Hi,
I would like to write a function that rewrites an expression to
eliminate square root signs. I have read through the simplify module,
but I don't quite see how to do this. Is there something in the new
polys module that would help me?
Here is an example. I can assume that everything is real if that helps
somehow.
Sigma_12 = Symbol("Sigma_12")
Sigma_13 = Symbol("Sigma_13")
Sigma_14 = Symbol("Sigma_14")
Sigma_23 = Symbol("Sigma_23")
Sigma_24 = Symbol("Sigma_24")
Sigma_34 = Symbol("Sigma_34")
tau_11 = Symbol("tau_11")
tau_22 = Symbol("tau_22")
tau_33 = Symbol("tau_33")
tau_44 = Symbol("tau_44")
expr = ((Sigma_34/(tau_33*tau_44) - Sigma_13*Sigma_14/
(tau_11**2*tau_33*tau_44))/((1 - Sigma_13**2/(tau_11**2*tau_33**2))*(1
- Sigma_14**2/(tau_11**2*tau_44**2)))**(S(1)/2) - (Sigma_24/
(tau_22*tau_44) - Sigma_12*Sigma_14/
(tau_11**2*tau_22*tau_44))*(Sigma_23/(tau_22*tau_33) -
Sigma_12*Sigma_13/(tau_11**2*tau_22*tau_33))/(((1 - Sigma_12**2/
(tau_11**2*tau_22**2))*(1 - Sigma_13**2/(tau_11**2*tau_33**2)))**(S(1)/
2)*((1 - Sigma_12**2/(tau_11**2*tau_22**2))*(1 - Sigma_14**2/
(tau_11**2*tau_44**2)))**(S(1)/2)))**2
expr
So if I wanted to simplify expr to eliminate the radicals, I would
need to
0) Combine these last two two square roots together
((1 - Sigma_12**2/(tau_11**2*tau_22**2))*(1 - Sigma_13**2/
(tau_11**2*tau_33**2)))**(S(1)/2)*((1 - Sigma_12**2/
(tau_11**2*tau_22**2))*(1 - Sigma_14**2/(tau_11**2*tau_44**2)))**(S(1)/
2)
to get
((1 - Sigma_12**2/(tau_11**2*tau_22**2))*(1 - Sigma_13**2/
(tau_11**2*tau_33**2))*(1 - Sigma_12**2/(tau_11**2*tau_22**2))*(1 -
Sigma_14**2/(tau_11**2*tau_44**2)))**(S(1)/2)
1) Recognize that there is now a squared term under the radical and
pull that out to get
(1 - Sigma_12**2/(tau_11**2*tau_22**2)) * ((1 - Sigma_13**2/
(tau_11**2*tau_33**2))*(1 - Sigma_14**2/(tau_11**2*tau_44**2)))**(S(1)/
2)
2) Make a common denominator with the first term in expr to get this
within the outermost parentheses
((1 - Sigma_12**2/(tau_11**2*tau_22**2)) * (Sigma_34/(tau_33*tau_44) -
Sigma_13*Sigma_14/(tau_11**2*tau_33*tau_44)) - (Sigma_23/
(tau_22*tau_33) - Sigma_12*Sigma_13/(tau_11**2*tau_22*tau_33))) / (((1
- Sigma_13**2/(tau_11**2*tau_33**2))*(1 - Sigma_14**2/
(tau_11**2*tau_44**2)))**(S(1)/2) * (1 - Sigma_12**2/
(tau_11**2*tau_22**2)))
3) Square both the numerator and denominator to finally get
(((1 - Sigma_12**2/(tau_11**2*tau_22**2)) * (Sigma_34/(tau_33*tau_44)
- Sigma_13*Sigma_14/(tau_11**2*tau_33*tau_44)) - (Sigma_23/
(tau_22*tau_33) - Sigma_12*Sigma_13/(tau_11**2*tau_22*tau_33))) / (((1
- Sigma_13**2/(tau_11**2*tau_33**2))*(1 - Sigma_14**2/
(tau_11**2*tau_44**2)))**(S(1)/2) * (1 - Sigma_12**2/
(tau_11**2*tau_22**2))))**2
That would be perfect if I could automate these steps, or it would
also be okay if it wanted to expand or simplify the numerator further.
But I haven't been able to figure out how to do that without manual
intervention. Everything I have tried takes a long time to yield a
giant expression that still has square root signs. Can anyone get me
started?
Thanks,
Ben
--
You received this message because you are subscribed to the Google Groups
"sympy" group.
To post to this group, send email to sy...@googlegroups.com.
To unsubscribe from this group, send email to
sympy+unsubscr...@googlegroups.com.
For more options, visit this group at
http://groups.google.com/group/sympy?hl=en.
