DomainCondition disagrees with the value for five nodes #2256

DomainCondition is where an expression has a value, and Simplify relies on it: a rewrite that hides a singularity adds a provided from it. A new workspace harness, work/domaincheck, compares the condition at exact points with the value there. Each function is checked alone, and then in random compositions. Five nodes disagree. Each one lets Simplify give a value where there is none, or none where there is one. 2.6.0 and master are the same:

• The factorial and the gamma function require a real argument: "x!".ToEntity().DomainCondition is x in RR and (x >= 0 or not x in ZZ). i! is 0.498 - 0.155i, and the only poles are the negative integers. "x!/x!".ToEntity().Simplify() is 1 provided x in RR and (x >= 0 or not x in ZZ), which has no value at i.
• max and min hold everywhere, but they have no value at a complex argument. max(i, i) is NaN, as the node is read over the reals. "max(x, x)".ToEntity().Simplify() is x, which has a value at i.
• arctan and arccot hold at their poles: arctan(i) is +oo i. "arctan(x) - arctan(x)".ToEntity().Simplify() is 0 there. The tangent's condition excludes its poles, and the logarithm's excludes 0, where it is -oo.
• lambertw has the same condition over the reals as over the complex numbers. "lambertw(0, x)".ToEntity().DomainConditionIn(Domain.Real) is True, but W_0 is real only for x >= -1/e, and W_(-1) only on [-1/e, 0).
• DomainConditionIn of a piecewise asks every case to be defined. DomainCondition asks only the case that applies (A piecewise's domain condition asks every case's predicate to be defined #1817). tan(piecewise(pi / x provided x > 0, x / 2)) is 0 at 0, but its condition over the reals, piecewise((not cos(pi / x) = 0 and not x = 0 and x in RR) provided (x > 0), (not cos(x / 2) = 0 and not x = 0 and x in RR) provided True), fails there.

Two disagreements are evaluation's, not the conditions': #2253 (Im(1/0) is 0) and #2255 (log(0, 2) is 0). The power's condition is left permissive for a symbolic exponent on purpose, which Powf explains, so x^x at -1/2 over the reals is not listed.