Parameter list from newton equation report is out of order in CGI interface

[janithpet]

Describe the bug
When using the CGI interface (after fixing Issues #615, #616, #617 and #618) with bitmaps 0 and 63 for backends and IR passes respectively, the parameters in the generated Equation Report seem to be out order compared to the Information Report.

The information Report states the following,

whereas the Equation Report looks like,

To Reproduce
Steps to reproduce the behavior:

1. After setting up the CGI interface, run the [Buckingham 1914] example.

Expected behavior
TBA

Host OS (please complete the following information):

• Run on the CGI tool currently hosted on [cpu](https://cpu0.physical-computation.org

You local changes (please complete the following information):

• Output of git diff.
• Output of git remote -v.

[janithpet]

The newton description used above:

#
#	Authored 2018, Phillip Stanley-Marbell.
#
#	All rights reserved.
#
#	Redistribution and use in source and binary forms, with or without
#	modification, are permitted provided that the following conditions
#	are met:
#
#	*	Redistributions of source code must retain the above
#		copyright notice, this list of conditions and the following
#		disclaimer.
#
#	*	Redistributions in binary form must reproduce the above
#		copyright notice, this list of conditions and the following
#		disclaimer in the documentation and/or other materials
#		provided with the distribution.
#
#	*	Neither the name of the author nor the names of its
#		contributors may be used to endorse or promote products
#		derived from this software without specific prior written
#		permission.
#
#	THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
#	"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
#	LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
#	FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
#	COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
#	INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
#	BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
#	LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
#	CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
#	LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
#	ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
#	POSSIBILITY OF SUCH DAMAGE.
#
#
#	Description:	Empty invariant for auto-generating synthetic invariants
#			for first example from the original Buckingham paper.
#
#	Parameters
#
#		F	:
#		rho	:
#		D	:
#		S	:
#		n	:
#		mu	:
#		g	:
#

include "NewtonBaseSignals.nt"

nDimension: signal =
{
	derivation = 1/time;
}

muDimension: signal =
{
	derivation = mass / (distance*time);
}

BuckinghamPaperFirstExampleForPiGroups: invariant(	F_param:	force,
							rho_param:	density,
							D_param:	distance,
							S_param:	speed,
							n_param:	nDimension,
							mu_param:	muDimension,
							g_param:	acceleration) =
{
}

[janithpet]

Running ./newton-linux-EN <newton description in [comment above](https://github.com/phillipstanleymarbell/Noisy-lang-compiler/issues/619#issuecomment-1203592113)> -v 2 -x -p yielded the following outputs:

root@ip-172-31-34-27:/home/janith/Noisy-lang-compiler/src/newton# ./newton-linux-EN /var/www/cpu0.physical-computation.org/tmp/input-109.175.246.255-XXXXwcYSBs.nt -v 2 -x -p

LaTeX Backend Output:
---------------------
\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage[a0paper, portrait]{geometry}
\usepackage{color}
\definecolor{DarkSlateGray}{rgb}{0.1843,0.3098,0.3098}
\definecolor{DeepSkyBlue}{rgb}{0,0.7490,1}
\definecolor{DarkGreen}{rgb}{0,0.3922,0}
\begin{document}
\tiny


