## table of contents

redund|minrep(1) | lrslib 7.3 | redund|minrep(1) |

## Name¶

redund|minrep - Remove redundant inequalities from an
H-representation or redundant vertices (non-extreme points) from a
V-representation. **minrep** also identifies hidden linearities.

## Synopsis¶

**redund** *[input-file] [output-file]*

**minrep** *[input-file] [output-file]*

**mpirun** -np [procs] **mplrs
-minrep** *[input-file] [output-file] [option...]*

## Description¶

**redund** and **minrep** are aliases to **lrs** which is
part of the C library **lrslib(5)**. This functionality can also be
performed by **lrs** directly by using the options described below. All
computations are done in exact arithmetic. For input file descriptions see
**lrs(1)**. A parallel version of **minrep** is given by **mplrs
-minrep**. The **-redund** option performs the same function and is
retained for legacy. (see **mplrs(1)**)

*redund*

*H-representation:* redundant inequalities in an input H-representation
are removed and the remaining inequalities output. Hidden linearities are
not detected unless the **testlin** option is included, in which case the
output is a minimum representation and the dimension is reported.

*V-representation:* outputs all extreme points and extreme rays, often
called the *convex hull* problem. The **testlin** option cause
linearities to be detected and explicitly output.

Outputs can be piped directly into *lrs*. *redund* is a link to
*lrs* which can also perform these functions via the **testlin**,
**redund** and **redund_list** options. **mplrs -redund** always
sets the **testlin** option, so always produces minimum
representations.

*minrep*

Equivalent to **redund** with the **testlin** option.

With no options minrep|redund will process the entire input file.

**redund start end **

Check input lines with line numbers from start to end and remove any redundant
lines.

**redund 0 0** will check all input lines.

**redund_list k i_1 i_2 ... i_k**

Check the k input line numbers with indices i_1 i_2 ... i_k and remove any
redundant lines.

**testlin** **(before the begin line only)** (new 7.3)

*redund* An LP test will be made for hidden linearities at the beginning
of the run and is reported. If there are no hidden linearities one LP per
constraint tests for redundancy. If hidden linearities exist two LPs per
constraint search for hidden linearities and remove redundancies. In both
cases the run ends with a minimum set of linearities and inequalities (ie.
no hidden inequalities or duplicates) and the dimension is reported.

*lrs* If neither **redund** or **redund_list** options are present
the initial LP test is made, reported and the run halted. Otherwise as above
for *redund*.

*mplrs* This option is ignored. In redund/minrep mode a minimum
representation is always found.

**verbose**

As each input line is checked a message is printed telling its status

*nr :non-redundant

*re :redundant

*sr :strongly redundant

For an H-representation strongly redundant means the feasible region lies in
its open half-space. For a V-representation it means that the point lies in
the (relative) interior of the convex hull.

In addition *minrep* may report

*li :linearity

## Examples¶

(1) Remove hidden linearities and minimum representation of an
H-representation.

% cat cube.ine

H-representation

begin

7 4 rational

0 1 0 0

0 0 1 0

0 0 0 1

1 -1 0 0

1 0 -1 0

1 0 0 -1

-1 0 0 1

end

verbose

% minrep cube.ine

minrep:lrslib_v.7.3_2024.1.10(64bit,lrslong.h,hybrid_arithmetic)

*Input taken from cube.ine

*hidden linearities exist

*finding minimum representation

*nr 0 1 0 0

*nr 0 0 1 0

*sr 0 0 0 1

*nr 1 -1 0 0

*nr 1 0 -1 0

*li 1 0 0 -1

*li-1 0 0 1

*linearity in row=6 removed or in cobasis, independent

*linearity in row=7 dependent, made redundant

H-representation

linearity 1 1

begin

5 4 rational

1 0 0 -1

0 1 0 0

0 0 1 0

1 -1 0 0

1 0 -1 0

end

*input had 7 rows and 4 columns

* 2 redundant row(s) found

3 7

* 1 hidden linearity found

(2) Compute the extreme points of a set of 10 points in R^3

% cat c.ext

V-representation

begin

10 4 rational

1 1 1 1

1 0 1 1

1 1/2 0 1/3

1 1 1 0

1 0 1 0

1 1 0 0

1 0 0 0

1 0 1/3 1/4

1 1 0 1

1 0 0 1

end

% redund c.ext

*redund:lrslib v.7.2 2020.6.8(64bit,lrslong.h,hybrid arithmetic)

*Input taken from c.ext

V-representation

begin

8 4 rational

1 1 1 1

1 0 1 1

1 1 1 0

1 0 1 0

1 1 0 0

1 0 0 0

1 1 0 1

1 0 0 1

end

*Input had 10 rows and 4 columns

* 2 redundant row(s) found:

3 8

## Notes¶

- 1.
- FAQ page

- 2.
- redund: extreme point enumeration and eliminating redundant inequalities

- 3.
- User's guide for lrslib

## Author¶

David Avis <avis at cs dot mcgill dot ca >

## See also¶

**lrs**(1), **mplrs**(1), **lrslib**(5),

2024.1.10 | January 2024 |