Simplify with assumptions failing using Power

[mmatera]

This PR fixes #153, which was due to a but in the Simplify implementation of the rule Simplify[b_^a_, assumptions_]

[rocky]

This is good, but what I would ask is (and I don't know if this is relevant here) whether this is a workaround for a misfeature of the code or something you might reasonably find in any WL implementation?

I looked in Symja for something like this and don't see anything, but I could have missed something.

If it should be something that we may want to revisit in the future, it would be great if this could be tagged in some way. Even better would be segregated this to a section which makes it easier to review such decisions should things change to make it not necessary.

But, again, I don't know if this is relevant here.

[mmatera]

This is good, but what I would ask is (and I don't know if this is relevant here) whether this is a workaround for a misfeature of the code or something you might reasonably find in any WL implementation?

I looked in Symja for something like this and don't see anything, but I could have missed something.

If it should be something that we may want to revisit in the future, it would be great if this could be tagged in some way. Even better would be segregated this to a section which makes it easier to review such decisions should things change to make it not necessary.

But, again, I don't know if this is relevant here.

No, this is just a fix for a bug in the implementation of Simplify, that has some consequences in Integrate. Maybe the rule shouldn't be there, or maybe Symja does not have support for the parameter assumptions.
For example, in Mathics (and WMA)

In[1]:=0^a
Out[1]=0^a

while

In[2]:=Simplify[0^a,a>0]
Out[2]=0

or

In[3]:=$Assumptions={a>0}; Simplify[0^a]
Out[3]=0

What is the output in Symja?

[rocky]

But, again, I don't know if this is relevant here.

No, this is just a fix for a bug in the implementation of Simplify, that has some consequences in Integrate. Maybe the rule shouldn't be there, or maybe Symja does not have support for the parameter assumptions. For example, in Mathics (and WMA)

In[1]:=0^a
Out[1]=0^a

while

In[2]:=Simplify[0^a,a>0]
Out[2]=0

or

In[3]:=$Assumptions={a>0}; Simplify[0^a]
Out[3]=0

What is the output in Symja?

[mmatera]

OK, so in that case, we are doing it better...

[rocky]

Ok - so then let's merge and iterate.

[TiagoCavalcante]

@rocky could you open an issue in Symja for this?

[rocky]

I am not the right person for this. I am not really a Symja user.

[axkr]

Changed it in the code base:

• Simplify[0^x, x>0] should return 0 axkr/symja_android_library#456

[rocky]

@mmatera @axkr noticed something that is still amiss in our code:

In[1]:= Simplify[0^x, x<0]
Out[1]= Undefined

It should be instead ComplexInfinity, right?