$$
\begin{aligned}
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }0, \text{ with column order } \left(P4,P5,P6,P3,P0,P1,P2\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(speed.P3)(nDimension.P0)}{(acceleration.P2)}},\quad\textcolor{DarkGreen}{\dfrac{(force.P4)(nDimension.P0^{3})}{(muDimension.P1)(acceleration.P2^{2})}},\quad\textcolor{DarkGreen}{\dfrac{(density.P5)(acceleration.P2^{2})}{(nDimension.P0^{3})(muDimension.P1)}},\quad\textcolor{DarkGreen}{\dfrac{(distance.P6)(nDimension.P0^{2})}{(acceleration.P2)}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }1, \text{ with column order } \left(P3,P5,P6,P0,P4,P1,P2\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(force.P3)(acceleration.P2)}{(speed.P0^{3})(muDimension.P1)}},\quad\textcolor{DarkGreen}{\dfrac{(speed.P0)(nDimension.P4)}{(acceleration.P2)}},\quad\textcolor{DarkGreen}{\dfrac{(density.P5)(speed.P0^{3})}{(muDimension.P1)(acceleration.P2)}},\quad\textcolor{DarkGreen}{\dfrac{(distance.P6)(acceleration.P2)}{(speed.P0^{2})}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }2, \text{ with column order } \left(P3,P4,P6,P0,P1,P5,P2\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(acceleration.P2)}{(speed.P0)(nDimension.P1)}},\quad\textcolor{DarkGreen}{\dfrac{(density.P4)(speed.P0^{4})}{(force.P3)(nDimension.P1^{2})}},\quad\textcolor{DarkGreen}{\dfrac{(speed.P0^{2})(muDimension.P5)}{(force.P3)(nDimension.P1)}},\quad\textcolor{DarkGreen}{\dfrac{(distance.P6)(nDimension.P1)}{(speed.P0)}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }3, \text{ with column order } \left(P3,P4,P5,P0,P1,P2,P6\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(force.P3)(nDimension.P1)}{(speed.P0^{2})(muDimension.P2)}},\quad\textcolor{DarkGreen}{\dfrac{(density.P4)(speed.P0^{2})}{(nDimension.P1)(muDimension.P2)}},\quad\textcolor{DarkGreen}{\dfrac{(distance.P5)(nDimension.P1)}{(speed.P0)}},\quad\textcolor{DarkGreen}{\dfrac{(acceleration.P6)}{(speed.P0)(nDimension.P1)}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }4, \text{ with column order } \left(P2,P5,P6,P3,P4,P1,P0\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(speed.P3^{2})}{(distance.P6)(acceleration.P0)}},\quad\textcolor{DarkGreen}{\dfrac{(distance.P6)(nDimension.P4^{2})}{(acceleration.P0)}},\quad\textcolor{DarkGreen}{\dfrac{(density.P5^{2})(distance.P6^{3})(acceleration.P0)}{(muDimension.P1^{2})}},\quad\textcolor{DarkGreen}{\dfrac{(force.P2^{2})}{(distance.P6^{3})(muDimension.P1^{2})(acceleration.P0)}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }5, \text{ with column order } \left(P2,P4,P6,P3,P1,P5,P0\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(acceleration.P0)}{(distance.P6)(nDimension.P1^{2})}},\quad\textcolor{DarkGreen}{\dfrac{(speed.P3)}{(distance.P6)(nDimension.P1)}},\quad\textcolor{DarkGreen}{\dfrac{(muDimension.P5)}{(density.P4)(distance.P6^{2})(nDimension.P1)}},\quad\textcolor{DarkGreen}{\dfrac{(force.P2)}{(density.P4)(distance.P6^{4})(nDimension.P1^{2})}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }6, \text{ with column order } \left(P2,P4,P5,P3,P1,P0,P6\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(speed.P3)}{(distance.P5)(nDimension.P1)}},\quad\textcolor{DarkGreen}{\dfrac{(density.P4)(distance.P5^{2})(nDimension.P1)}{(muDimension.P0)}},\quad\textcolor{DarkGreen}{\dfrac{(force.P2)}{(distance.P5^{2})(nDimension.P1)(muDimension.P0)}},\quad\textcolor{DarkGreen}{\dfrac{(acceleration.P6)}{(distance.P5)(nDimension.P1^{2})}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }7, \text{ with column order } \left(P2,P3,P6,P1,P4,P5,P0\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(distance.P6)(acceleration.P0)}{(speed.P1^{2})}},\quad\textcolor{DarkGreen}{\dfrac{(distance.P6)(nDimension.P4)}{(speed.P1)}},\quad\textcolor{DarkGreen}{\dfrac{(muDimension.P5)}{(density.P3)(distance.P6)(speed.P1)}},\quad\textcolor{DarkGreen}{\dfrac{(force.P2)}{(density.P3)(distance.P6^{2})(speed.P1^{2})}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }8, \text{ with column order } \left(P2,P3,P5,P1,P4,P0,P6\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(density.P3)(distance.P5)(speed.P1)}{(muDimension.P0)}},\quad\textcolor{DarkGreen}{\dfrac{(distance.P5)(nDimension.P4)}{(speed.P1)}},\quad\textcolor{DarkGreen}{\dfrac{(force.P2)}{(distance.P5)(speed.P1)(muDimension.P0)}},\quad\textcolor{DarkGreen}{\dfrac{(distance.P5)(acceleration.P6)}{(speed.P1^{2})}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }9, \text{ with column order } \left(P2,P3,P4,P1,P0,P5,P6\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(distance.P4)(nDimension.P0)}{(speed.P1)}},\quad\textcolor{DarkGreen}{\dfrac{(force.P2)}{(density.P3)(distance.P4^{2})(speed.P1^{2})}},\quad\textcolor{DarkGreen}{\dfrac{(muDimension.P5)}{(density.P3)(distance.P4)(speed.P1)}},\quad\textcolor{DarkGreen}{\dfrac{(distance.P4)(acceleration.P6)}{(speed.P1^{2})}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }10, \text{ with column order } \left(P1,P5,P6,P3,P4,P0,P2\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(density.P5^{1.5012e+15})(speed.P3^{4.5036e+15})}{(muDimension.P0^{1.5012e+15})(acceleration.P2^{1.5012e+15})}},\quad\textcolor{DarkGreen}{\dfrac{(nDimension.P4^{4.5036e+15})(muDimension.P0^{1.5012e+15})}{(density.P5^{1.5012e+15})(acceleration.P2^{3.0024e+15})}},\quad\textcolor{DarkGreen}{\dfrac{(force.P1^{4.5036e+15})(density.P5^{4.5036e+15})}{(muDimension.P0^{9.0072e+15})(acceleration.P2)}},\quad\textcolor{DarkGreen}{\dfrac{(density.P5^{3.0024e+15})(distance.P6^{4.5036e+15})(acceleration.P2^{1.5012e+15})}{(muDimension.P0^{3.0024e+15})}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }11, \text{ with column order } \left(P1,P4,P6,P3,P0,P5,P2\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(speed.P3)(nDimension.P0)}{(acceleration.P2)}},\quad\textcolor{DarkGreen}{\dfrac{(force.P1)(nDimension.P0^{6})}{(density.P4)(acceleration.P2^{4})}},\quad\textcolor{DarkGreen}{\dfrac{(nDimension.P0^{3})(muDimension.P5)}{(density.P4)(acceleration.P2^{2})}},\quad\textcolor{DarkGreen}{\dfrac{(distance.P6)(nDimension.P0^{2})}{(acceleration.P2)}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }12, \text{ with column order } \left(P1,P4,P5,P3,P0,P2,P6\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(density.P4^{2.2518e+15})(speed.P3^{4.5036e+15})}{(nDimension.P0^{2.2518e+15})(muDimension.P2^{2.2518e+15})}},\quad\textcolor{DarkGreen}{\dfrac{(force.P1^{4.5036e+15})(density.P4^{4.5036e+15})}{(nDimension.P0)(muDimension.P2^{9.0072e+15})}},\quad\textcolor{DarkGreen}{\dfrac{(density.P4^{2.2518e+15})(distance.P5^{4.5036e+15})(nDimension.P0^{2.2518e+15})}{(muDimension.P2^{2.2518e+15})}},\quad\textcolor{DarkGreen}{\dfrac{(density.P4^{2.2518e+15})(acceleration.P6^{4.5036e+15})}{(nDimension.P0^{6.7554e+15})(muDimension.P2^{2.2518e+15})}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }13, \text{ with column order } \left(P1,P3,P6,P0,P4,P5,P2\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(force.P1)(acceleration.P2^{2})}{(density.P3)(speed.P0^{6})}},\quad\textcolor{DarkGreen}{\dfrac{(speed.P0)(nDimension.P4)}{(acceleration.P2)}},\quad\textcolor{DarkGreen}{\dfrac{(muDimension.P5)(acceleration.P2^{1})}{(density.P3)(speed.P0^{3})}},\quad\textcolor{DarkGreen}{\dfrac{(distance.P6)(acceleration.P2)}{(speed.P0^{2})}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }14, \text{ with column order } \left(P1,P3,P5,P0,P4,P2,P6\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(force.P1^{1.5012e+15})(density.P3^{1.5012e+15})}{(speed.P0)(muDimension.P2^{3.0024e+15})}},\quad\textcolor{DarkGreen}{\dfrac{(nDimension.P4^{1.5012e+15})(muDimension.P2^{1.5012e+15})}{(density.P3^{1.5012e+15})(speed.P0^{3.0024e+15})}},\quad\textcolor{DarkGreen}{\dfrac{(density.P3^{1.5012e+15})(distance.P5^{1.5012e+15})(speed.P0^{1.5012e+15})}{(muDimension.P2^{1.5012e+15})}},\quad\textcolor{DarkGreen}{\dfrac{(muDimension.P2^{1.5012e+15})(acceleration.P6^{1.5012e+15})}{(density.P3^{1.5012e+15})(speed.P0^{4.5036e+15})}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }15, \text{ with column order } \left(P1,P3,P4,P0,P2,P5,P6\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(force.P1)(nDimension.P2^{2})}{(density.P3)(speed.P0^{4})}},\quad\textcolor{DarkGreen}{\dfrac{(distance.P4)(nDimension.P2)}{(speed.P0)}},\quad\textcolor{DarkGreen}{\dfrac{(nDimension.P2^{1})(muDimension.P5)}{(density.P3)(speed.P0^{2})}},\quad\textcolor{DarkGreen}{\dfrac{(acceleration.P6)}{(speed.P0)(nDimension.P2)}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }16, \text{ with column order } \left(P1,P2,P6,P3,P4,P5,P0\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(speed.P3^{2})}{(distance.P6)(acceleration.P0)}},\quad\textcolor{DarkGreen}{\dfrac{(distance.P6)(nDimension.P4^{2})}{(acceleration.P0)}},\quad\textcolor{DarkGreen}{\dfrac{(muDimension.P5^{2})}{(density.P2^{2})(distance.P6^{3})(acceleration.P0)}},\quad\textcolor{DarkGreen}{\dfrac{(force.P1^{2})}{(density.P2^{2})(distance.P6^{6})(acceleration.P0^{2})}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }17, \text{ with column order } \left(P1,P2,P5,P3,P4,P0,P6\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(density.P2^{1.1259e+15})(distance.P5^{1.1259e+15})(speed.P3^{1.1259e+15})}{(muDimension.P0^{1.1259e+15})}},\quad\textcolor{DarkGreen}{\dfrac{(density.P2^{1.1259e+15})(distance.P5^{2.2518e+15})(nDimension.P4^{1.1259e+15})}{(muDimension.P0^{1.1259e+15})}},\quad\textcolor{DarkGreen}{\dfrac{(force.P1^{1.1259e+15})(density.P2^{1.1259e+15})(distance.P5)}{(muDimension.P0^{2.2518e+15})}},\quad\textcolor{DarkGreen}{\dfrac{(density.P2^{2.2518e+15})(distance.P5^{3.3777e+15})(acceleration.P6^{1.1259e+15})}{(muDimension.P0^{2.2518e+15})}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }18, \text{ with column order } \left(P1,P2,P4,P3,P0,P5,P6\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(speed.P3)}{(distance.P4)(nDimension.P0)}},\quad\textcolor{DarkGreen}{\dfrac{(force.P1)}{(density.P2)(distance.P4^{4})(nDimension.P0^{2})}},\quad\textcolor{DarkGreen}{\dfrac{(muDimension.P5)}{(density.P2)(distance.P4^{2})(nDimension.P0)}},\quad\textcolor{DarkGreen}{\dfrac{(acceleration.P6)}{(distance.P4)(nDimension.P0^{2})}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }19, \text{ with column order } \left(P1,P2,P3,P0,P4,P5,P6\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(force.P1)}{(density.P2)(distance.P3^{2})(speed.P0^{2})}},\quad\textcolor{DarkGreen}{\dfrac{(distance.P3)(nDimension.P4)}{(speed.P0)}},\quad\textcolor{DarkGreen}{\dfrac{(muDimension.P5)}{(density.P2)(distance.P3^{1})(speed.P0)}},\quad\textcolor{DarkGreen}{\dfrac{(distance.P3)(acceleration.P6)}{(speed.P0^{2})}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }20, \text{ with column order } \left(P0,P5,P6,P3,P4,P1,P2\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(speed.P3^{3})(muDimension.P1^{1})}{(force.P0)(acceleration.P2^{1})}},\quad\textcolor{DarkGreen}{\dfrac{(force.P0)(nDimension.P4^{3})}{(muDimension.P1^{1})(acceleration.P2^{2})}},\quad\textcolor{DarkGreen}{\dfrac{(force.P0^{3})(density.P5^{3})}{(muDimension.P1^{6})}},\quad\textcolor{DarkGreen}{\dfrac{(distance.P6^{3})(muDimension.P1^{2})(acceleration.P2^{1})}{(force.P0^{2})}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }21, \text{ with column order } \left(P0,P4,P6,P3,P1,P5,P2\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(speed.P3)(nDimension.P1)}{(acceleration.P2)}},\quad\textcolor{DarkGreen}{\dfrac{(density.P4)(acceleration.P2^{4})}{(force.P0)(nDimension.P1^{6})}},\quad\textcolor{DarkGreen}{\dfrac{(muDimension.P5)(acceleration.P2^{2})}{(force.P0)(nDimension.P1^{3})}},\quad\textcolor{DarkGreen}{\dfrac{(distance.P6)(nDimension.P1^{2})}{(acceleration.P2)}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }22, \text{ with column order } \left(P0,P4,P5,P3,P1,P2,P6\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(speed.P3^{2})(muDimension.P2)}{(force.P0)(nDimension.P1)}},\quad\textcolor{DarkGreen}{\dfrac{(force.P0^{2})(density.P4^{2})}{(muDimension.P2^{4})}},\quad\textcolor{DarkGreen}{\dfrac{(distance.P5^{2})(nDimension.P1)(muDimension.P2)}{(force.P0)}},\quad\textcolor{DarkGreen}{\dfrac{(muDimension.P2)(acceleration.P6^{2})}{(force.P0)(nDimension.P1^{3})}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }23, \text{ with column order } \left(P0,P3,P6,P1,P4,P5,P2\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(density.P3)(speed.P1^{6})}{(force.P0)(acceleration.P2^{2})}},\quad\textcolor{DarkGreen}{\dfrac{(speed.P1)(nDimension.P4)}{(acceleration.P2)}},\quad\textcolor{DarkGreen}{\dfrac{(speed.P1^{3})(muDimension.P5)}{(force.P0)(acceleration.P2)}},\quad\textcolor{DarkGreen}{\dfrac{(distance.P6)(acceleration.P2)}{(speed.P1^{2})}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }24, \text{ with column order } \left(P0,P3,P5,P1,P4,P2,P6\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(force.P0)(density.P3)}{(muDimension.P2^{2})}},\quad\textcolor{DarkGreen}{\dfrac{(force.P0)(nDimension.P4)}{(speed.P1^{2})(muDimension.P2)}},\quad\textcolor{DarkGreen}{\dfrac{(distance.P5)(speed.P1)(muDimension.P2)}{(force.P0)}},\quad\textcolor{DarkGreen}{\dfrac{(force.P0)(acceleration.P6)}{(speed.P1^{3})(muDimension.P2)}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }25, \text{ with column order } \left(P0,P3,P4,P1,P2,P5,P6\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(density.P3)(speed.P1^{4})}{(force.P0)(nDimension.P2^{2})}},\quad\textcolor{DarkGreen}{\dfrac{(distance.P4)(nDimension.P2)}{(speed.P1)}},\quad\textcolor{DarkGreen}{\dfrac{(speed.P1^{2})(muDimension.P5)}{(force.P0)(nDimension.P2)}},\quad\textcolor{DarkGreen}{\dfrac{(acceleration.P6)}{(speed.P1)(nDimension.P2)}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }26, \text{ with column order } \left(P0,P2,P6,P3,P4,P5,P1\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(speed.P3^{2})}{(distance.P6)(acceleration.P1)}},\quad\textcolor{DarkGreen}{\dfrac{(distance.P6)(nDimension.P4^{2})}{(acceleration.P1)}},\quad\textcolor{DarkGreen}{\dfrac{(distance.P6^{3})(muDimension.P5^{2})(acceleration.P1)}{(force.P0^{2})}},\quad\textcolor{DarkGreen}{\dfrac{(density.P2^{2})(distance.P6^{6})(acceleration.P1^{2})}{(force.P0^{2})}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }27, \text{ with column order } \left(P0,P2,P5,P3,P4,P1,P6\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(distance.P5)(speed.P3)(muDimension.P1)}{(force.P0)}},\quad\textcolor{DarkGreen}{\dfrac{(distance.P5^{2})(nDimension.P4)(muDimension.P1)}{(force.P0)}},\quad\textcolor{DarkGreen}{\dfrac{(force.P0)(density.P2)}{(muDimension.P1^{2})}},\quad\textcolor{DarkGreen}{\dfrac{(distance.P5^{3})(muDimension.P1^{2})(acceleration.P6)}{(force.P0^{2})}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }28, \text{ with column order } \left(P0,P2,P4,P3,P1,P5,P6\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(speed.P3)}{(distance.P4)(nDimension.P1)}},\quad\textcolor{DarkGreen}{\dfrac{(density.P2)(distance.P4^{4})(nDimension.P1^{2})}{(force.P0)}},\quad\textcolor{DarkGreen}{\dfrac{(distance.P4^{2})(nDimension.P1)(muDimension.P5)}{(force.P0)}},\quad\textcolor{DarkGreen}{\dfrac{(acceleration.P6)}{(distance.P4)(nDimension.P1^{2})}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }29, \text{ with column order } \left(P0,P2,P3,P1,P4,P5,P6\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(density.P2)(distance.P3^{2})(speed.P1^{2})}{(force.P0)}},\quad\textcolor{DarkGreen}{\dfrac{(distance.P3)(nDimension.P4)}{(speed.P1)}},\quad\textcolor{DarkGreen}{\dfrac{(distance.P3)(speed.P1)(muDimension.P5)}{(force.P0)}},\quad\textcolor{DarkGreen}{\dfrac{(distance.P3)(acceleration.P6)}{(speed.P1^{2})}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }30, \text{ with column order } \left(P0,P1,P6,P3,P4,P5,P2\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(density.P1^{1})(speed.P3^{6})}{(force.P0)(acceleration.P2^{2})}},\quad\textcolor{DarkGreen}{\dfrac{(force.P0)(nDimension.P4^{6})}{(density.P1^{1})(acceleration.P2^{4})}},\quad\textcolor{DarkGreen}{\dfrac{(muDimension.P5^{6})}{(force.P0^{3})(density.P1^{3})}},\quad\textcolor{DarkGreen}{\dfrac{(density.P1^{2})(distance.P6^{6})(acceleration.P2^{2})}{(force.P0^{2})}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }31, \text{ with column order } \left(P0,P1,P5,P3,P4,P2,P6\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(muDimension.P2^{2})}{(force.P0^{1})(density.P1^{1})}},\quad\textcolor{DarkGreen}{\dfrac{(force.P0^{1})(nDimension.P4^{2})}{(density.P1^{1})(speed.P3^{4})}},\quad\textcolor{DarkGreen}{\dfrac{(density.P1^{1})(distance.P5^{2})(speed.P3^{2})}{(force.P0^{1})}},\quad\textcolor{DarkGreen}{\dfrac{(force.P0)(acceleration.P6^{2})}{(density.P1^{1})(speed.P3^{6})}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }32, \text{ with column order } \left(P0,P1,P4,P3,P2,P5,P6\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(density.P1^{1})(speed.P3^{4})}{(force.P0)(nDimension.P2^{2})}},\quad\textcolor{DarkGreen}{\dfrac{(density.P1^{1})(distance.P4^{4})(nDimension.P2^{2})}{(force.P0^{1})}},\quad\textcolor{DarkGreen}{\dfrac{(muDimension.P5^{4})}{(force.P0^{2})(density.P1^{2})}},\quad\textcolor{DarkGreen}{\dfrac{(density.P1^{1})(acceleration.P6^{4})}{(force.P0^{1})(nDimension.P2^{6})}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }33, \text{ with column order } \left(P0,P1,P3,P2,P4,P5,P6\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(density.P1^{1})(distance.P3^{2})(speed.P2^{2})}{(force.P0^{1})}},\quad\textcolor{DarkGreen}{\dfrac{(force.P0^{1})(nDimension.P4^{2})}{(density.P1^{1})(speed.P2^{4})}},\quad\textcolor{DarkGreen}{\dfrac{(muDimension.P5^{2})}{(force.P0^{1})(density.P1^{1})}},\quad\textcolor{DarkGreen}{\dfrac{(force.P0)(acceleration.P6^{2})}{(density.P1^{1})(speed.P2^{6})}}\\
        \qquad\qquad\textcolor{DarkSlateGray}{\mathbf{\Pi\text{ group }34, \text{ with column order } \left(P0,P1,P2,P3,P4,P5,P6\right)}} \qquad&\textcolor{DeepSkyBlue}{\dashrightarrow}\qquad\textcolor{DarkGreen}{\dfrac{(density.P1)(distance.P2^{2})(speed.P3^{2})}{(force.P0)}},\quad\textcolor{DarkGreen}{\dfrac{(density.P1)(distance.P2^{4})(nDimension.P4^{2})}{(force.P0)}},\quad\textcolor{DarkGreen}{\dfrac{(muDimension.P5^{2})}{(force.P0)(density.P1)}},\quad\textcolor{DarkGreen}{\dfrac{(density.P1^{2})(distance.P2^{6})(acceleration.P6^{2})}{(force.P0^{2})}}
\end{aligned}
$$
\end{document}

