After a bit of experimentation, the following code fragment worked:
dexpr_dx = se.Derivative(expr, x, 1).subs(
(Ho - y*(x**2 + sp.Rational(-1, 3)*y**2) +
sp.Rational(-1, 2)*x**2 +
sp.Rational(-1, 2)*y**2), sp.Symbol('(Ho - V(x, y))'))
yielding
dexpr_dx -(-x - 2*x*y)/(Ho - V(x, y))**2
Thank you both for your advice.
On Wednesday, January 26, 2022 at 5:52:21 AM UTC-5 hanspete...@fhnw.ch
wrote:
> Regarding 1), if you write 1/3, then Python converts this into a float
> before it is handed over to sympy. To prevent it, you could import S
> (Singleton) from sympy and write S(1)/3.
>
> dexpr_dx = se.Derivative(expr, x, 1).xreplace({y*(x**2 + (-S(1)/3)*y**2) +
> (-S(1)/2)*x**2 + (-S(1)/2)*y**2: V(x, y)})
>
> smi...@gmail.com schrieb am Dienstag, 25. Januar 2022 um 21:53:27 UTC+1:
>
>> There are a few reasons this is not working.
>>
>> 1) if you have floats like (1/3) those will not match the rationals like
>> Rational(1, 3)
>> 2) xreplace will target full nodes, not sub-nodes. So when trying to
>> match an Add that is a subexpression, it will fail.
>> 3) you have a sign error in the key of the replacement dictionary: the
>> first term should be `-y*...`
>> 4) the replacement value, `V(x, y)` recreates the thing you are replacing.
>>
>> Try the following:
>>
>> >>> d = Derivative(expr, x, 1)
>> >>> d.subs(V(x,y), Symbol('V(x,y)'))
>> Derivative(1/(Ho - V(x,y)), x)
>>
>>
>> /c
>> On Monday, January 24, 2022 at 3:28:50 PM UTC-6 Audrius-St wrote:
>>
>>> Hello, In the following test code I am attempting to simplify the
>>> resulting expression
>>> by replacing a subexpression with a function
>>>
>>> import symengine as se
>>> import sympy as sp
>>>
>>> # Potential V
>>> def V(x, y):
>>> v = (x*x + y*y)/2 + y*(x*x - (y*y)/3)
>>> return v
>>>
>>> def main():
>>>
>>> # Symbols
>>> x, y, Ho = sp.symbols('x, y, Ho')
>>>
>>> expr = sp.Pow(Ho - V(x, y), -1)
>>> dexpr_dx = se.Derivative(expr, x, 1).xreplace({y*(x**2 +
>>> (-1/3)*y**2) + (-1/2)*x**2 + (-1/2)*y**2: V(x, y)})
>>>
>>> print("dexpr_dx =", dexpr_dx)
>>>
>>> if __name__ == "__main__":
>>> main()
>>>
>>> Taking in derivative w.r.t. x resulting in V(x, y) being replace the
>>> expression
>>> dexpr_dx = -(-x - 2*x*y)/(Ho - y*(x**2 + (-1/3)*y**2) + (-1/2)*x**2 +
>>> (-1/2)*y**2)**2
>>>
>>> which I would like to rewrite as -(-x - 2*x*y)/(Ho - V(x, y))**2 as I
>>> will be repeating the differentiation in the actual code.
>>> In other words, I would like to reduce the output code bloat.
>>>
>>> I've tried subs(), replace(), and xreplace() with no success. Any
>>> insight in how to do this would be appreciated.
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
--
You received this message because you are subscribed to the Google Groups
"sympy" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to sympy+unsubscr...@googlegroups.com.
To view this discussion on the web visit
https://groups.google.com/d/msgid/sympy/8a54a52a-b4e1-441a-bb14-0b9c96a80ce7n%40googlegroups.com.
