Bsrgvty

So I have this basic code:

But the fractional alignment looks awful, any tips to fix this?

documentclass[11pt, a4paper]report
usepackagebm
usepackageamsfonts, graphicx, verbatim, amsmath,amssymb, amsthm, mathrsfs, eufrak
usepackagecolor
usepackagearray
usepackagesetspace% if you must (for double spacing thesis)
usepackagefancyhdr
usepackageenumitem
usepackagetikz
usepackageparskip
usepackagelipsum
usepackagefloatrow
usepackagecommath
providecommandU[1]protectrule.1in.1in


begindocument

Let $h$ be a linear mapping of $V_1$ into $V_2$. Let
[
h^0 = frac1abs G sum_tin G (rho_t^2)^-1 h rho_t^1
]
where $abs G$ is the order of $G$. Then
beginenumerate[label=(roman*)]
item If $rho^1$ and $rho^2$ are not isomorphic then we have $h^0=0$
item If $V_1 = V_2$ and $rho^1 = rho^2$, $h^0$ is a scalar multiple of the identity, the scalar being $frac1n Tr(h)$ where $n = dim(V_1)$
endenumerate

enddocument

as you notice, it looks awful.

The commath package provides a highly questionable implementation of abs. Don't load this package unless you absolutely have to. (Aside: You do not have to for the example at hand.)

Instead of loading this package, I suggest you

• load the mathtools package instead of the amsmath package. The mathtools package is, for all intents and purposes, a superset of the amsmath package; and



• 
  

  issue the instruction

  
  
  

  DeclarePairedDelimiterabslvertrvert
  

  
  
  

  in the preamble. This sets up a proper implementation of abs.... If you need to auto-size the vertical bars, simply use abs*....

  
  

*Addendum": More about how commath implements envert (abs is just an alias for envert): If envert<arg> is invoked without an optional sizing argument (a whole number between 0 and 4), the following code gets executed:

 !leftlvert#2rightrvert

It's the ! ("negative thinspace") instruction that messes up the symmetry of the full expression. Either write abs[0]<arg> to execute lvert#2rvert or, more safely, don't load commath at all and go for a cleaner definition of abs. The definitions of abs[1]... thru abs[4]... are also messed up, by the way, as are the definitions of norm and norm[1] thru norm]4]. While it's possible, in principle, to correct the faulty definitions of envert, abs, enVert, and norm, one is better off going for a setup that avoids these complications...

Compare the output of

documentclass[11pt, a4paper]report
usepackageamsmath
usepackageenumitem
usepackagecommath

DeclareMathOperatorTrTr

begindocument

Let $h$ be a linear mapping of $V_1$ into $V_2$. Let
[
h^0 = frac1abs G sum_tin G (rho_t^2)^-1 h rho_t^1
]
where $abs G$ is the order of $G$. Then
beginenumerate[label=(roman*)]
item If $rho^1$ and $rho^2$ are not isomorphic then we have $h^0=0$
item If $V_1 = V_2$ and $rho^1 = rho^2$, $h^0$ is a scalar multiple of the identity,
 the scalar being $frac1n Tr(h)$ where $n = dim(V_1)$
endenumerate

enddocument

with the output of

documentclass[11pt, a4paper]report
usepackageamsmath
usepackageenumitem

makeatletter
% begin definitions for a "better commath"

newcommanddifmathop!mathrmd
newcommandDifmathop!mathrmD

newcommandspx[1]%
 ifrelaxdetokenize#1relax
 expandafter@gobble
 else
 expandafter@firstofone
 fi
 ^#1%


newcommandpd[3][]fracpartialspx#1#2partial#3spx#1
newcommandtpd[3][]tfracpartialspx#1#2partial#3spx#1
newcommanddpd[3][]dfracpartialspx#1#2partial#3spx#1

newcommandmd[6]fracpartialspx#2#1partial#3spx#4partial#5spx#6
newcommandtmd[6]tfracpartialspx#2#1partial#3spx#4partial#5spx#6
newcommanddmd[6]dfracpartialspx#2#1partial#3spx#4partial#5spx#6

newcommandod[3][]fracdifspx#1#2dif#3spx#1
newcommandtod[3][]tfracdifspx#1#2dif#3spx#1
newcommanddod[3][]dfracdifspx#1#2dif#3spx#1

newcommandgenericdel[4]%
 ifcase#3relax
 ifx#1.else#1fi#4ifx#2.else#2fior
 bigl#1#4bigr#2or
 Bigl#1#4Bigr#2or
 biggl#1#4biggr#2or
 Biggl#1#4Biggr#2else
 left#1#4right#2fi

newcommanddel[2][-1]genericdel()#1#2
newcommandset[2][-1]genericdel#1#2
letcbrset
newcommandsbr[2][-1]genericdel[]#1#2
letintoodel
letintccsbr
newcommandintoc[2][-1]genericdel(]#1#2
newcommandintco[2][-1]genericdel[)#1#2
newcommandeval[2][-1]#1#2
newcommandenvert[2][-1]genericdel
letabsenvert
newcommandsVert[1][0]%
 ifcase#1relax
 rvertorbigr
newcommandenVert[2][-1]genericdel
letnormenVert
newcommandfullfunction[5]%
 beginarray@r@r@c@l@
 #1 colon & #2 & longrightarrow & #3 \
 & #4 & longmapsto & #5
 endarray

%%% end of the definitions
makeatother


DeclareMathOperatorTrTr

begindocument

Let $h$ be a linear mapping of $V_1$ into $V_2$. Let
[
h^0 = frac1abs G sum_tin G (rho_t^2)^-1 h rho_t^1
]
where $abs G$ is the order of $G$. Then
beginenumerate[label=(roman*)]
item If $rho^1$ and $rho^2$ are not isomorphic then we have $h^0=0$
item If $V_1 = V_2$ and $rho^1 = rho^2$, $h^0$ is a scalar multiple of the identity, 
 the scalar being $frac1n Tr(h)$ where $n = dim(V_1)$
endenumerate

enddocument

The code has already been presented in https://tex.stackexchange.com/a/135985/4427 and provides a full replacement of commath, avoiding all its weaknesses. If you're tied to commath because you use its macros and features in other places, this can save you. Otherwise define abs with DeclarePairedDelimiter as suggested by Mico.

For instance, you can notice the reduced space between “where” and “|G|” in the commath version.

You should define anyway an operator name for “Tr”.

If you decide to go for this, save the part between

% begin definitions for a "better commath"

and

% end of the definitions

in a file called bettercommath.sty in the working directory and do usepackagebettercommath.