Informational Report:
---------------------
        Constant identifier "kNewtonUnithave_SpeedOfLight"
        Dimension "second" with exponent -1.000000
        Dimension "meter" with exponent 1.000000
        Dimension "kilogram" with exponent 0.000000
        Dimension "mole" with exponent 0.000000
        Dimension "Kelvin" with exponent 0.000000
        Dimension "Coulomb" with exponent 0.000000
        Dimension "concentration" with exponent 0.000000
        Dimension "Relative Humidity" with exponent 0.000000

        Constant identifier "kNewtonUnithave_AccelerationDueToGravity"
        Dimension "second" with exponent -2.000000
        Dimension "meter" with exponent 1.000000
        Dimension "kilogram" with exponent 0.000000
        Dimension "mole" with exponent 0.000000
        Dimension "Kelvin" with exponent 0.000000
        Dimension "Coulomb" with exponent 0.000000
        Dimension "concentration" with exponent 0.000000
        Dimension "Relative Humidity" with exponent 0.000000

        Constant identifier "kNewtonUnithave_GravitationalConstant"
        Dimension "second" with exponent -2.000000
        Dimension "meter" with exponent 3.000000
        Dimension "kilogram" with exponent -1.000000
        Dimension "mole" with exponent 0.000000
        Dimension "Kelvin" with exponent 0.000000
        Dimension "Coulomb" with exponent 0.000000
        Dimension "concentration" with exponent 0.000000
        Dimension "Relative Humidity" with exponent 0.000000

