integral competition HP50g vs. DM42

[peacecalc]

Hello Thomas,

thank you for your reply. I'm not shure that we are talking of the same thing, but in usual it is possible to convert every complex integral into the RxR space:

My textbook about complex analysis tells me:

\[ \displaystyle \int_C f(z) dz = \int^{t_1}_{t_o} \left( u(x,y) \frac{dx}{dt} - v(x,y)\frac{dy}{dt}\right) dt + i\cdot \int_{t_o}^{t_1} \left( v(x,y)\frac{dx}{dt} + u(x,y) \frac{dy}{dt} \right) dt
\]

\[z = x + iy; \quad dz = dx + idy; \quad u(x,y) = \Re f(z); \quad v(x,y) = \Im f(z); \quad x= x(t); \quad y=y(t); \quad u,v,x,y,t \in IR \]
C is an arbitray curve in the complex plane and t is the parameter. When our TR is able to operate with complex numbers and even operate with regular expressions (like the CAS from HP50g), then I see the chance to make a RPL program which can integrate (not for all cases) exact complex integrals. For closed curves for instance it is possible to calculate complex residues.

And if not the build in numerical integration will give us results, yes you have to calculate two integrals, but it should works.

And that should be possible for even non-analytical functions, because they are defined that their integral over a closed curve is not zero.