derivative of a Boolean

[Chris Smith]

In PR #13204 I encountered the question of what to do with the derivative if a Boolean. A Boolean is true or false but may contain expressions within relationals, For example, `x**2 < y` depends on x and y but the Boolean value is a "square wave" for this relational. Does a derivative wrt x or y even make sense? Should an error, 0 or something else be done for a return value?

/c

[Aaron Meurer]

I'm not sure the derivative really makes sense. I would either error
or leave it unevaluated.

Aaron Meurer

> --
> 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+un...@googlegroups.com.
> To post to this group, send email to sy...@googlegroups.com.
> Visit this group at https://groups.google.com/group/sympy.
> To view this discussion on the web visit
> https://groups.google.com/d/msgid/sympy/13fc1fdc-caba-4336-a7df-148efa2f716a%40googlegroups.com.
> For more options, visit https://groups.google.com/d/optout.

[Alan Bromborsky]

See link -

https://www.encyclopediaofmath.org/index.php/Boolean_differential_calculus

[Chris Smith]

I will need some help interpreting that. Here's my attempt:

>>> f = eq = ITE(x<1,x,Eq(y,1)).to_nnf(); eq
(x∨x≥1)∧(y=1∨x<1)(x∨x≥1)∧(y=1∨x<1)
>>> eq.subs(x, 0)
False
>>> eq.subs(x, 1)
y = 1

I'm not sure how I am supposed to add these mod 2. Maybe `(0 + ITE(Eq(y,1), 1, 0)) % 2`? So does x change the value of f? The answer depends on y, doesn't it? If y is 0 then the value of x doesn't change f but it it is 1 then it does. So is the derivative wrt x `Eq(y, 1)`?

[Alan Bromborsky]

I afraid I can't help there.  I am good at finding things with google.  This might help, maybe?

http://pyeda.readthedocs.io/en/latest/reference/boolalg/boolfunc.html

To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/2364638a-ed60-4a6d-aa09-af6b9f738a01%40googlegroups.com.

[Aaron Meurer]

The definition given by Alan is the derivative of a boolean function
wrt a boolean variable. In Chris's expression, the variable is real,
not boolean.

Aaron Meurer

> https://groups.google.com/d/msgid/sympy/bb2fbf12-55d8-fcbe-23f6-1406d7cac078%40gmail.com.