PowerCount

Overview

PowerCount is a Mathematica package performing power counting on an expression.

Usage

First, one needs to set the symbols to be included in or excluded from the power counting.

IsCnt[x1,x2,...] sets symbols $x_1,x_2,...$ to be included in power counting.

NoCnt[a1,a2,...] sets symbols $a_1,a_2,...$ to be excluded from power counting. Numerical constants (e.g. $\pi, e...$ are excluded from power counting automatically).

CntQ[x] returns whether a symbol $x$ is included in the power counting. NCntQ[x] returns whether a symbol $x$ is excluded from power counting.

SetScl[{{x1,x2...},{x3,x4...},...},{M1,M2,...}] sets the scale of symbols $x1,x_2,...\sim M_1$; $x_3,x_4,...\sim M_2; ...$.

SetHrchy[M1>M2>...>1>m_1>m_2>...>0] sets the hierarchy of scales, $M_1>M_2>...>1$ are treated as large scales, while $1>m_1>m_2>...$ are treated as small scales.

SclHrchy is a symbol set by SetHrchy[...], which are used as an assumption in power counting to compare different scales.

PwrCnt[x] gives the scale of symbol $x$.

ShowPwr[exp] assembles the expression $exp$'s terms which has the same power counting together, and display the corresponding power counting as subscripts.

SrtByPwr[exp] assembles the expression $exp$'s terms which has the same power counting together, and sort the terms in the order of descending power counting.