Simplifications in Dirac Delta function

[mohit3011]

It seems that the Dirac Delta function might be more useful if certain simplifications can be done.
For Example:

• For using the symmetry property of the dirac delta function i.e DiracDelta(x)==DiracDelta(-x) . The existing provision for this is DiracDelta(-x).expand(diracdelta=True, wrt=x) . As of now we have this

>>> DiracDelta(-x)
DiracDelta(-x)

What I hope after this issue would be

>>> DiracDelta(-x)
DiracDelta(x)

• Also we can include the property like DiracDelta(m*x) = DiracDelta(x)/m , where m is an integer . This feature is also presently implemented like DiracDelta(2*x).expand(diracdelta=True, wrt=x)

We can have the existing way when more than one variables are involved . For constants, we can include it in basic cases.

I have read the code regarding this and it would be really nice , if someone could guide me in this.

[mohit3011]

@jksuom , @Upabjojr , can I go with this issue ?

[jksuom]

It seems that something like this has been implemented in deltaintegrate. Maybe that could be expanded.

[mohit3011]

@jksuom , yes you are right, I think we can do something similar here too.

    @deprecated(useinstead="expand(diracdelta=True, wrt=x)", deprecated_since_version="1.0.1")
    def simplify(self, x):
        return self.expand(diracdelta=True, wrt=x)

This is the code in delta_functions.py which canbe used.

[mohit3011]

@jksuom , should I proceed with this issue ?

[jksuom]

The functionality exists already though it may look a bit clumsy:

>>> DiracDelta(-x).expand(diracdelta=True, wrt=x)
DiracDelta(x)

I'm not sure if the conversion DiracDelta(-x) -> DiracDelta(x) should be made automatic. Maybe someone with more practical experience on these matters could have an opinion.

[mohit3011]

@jksuom Yes, that is the whole point of this issue . The existing functionality is clumsy and could be shortened when we arguments of DIrac Delta as like "2*x" , "-x" etc . Here simply we write like (using the property of DIracDelta)

>>> DIracDelta(2*x)
DiracDelta(x)/2

So what do you think ?

[asmeurer]

The trig functions automatically canonicalize negative signs, so there is precedent. We should definitely have a way to do it the only question is if it should be automatic or not. I'm not sure if many practical applications create delta functions that aren't of the form DiracDelta(x - a).

[jksuom]

It seems that the principal means of producing Dirac deltas in SymPy is _eval_expand_diracdelta which only creates expressions of the form DiracDelta(x - a).

[mohit3011]

@asmeurer , @jksuom , sorry for replying late. I wanted to know whether I should give this issue a try ?