AngouriMath
WhereBothSidesAgree(AngouriMath.Entity,AngouriMath.Entity.Variable,AngouriMath.Entity)
Method (no overloads)
Summary
The limit where the two one-sided limits agree, asked of each side through the
whole of ComputeLimit(AngouriMath.Entity,AngouriMath.Entity.Variable,AngouriMath.Entity,AngouriMath.Core.ApproachFrom,System.Boolean), ornull where either side
has no answer, the two differ, or the reading is not of real-valued functions.
whole of ComputeLimit(AngouriMath.Entity,AngouriMath.Entity.Variable,AngouriMath.Entity,AngouriMath.Core.ApproachFrom,System.Boolean), or
has no answer, the two differ, or the reading is not of real-valued functions.
Remarks
A two-sided limit is the two one-sided ones agreeing, and the branch that compares
them compares twoComputeLimitDivideEtImpera results -- the bare descent --
where a caller who names a side gets that descent *and* everything behind it:
SolveAsIndeterminatePower(AngouriMath.Entity,AngouriMath.Entity.Variable,AngouriMath.Entity,AngouriMath.Core.ApproachFrom), l'Hopital's rule, and the substitution
that moves a finite destination out to infinity.
promotion cannot be made over the complex plane, because there the one-sided limits
do not stay inside the reals: `lim x->0- x^x` answers 1 from the continuation, so
promoting agreement would give `lim x->0 x^x` the value 1 where `x^x` is not real
to the left of 0 at all, and `LimitTest.TestNoLimit` pins it as non-existent.
Under Real that side has no value to agree
with, so the case this could get wrong is the case that no longer arises.
pays for it, and it can only ever turn a refusal into an answer.
#719,
#596
them compares two
where a caller who names a side gets that descent *and* everything behind it:
SolveAsIndeterminatePower(AngouriMath.Entity,AngouriMath.Entity.Variable,AngouriMath.Entity,AngouriMath.Core.ApproachFrom), l'Hopital's rule, and the substitution
that moves a finite destination out to infinity.
promotion cannot be made over the complex plane, because there the one-sided limits
do not stay inside the reals: `lim x->0- x^x` answers 1 from the continuation, so
promoting agreement would give `lim x->0 x^x` the value 1 where `x^x` is not real
to the left of 0 at all, and `LimitTest.TestNoLimit` pins it as non-existent.
Under Real that side has no value to agree
with, so the case this could get wrong is the case that no longer arises.
pays for it, and it can only ever turn a refusal into an answer.
#719,
#596
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