AngouriMath
ArmOffTheRealLine(AngouriMath.Entity,AngouriMath.Entity[])
Method (no overloads)
Summary
The arm that a piecewise on a sign owes a quadratic off the real line, answered by
form wherever one of coefficients is not real;
null where none of them holds the imaginary unit, and the sign arms
are left to decide.
are left to decide.
Remarks
The sign arms choose between forms by which is real where the integrand is, and off
the real line that has nothing to go on.i < 0 and i > 0 are each
NaN, the complex numbers not being ordered, and a piecewise with no arm that holds is
NaN with them:1/(x^2 + i) and 1/sqrt(i x^2 + 1) answered NaN + C ,
and1/sqrt(i a x^2 + 1) a piecewise that is NaN for every real a but zero.
Nor is a real sign any help where the rest of the quadratic is not real: with
E = b^2 - 4ac the arcsine differentiates back to 1/sqrt(Q) only where
sqrt(E) sqrt(Q/E) is sqrt(Q) , and 1/sqrt(-x^2 + (1 + i) x + 1) came back as minus its integrand below -2. The arctangent and the logarithm use nothing about their root but
sqrt(q)^2 = q , and are antiderivatives off the real line as well.
https://github.com/asc-community/AngouriMath/issues/1598
the real line that has nothing to go on.
NaN, the complex numbers not being ordered, and a piecewise with no arm that holds is
NaN with them:
and
Nor is a real sign any help where the rest of the quadratic is not real: with
https://github.com/asc-community/AngouriMath/issues/1598
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