08-09-2015, 02:24 PM

Hello friends,

on hpcalc.org there exist a nice little libary which makes it possible, that the hp 50g is able to solve exact equations of 4th order.

For instance: \[ x^4 - 16 = 0 \]

Okay it is very easy and even the hp 50g is able to factorize it, but that is not the point. The program "polyroot" gives a list with four entries. One of the entries looks like:

\[ \frac{1}{6\cdot \sqrt[3]{\frac{8\cdot \sqrt{3}}{9}}}\cdot \sqrt{- \left(3+3\cdot i\cdot \sqrt{3}\right)\cdot {\sqrt[3]{\frac{8\cdot \sqrt{3}}{9}}}^{3}-\left(4-4\cdot i\cdot \sqrt{3}\right)\cdot \sqrt[3]{\frac{8\cdot \sqrt{3}}{9}}}\cdot \sqrt{6}-\frac{1}{6\cdot \sqrt[3]{\frac{8\cdot \sqrt{3}}{9}}}\cdot \sqrt{- \left(3-3\cdot i\cdot \sqrt{3}\right)\cdot {\sqrt[3]{\frac{8\cdot \sqrt{3}}{9}}}^{3}-\left(4+4\cdot i\cdot \sqrt{3}\right)\cdot \sqrt[3]{\frac{8\cdot \sqrt{3}}{9}}}\cdot \sqrt{6} \\ -\frac{1}{3\cdot \sqrt[3]{\frac{8\cdot \sqrt{3}}{9}}}\cdot \sqrt{3\cdot {\sqrt[3]{\frac{8\cdot \sqrt{3}}{9}}}^{3}-4\cdot \sqrt[3]{\frac{8\cdot \sqrt{3}}{9}}}\cdot \sqrt{3} \]

Holy cow! If you take the command "->NUM" you get the short and expected short answer, but not as a simplified symbolic answer. I test a lot of combinations of the commands "SIMPLIFY" "COLLECT" and with the special commands "EXPLN" and so on.

I hope there is somebody in this universe who knows the trick(s) for reducing such a

monster expression to a simple complex number.

Thank you in advance

peacecalc

on hpcalc.org there exist a nice little libary which makes it possible, that the hp 50g is able to solve exact equations of 4th order.

For instance: \[ x^4 - 16 = 0 \]

Okay it is very easy and even the hp 50g is able to factorize it, but that is not the point. The program "polyroot" gives a list with four entries. One of the entries looks like:

\[ \frac{1}{6\cdot \sqrt[3]{\frac{8\cdot \sqrt{3}}{9}}}\cdot \sqrt{- \left(3+3\cdot i\cdot \sqrt{3}\right)\cdot {\sqrt[3]{\frac{8\cdot \sqrt{3}}{9}}}^{3}-\left(4-4\cdot i\cdot \sqrt{3}\right)\cdot \sqrt[3]{\frac{8\cdot \sqrt{3}}{9}}}\cdot \sqrt{6}-\frac{1}{6\cdot \sqrt[3]{\frac{8\cdot \sqrt{3}}{9}}}\cdot \sqrt{- \left(3-3\cdot i\cdot \sqrt{3}\right)\cdot {\sqrt[3]{\frac{8\cdot \sqrt{3}}{9}}}^{3}-\left(4+4\cdot i\cdot \sqrt{3}\right)\cdot \sqrt[3]{\frac{8\cdot \sqrt{3}}{9}}}\cdot \sqrt{6} \\ -\frac{1}{3\cdot \sqrt[3]{\frac{8\cdot \sqrt{3}}{9}}}\cdot \sqrt{3\cdot {\sqrt[3]{\frac{8\cdot \sqrt{3}}{9}}}^{3}-4\cdot \sqrt[3]{\frac{8\cdot \sqrt{3}}{9}}}\cdot \sqrt{3} \]

Holy cow! If you take the command "->NUM" you get the short and expected short answer, but not as a simplified symbolic answer. I test a lot of combinations of the commands "SIMPLIFY" "COLLECT" and with the special commands "EXPLN" and so on.

I hope there is somebody in this universe who knows the trick(s) for reducing such a

monster expression to a simple complex number.

Thank you in advance

peacecalc