Mfcttrf

What would be the best formatting of the following align and cases where the middle case has a very long math equation?

beginalign*
 V_ijk& = begincases
 dfracy_u+y_l2 - dfracx_u+x_l2,& textif x_u < y_l\[15pt]
 dfrac1C bigg[dfracx_u^3-y_l^36+dfracy_l^2+x_u^22x_l + (x_u-y_l)dfracx_l^22+ dfracy_u^2-x_u^22(x_u-x_l)& - (y_u-x_u)dfracx_u^2-x_l^22 bigg],
 \[12pt]& textif x_uinleft[y_l,y_uright]\[15pt]
 dfrac1x_u-x_lbigg[dfrac(y_u+y_l)^26 - dfracy_u+y_l2 x_l + dfracx_l^22bigg],& textotherwise
 endcases
endalign*

The main default of this current workaround which is nearly ok, is that there is an extra space before -(y_u-x_u) that is annoying. Note that I put the second if text under second equation because it would be too width for my memoir otherwise. Please favour simpliest solutions if possible :)

with mfrac from nccmath and multlined from the mathtools package:

documentclassarticle
usepackagemathtools, nccmath

%---------------- show page layout. don't use in a real document!
usepackageshowframe
renewcommandShowFrameLinethickness0.15pt
renewcommand*ShowFrameColorcolorred
%---------------------------------------------------------------%

begindocument

[
V_ijk = begincases 
 mfracy_u+y_l2 - mfracx_u+x_l2, &textif x_u < y_l \[3ex]
 beginmultlined 
 mfrac1C bigg[mfracx_u^3-y_l^36+mfracy_l^2+x_u^22x_l
 + (x_u-y_l)mfracx_l^22\[-2ex]
 + mfracy_u^2-x_u^22(x_u-x_l) - (y_u-x_u)mfracx_u^2-x_l^22 biggr]
 endmultlined,
 & textif x_uin [y_l,y_u ]
 \[5ex]
 mfrac1x_u-x_lbiggl[mfrac(y_u+y_l)^26 - mfracy_u+y_l2 x_l
 + mfracx_l^22biggr],& textotherwise
 endcases
 ]
enddocument

I'm pretty sure it is a duplicate. But it is also easy to solve using aligned

documentclassarticle

usepackageamsmath

begindocument

beginalign*
 V_ijk& = begincases dfracy_u+y_l2 - dfracx_u+x_l2,&
 textif x_u < y_l
 \[15pt]
 beginaligned[b]
 &dfrac1C bigg[dfracx_u^3-y_l^36+dfracy_l^2+x_u^22x_l
 + (x_u-y_l)dfracx_l^22
 \
 &+ dfracy_u^2-x_u^22(x_u-x_l) -
 (y_u-x_u)dfracx_u^2-x_l^22 bigg]
 endaligned,
 & textif x_uinleft[y_l,y_uright]
 \[15pt]
 dfrac1x_u-x_lbigg[dfrac(y_u+y_l)^26 - dfracy_u+y_l2 x_l
 + dfracx_l^22bigg],& textotherwise
 endcases
 endalign*
enddocument

My suggestion is not to use cases, because it increases the interline spaces also inside nested alignments.

Using multlined for the long middle equation does the job.

documentclassarticle
usepackageamsmath,mathtools

begindocument

beginequation*
V_ijk = left{
beginaligned
& dfracy_u+y_l2 - dfracx_u+x_l2, && textif x_u < y_l
\[2ex]
& beginmultlined[b]
 dfrac1C biggl[
 dfracx_u^3-y_l^36+dfracy_l^2+x_u^22x_l + (x_u-y_l)dfracx_l^22 \
 + dfracy_u^2-x_u^22(x_u-x_l) - (y_u-x_u)dfracx_u^2-x_l^22
 biggr],
 endmultlined && textif x_uin [y_l,y_u]
\[2ex]
& dfrac1x_u-x_lbiggl[
 dfrac(y_u+y_l)^26 - dfracy_u+y_l2 x_l + dfracx_l^22
 biggr], && textotherwise
endaligned
right.
endequation*

enddocument

Avoid code such as frac1C that's hard to read and to maintain. Also note biggl and biggr instead of the unqualified bigg.

Also avoid align for single equations (which this is an example of).

Here's a solution that employs a dcases* environment instead of the cases environment. The d in dcases denotes "display style"; this means, among other things, that one can write frac instead of dfrac in order to get "large" fraction terms.

Note that I've removed unnecessary left and right directives.

documentclassarticle
usepackagemathtools % for 'dcases*' environment

begindocument
[
V_ijk = 
begindcases* 
fracy_u+y_l2 - fracx_u+x_l2,,
 &if $x_u < y_l$\[1ex]
beginaligned[b]
&frac1C biggl[
 fracx_u^3-y_l^36+fracy_l^2+x_u^22x_l
 + (x_u-y_l)fracx_l^22\
&quad + fracy_u^2-x_u^22(x_u-x_l) 
 - (y_u-x_u)fracx_u^2-x_l^22 ,biggr],,
endaligned
 &if $x_uin[y_l,y_u]$ \[1ex]
frac1x_u-x_l biggl[ 
 frac(y_u+y_l)^26 
 - fracy_u+y_l2 x_l 
 + fracx_l^22 ,biggr],,
 & otherwise
enddcases*
]
enddocument