Central Expression Files

Central Expressions
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System Requirment:

    -Windows XP/7.
    -.NET Framework 3.5/4.0 (for complied file: center exp.exe).
    -Microsoft Visual Studio 2008/2010 (for VB code: Module1.vb).

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Central Expression is a Windows console program, which performs different tasks concerning central elements of baby and toroidal extended affine Weyl group of type $A_1$ and nullity 2. Different options of the program are as follows:

    1-Calculate z^n for a given n (Baby Case):
        For a given even integer n, calculates all possible expressions of $z^n$, by induction.

    2-Calculate any possible expression of given length n:
        For a given even integer n, first calculates any possible expression in the group, then finds out which are central. If a specific power m is given, it gives the list of expressions on length n which are equal to $z^m$.

    3-Calculate the action of a given element on the basis:
        For baby case, calculates the action of a given expression on $\lambda_1$ and $\lambda_2$, elements of the basis of $(\v^0)^*$.

    4-Calculate any possible expression of a given central element:
        For a given expression, in baby case, calculates any possible expression of that element, by commuting the generators.

    5-Calculate z^n for a given n (Toroidal Case)
        Same as (1) for toroidal case.

    6-Calculate any possible reduced expression of z^n
        For a given even integer n, calculates all the reduced expressions of $z^n$.


Note:

    -All the sub algorithms write their output as plain text to the same folder of the program.

    -For ease of calculation, we used 0, 1, 2 and 3 instead of $w_\epsilon$, $w_{\epsilon+\sigma_1}, $w_{\epsilon+\sigma_2}$ and $w_{\epsilon+\sigma_1+\simga_2}$.

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