FullSimplify does not eliminate factors that can be eliminated

[HannesWell]

Describe the bug

Applying FullSimplify or just Simplify to an expression does not always eliminate factors even if it would be possible.

To Reproduce

Steps to reproduce the behavior:

Example input Symja input expression:

>> FullSimplify(a-Max(x1*a,x2*a)==0)

Undesired result:

−Max(a⋅x1,a⋅x2)+a==0

Expected behavior

Expected (correct) result expression:

1−Max(x1,x2)==0

But the problem seems not to be limited to non-continuous functions like Min or Max, even for simpler expressions like

>>FullSimplify(a-x1*a==0)

the result is -a*x1+a==0, while it could be -x1+1==0.

[axkr]

What if a is a negative number and x1, x2 are positive numbers?

[HannesWell]

That would indeed change Min respectively Max to the opposite.

But even the simple case

>>FullSimplify(a-x1*a==0)

does not result in a simplification, even the sign does not matter. The only problem would be a==0.
If I use assumptions:

FullSimplify(a-x1*a==0, Assumptions -> a>0)

the result is still -a*x1+a==0.
Or am I doing something wrong?

[axkr]

With the last commit Simplify is more consistent with factoring out common factors from a Plus expression:

• Simplify(a-a*b-a*c) -> a*(1-b-c)
• Simplify(a-a*b+a*c) -> a*(1-b+c)

Note: Simplify determines the "simplicity" with a variant of the function LeafCount:

• https://github.com/axkr/symja_android_library/blob/master/symja_android_library/doc/functions/LeafCount.md

Unfortunately for the system the following expression determine the following leaf counts:

• LeafCount(a-a*b) -> 6
• LeafCount(a*(1-b)) ->7

so that Simplify(a*(1-b)) will not be considered as "simpler" and not be transformed.

Thereas this expression will be transformed by Simplify, because it has the same leaf count:

• LeafCount(a+a*b) -> 5
• LeafCount(a*(1+b)) -> 5