(poly, dilation, sumrule, $): computing the L_2 smoothness of a mask, i.e. the quantities defined in [Han2003].__D1CriticalExponentV2__- Refinement Equation(in Tex form)

\Phi(x) = [\Phi_1(x) ... \Phi_r(x)]^T \Phi(x) = |detM|\sum_{\beta in Z^s}{a(\beta)*\Phi(Mx-\beta)}- Parameters

dimension: s = 1

multiplicity: r integerInput <=

3.1 "poly" is the mask a in the form of polynomials in x

3.2 "dilation" is an integer larger than 1.

3.3 "sumrule" mask_a satisfies the sum rules of oder k with respect to some vector \hat{y}(\xi).Output =>

smoothness: the estimate of the L_2 critical exponent. see the definition in the above paper.

- NOTE: Here we don't check the sum rule of the mask a. We assume that mask a is obtained previously and already satisfied the sum rule of order k but not k+1 (k>=1).

- Parameters

**List of Commands**