HOROCYCLIC WORD SIMPLIFIER FOR HNN EXTENSIONS

Put in a word in the horocyclic subgroup $\mathbb{Z}^3 < \mathbb{Z}^3 *$ subject to the HNN extensions sending $taT$ to $a^{p_1} b^{q_1} c^{r_1}$, $tbT$ to $a^{p_2} b^{q_2} c^{r_2}$, and $tcT$ to $a^{p_3} b^{q_3} c^{r_3}$. As usual, we work with the standard generating set, using capital letters to denote inverses.

You can specify such an HNN extension by entering integer powers $(p_1,p_2,p_3)$ into the PowersP line and similar for PowersQ and PowersR.

Words you enter MUST be written in $\{a, b, c, t, A, B, C, T\}^*$, and must be of the form $t^n g_n T g_{n-1} T \ldots T g_0$ where $g_i \in \mathbb{Z}^3$.

The program will then output what the word simplifies to and the length of the word you entered.

Put in a word in the horocyclic subgroup $\mathbb{Z}^3 < \mathbb{Z}^3 *$ subject to the HNN extensions sending $taT$ to $a^{p_1} b^{q_1} c^{r_1}$, $tbT$ to $a^{p_2} b^{q_2} c^{r_2}$, and $tcT$ to $a^{p_3} b^{q_3} c^{r_3}$. As usual, we work with the standard generating set, using capital letters to denote inverses.

You can specify such an HNN extension by entering integer powers $(p_1,p_2,p_3)$ into the PowersP line and similar for PowersQ and PowersR.

Words you enter MUST be written in $\{a, b, c, t, A, B, C, T\}^*$, and must be of the form $t^n g_n T g_{n-1} T \ldots T g_0$ where $g_i \in \mathbb{Z}^3$.

The program will then output what the word simplifies to and the length of the word you entered.