        Constant identifier "kNewtonUnithave_AvogadroConstant"
        Dimension "second" with exponent 0.000000
        Dimension "meter" with exponent 0.000000
        Dimension "kilogram" with exponent 0.000000
        Dimension "mole" with exponent 1.000000
        Dimension "Kelvin" with exponent 0.000000
        Dimension "Coulomb" with exponent 0.000000
        Dimension "concentration" with exponent 0.000000
        Dimension "Relative Humidity" with exponent 0.000000

        Constant identifier "kNewtonUnithave_BoltzmannConstant"
        Dimension "second" with exponent -2.000000
        Dimension "meter" with exponent 2.000000
        Dimension "kilogram" with exponent 1.000000
        Dimension "mole" with exponent 0.000000
        Dimension "Kelvin" with exponent 1.000000
        Dimension "Coulomb" with exponent 0.000000
        Dimension "concentration" with exponent 0.000000
        Dimension "Relative Humidity" with exponent 0.000000

        Constant identifier "kNewtonUnithave_ElectronCharge"
        Dimension "second" with exponent 0.000000
        Dimension "meter" with exponent 0.000000
        Dimension "kilogram" with exponent 0.000000
        Dimension "mole" with exponent 0.000000
        Dimension "Kelvin" with exponent 0.000000
        Dimension "Coulomb" with exponent 1.000000
        Dimension "concentration" with exponent 0.000000
        Dimension "Relative Humidity" with exponent 0.000000

        Constant identifier "kNewtonUnithave_SpeedOfSound"
        Dimension "second" with exponent -1.000000
        Dimension "meter" with exponent 1.000000
        Dimension "kilogram" with exponent 0.000000
        Dimension "mole" with exponent 0.000000
        Dimension "Kelvin" with exponent 0.000000
        Dimension "Coulomb" with exponent 0.000000
        Dimension "concentration" with exponent 0.000000
        Dimension "Relative Humidity" with exponent 0.000000

        Constant identifier "kNewtonUnithave_EarthMass"
        Dimension "second" with exponent 0.000000
        Dimension "meter" with exponent 0.000000
        Dimension "kilogram" with exponent 1.000000
        Dimension "mole" with exponent 0.000000
        Dimension "Kelvin" with exponent 0.000000
        Dimension "Coulomb" with exponent 0.000000
        Dimension "concentration" with exponent 0.000000
        Dimension "Relative Humidity" with exponent 0.000000

Dimensional matrix for invariant "BuckinghamPaperFirstExampleForPiGroups":

        Parameter name mapping (autogenerated for shorter column headings):

        force --> P0
        density --> P1
        distance --> P2
        speed --> P3
        nDimension --> P4
        muDimension --> P5
        acceleration --> P6

                        P0 P1 P2 P3 P4 P5 P6 
        second          -2  0  0 -1 -1 -1 -2 
        meter            1 -3  1  1  0 -1  1 
        kilogram         1  1  0  0  0  1  0 

The pdf rendered from the LateX is below:
Buckingham_pi.pdf

It seems that this produces the expected output? Furthermore, the number of Pi groups generated here is different to the output of the CGI interface.