Add support for the derivative of the max function

[TongTianDaXia]

i want to simplify a long expression by vairable substitution, and the expression has a Derivative operator, like

Derivative(max(f1, f2), x)

when i set a map

map[Expression(max(f1, f2))] = s

and execute the subs.

expression.subs(map)

Then the term Derivative(max(f1, f2), x) = 0, and the whole expression collapse
So i find that the vairable substitution cut off the relation between the experssion and the variables

my question is how to deal with the operator Derivative when taking variable substitution,
can i remove it when there is an operator max?
or can i keep it when execute the variable substitution?

[rikardn]

I am not sure I understand what the max is supposed to mean.

[TongTianDaXia]

I am not sure I understand what the max is supposed to mean.

the symengine offer the operator max

class Max : public MultiArgFunction
{
public:
    IMPLEMENT_TYPEID(SYMENGINE_MAX)
    //! Max Constructor
    Max(const vec_basic &&arg);
    //! \return `true` if canonical
    bool is_canonical(const vec_basic &arg) const;
    //! \return canonicalized Max
    virtual RCP<const Basic> create(const vec_basic &arg) const;
};

//! Canonicalize Max:
RCP<const Basic> max(const vec_basic &arg);

the function is like
f(x, max(f1(x), f2(x)), ...)
and i'm computing the jacobian of $\partial f/\partial x$

[TongTianDaXia]

i find there is a piecewise function
is it possible to express the derivative operator in piecewise expression for discountinous function
like abs(), max() and the others.

[rikardn]

It seems as if derivatives of the max function is not yet handled by symengine.

Using sympy we get:

import sympy

x = sympy.Symbol('x')
f1 = x
f2 = x**2
expr = sympy.Max(f1, f2)
sympy.diff(expr, x)
Out[10]: 
2*x*Heaviside(x**2 - x) + Heaviside(-x**2 + x)

where if using symengine we get the unevaluated expression back Derivative(max(x, x**2), x)

The alternative to using the step function would be to use Piecewise, but I guess using Heaviside simplifies the calculations. Wolfram alpha uses the the piecewise form.

So to implement this in symengine first an implementation of the heaviside function is needed and then an entry in the derivative visitor for the max function.