Hello. I've been trying out Maxima, with the WxMaxima interface.
Although I have found Maxima to be very good for all manner of
things, I would like to be able to use it to solve non purely polynomial
equations (e.g. equations involving logarithms). I know that for this
purpose the equations can be plotted with graph software, they only
provide roots to a few significant places, which is why I would like to
use maxima to find roots to the precision I need. Endlessly zooming
into graphs to see where they cross the x axis is also rather tedious.
Although I know for a polynomial the command allroots(%); or
realroots(%); can be used to get a numerical output for an equation,
e.g. for realroots(x^2-1=0) would output x=1 or x=-1, these commands it
seems can only be used for pure polynomials: I've not been able to do
the same for any e.g. logarithmic equation.
When I request Maxima to solve equations which include logarithms, such
as 1) below, which has solutions for f(x)=0 at x= -2.838... and
+2.838..., I get the following output:
Entering 10-x^2-log(11x^2)=0 generates the answers:
[x=-sqrt(10-log(11*x^2)), x=sqrt(10-log(11*x^2))]
...not the [x=-2.838...] or [x=2.838...] I was looking for!
Even when I choose to solve the equation using the 'numer' command for
numerical output, it generates:
Even "Numerical toggle":
`rat' replaced 6.283185307179586 by 103993//16551 = 6.283185306023805
`rat' replaced 0.5 by 1//2 = 0.5
`rat' replaced 6.283185306023805 by 103283//16438 = 6.283185302348217
`rat' replaced 0.5 by 1//2 = 0.5
`rat' replaced 6.283185306023805 by 103283//16438 = 6.283185302348217
`rat' replaced 0.5 by 1//2 = 0.5
`rat' replaced 3.141592653589793 by 103993//33102 = 3.141592653011903
'rat' replaced 0.5 by 1//2 = 0.5
`rat' replaced 3.141592653011903 by 103638//32989 = 3.141592652096153
`rat' replaced 0.5 by 1//2 = 0.5
`rat' replaced 3.141592653011903 by 103638//32989 = 3.141592652096153
`rat' replaced 0.5 by 1//2 = 0.5
(%o16)
[x=%e^(3.1415926520961532*%i)*(10-log(11*x^2))^0.5,x=%e^(6.2831853023482
171*%i)*(10-log(11*x^2))^0.5]
...once more, not the [x=-2.838...] or [x=2.838...] I was
looking for.
Is Maxima not able to provide solutions in the forms I'd like?
x=123.456789... instead of
=%e^(3.1415926520961532*%i)*(10-log(11*x^2))^0.5? If so, how? If not,
then will this ever be included?
If maxima can handle complex numbers, or integrate logarithms etc., I
don't see why it shouldn't be able to solve logarithmic equations for
x=0 in numerical form.
Does anyone have any ideas???
Basically, I'd just like to find, to a few s.f., for what values of x
that f(x) will equal zero, e.g. [x=1.23456...] or [x=-1.23456...], when
f(x) equals something like log(x)-x^2=0 (in the same way that it can be
done with polynomials, using realroots(%))
Any feedback appreciated. Thanks.
L. Sharkey
FURTHER EXAMPLES:
2) inputting 5*x^5-log(16*x^2)+2-x=0 when selected 'solve', merely
outputted 5*x^5-log(16*x^2)+2-x=0 again as the solution!
(%o27) -log(16*x^2)+5*x^5-x+2=0
(%i28) solve([%], [x]);
(%o28) [0=-log(16*x^2)+5*x^5-x+2]
!!
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