))
(%o4) z^2*(z^2-2)
(%i5) e:B(f2) = B(z)^2
(%o5) B(z^2*(z^2-2)) = B(z)^2
(%i6) s:funcsolve(e,B(z))
expt: undefined: 0 to a negative exponent.
#0: rform(%r=[0,0])
#1: funcsol(%a=B(z^2*(z^2-2)) = B(z)^2,%f=B(z),l%=[])
#2: funcsolve(%a=B(z^2*(z^2-2)) = B(z)^2,%f=B(z))
#3: funcsolve(_l=[B(z^2*(z^2-2)) = B(z)^2,B(z)])
-- an error. To debug this try: debugmode(true);
我该怎么做? 它是另一种软件 /方法吗?
I have functional equation
B(2z^4 + 4z^6 + 9z^8 + 20z^{10} + 44z^{12} + 96z^{14}) = (B(z))^4
I try to solve it using Maxima CAS :
(%i2) e: B(2*z^4 + 4*z^6 + 9*z^8 + 20*z^10 + 44*z^12 + 96*z^14) = (B(z))^4;
14 12 10 8 6 4 4
(%o2) B(96 z + 44 z + 20 z + 9 z + 4 z + 2 z ) = B (z)
(%i3) funcsolve (e,B(z));
expt: undefined: 0 to a negative exponent.
#0: rform(%r=[0,0])
#1: funcsol(%a=B(96*z^14+44*z^12+20*z^10+9*z^8+4*z^6+2*z^4) = B(z)^4,%f=B(z),l%=[])
#2: funcsolve(%a=B(96*z^14+44*z^12+20*z^10+9*z^8+4*z^6+2*z^4) = B(z)^4,%f=B(z))
#3: funcsolve(_l=[B(96*z^14+44*z^12+20*z^10+9*z^8+4*z^6+2*z^4) = B(z)^4,B(z)])
-- an error. To debug this try: debugmode(true);
Here simpler example :
define(f(z),z^2-1)
(%o3) f(z):=z^2-1
(%i4) f2:factor(f(f(z)))
(%o4) z^2*(z^2-2)
(%i5) e:B(f2) = B(z)^2
(%o5) B(z^2*(z^2-2)) = B(z)^2
(%i6) s:funcsolve(e,B(z))
expt: undefined: 0 to a negative exponent.
#0: rform(%r=[0,0])
#1: funcsol(%a=B(z^2*(z^2-2)) = B(z)^2,%f=B(z),l%=[])
#2: funcsolve(%a=B(z^2*(z^2-2)) = B(z)^2,%f=B(z))
#3: funcsolve(_l=[B(z^2*(z^2-2)) = B(z)^2,B(z)])
-- an error. To debug this try: debugmode(true);
How should I do it?
Is it another software / method for it ?
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