AngouriMath
WhereRealValued(AngouriMath.Entity,AngouriMath.Entity.Variable)
Method (no overloads)
Summary
Where an expression that is not real everywhere is real on an open set: the
conjunction ofb > 0 over the bases b of its powers to a real
exponent that is not whole and the argumentsb of its logarithms to a positive
constant base, ornull where it has no such power or logarithm or
a shape IsRealValued(AngouriMath.Entity,AngouriMath.Entity.Variable) does not list.sqrt(1 + x) + 1/2 is real
where1 + x > 0 , x^(1/3) - 1 where x > 0 , and
ln(2 x^3) where 2 x^3 > 0 , which is all that is claimed: with the
downcasting off a cube root of a negative is the principal one. Strict for the reason
IsRealValued(AngouriMath.Entity,AngouriMath.Entity.Variable) reads only a strict bound: a derivative needs the
expression real on an interval around the point.
conjunction of
exponent that is not whole and the arguments
constant base, or
a shape IsRealValued(AngouriMath.Entity,AngouriMath.Entity.Variable) does not list.
where
downcasting off a cube root of a negative is the principal one. Strict for the reason
IsRealValued(AngouriMath.Entity,AngouriMath.Entity.Variable) reads only a strict bound: a derivative needs the
expression real on an interval around the point.
Remarks
Asked by differentiation where the sign or the modulus of such an expression is
differentiated, so that the real-line rule is claimed where the expression is real and
the derivative is left unevaluated elsewhere. The antiderivatives of
sqrt(1 + x + sqrt(1 + x)) and (x - 4)/((1 + x^(1/3)) sqrt(x)) carry
sgn(sqrt(1 + x) + 1/2) and sgn(x^(1/3)) , and could not be checked by
differentiating them back anywhere.
#1186
differentiated, so that the real-line rule is claimed where the expression is real and
the derivative is left unevaluated elsewhere. The antiderivatives of
differentiating them back anywhere.
#1186
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