[NOTE: I mistakenly sent several replies to individuals rather than to
the group. Several are moot, but I did not want to leave them off-list.
So I am resending below. Sorry about that! Bruce]
Dear Chris,
THANK YOU! That's an excellent solution for me. I did not know about
it and probably would not have found it on my own.
Cheers,
Bruce
On 02.04.21 01:04, Chris Smith wrote:
You can do this by simply factoring the expression with keyword `deep`::
```
>>> var('a')
a
>>> factor(sqrt(((4*a**2 + 1)/(4*a**6 - 15*a**4 + 12*a**2 + 4))),
deep=True)
1/Abs(a**2 - 2)
```
On Thursday, April 1, 2021 at 9:43:35 AM UTC-5 balle...@googlemail.com
wrote:
What is described above has worked well for me. But there is a
further simplification step that I need help with.
I have some long expressions containing terms contain terms which
look like this example:
sqrt(4*a**2 + 1)*sqrt(1/(4*a**6 - 15*a**4 + 12*a**2 + 4))
How can I instruct sympy to combine such square roots and factor the
arguments? In this example that would lead to:
sqrt(factor((4*a**2 + 1)/(4*a**6 - 15*a**4 + 12*a**2 + 4)))
=
1/Abs(a**2 - 2)
On Wednesday, March 31, 2021 at 9:03:08 AM UTC+2 B A wrote:
Dear Chris,
On 31.03.21 05:48, Chris Smith wrote:
> Oscar posted code at issue
https://github.com/sympy/sympy/issues/19164
<https://github.com/sympy/sympy/issues/19164>
> for a interva-based Newton solver.
Thank you, that's very useful. I didn't know about interval
arithmetic.
I just implemented the following, which works very well and
helps to
increase my confidence that problems will be caught:
d_abs={}
d_problems={}
def MyAbs(x):
# check if this argument is already in dictionary
if x in d_abs:
return d_abs[x]
# see if there are any roots nearby
soln_list = nsolve_interval(x, 0.563, 0.583)
# nearby roots provide a warning message and get saved
if len(soln_list) > 0:
print('WARNING: ambiguous case found, argument of Abs() is', x)
d_problems[x]=soln_list
# Check sign, determine correct output
x1 = x.evalf(subs={a:0.573})
if x1 < 0.0:
out = -x
else:
out = x
# save into dictionary and return
d_abs[x] = out
return out
Cheers,
Bruce
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