Hi,
I am working on the analytical solution to a specific problem. Nothing
special, I guess, just a few 2nd order differential equations. The real
burden, and thus the motivation for using sage, is that the resulting
equations are long and thus the possibility of introducing small typos or
errors. To keep equations manageable there's heavy use of intermediate
variables, and here where my question comes (minimal example):
------
reset()
var('a1 b1 c1')
f1(y)=(a1*sin(y)+b1*cos(y))+c1
# sage doesn't solve this
#sols=solve(f1,y)
# Do a change of variables
f2(u,v)=a1*u+b1*v+c1
f3(u,v)=u^2+v^2==1
sols=solve([f2,f3],[u,v]); print "sols = ",sols
# Now let's say I want to try some values for the params
a1=1; b1=-2; c1=3
------
How would you go back to get the value(s) of y? I am aware I can use the
subs() method, but if the list of parameters is long this ends up being
tedious and error prone. Also, subs() doesn't seem capable of substituting
a variable in all its forms (squared, etc.). I found in ask.sagemath.org
some questions regarding this issue [1][2], but because it seems a rather
infrequent question I have the feeling there must be another way of doing
it, or that I might be using sage in a "non intended" way.
Regards,
Jorge
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