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# `linopt`::`Transparent`

Return the ordinary simplex tableau of a linear program

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## Syntax

```linopt::Transparent(`[constr, obj, <NonNegative>, <seti>]`)
linopt::Transparent(`[constr, obj, <NonNegative>, <All>]`)
linopt::Transparent(`[constr, obj, <setn>, <seti>]`)
linopt::Transparent(`[constr, obj, <setn>, <All>]`)
```

## Description

`linopt::Transparent([constr, obj])` returns the ordinary simplex tableau of the given linear program given by the constraints `constr` and the linear objective function `obj`.

[`constr`, `obj`] is a Linear Optimization Problem of the same structure like in `linopt::maximize`. As the result the ordinary simplex tableau of the given problem is returned; this means that equations will be replaced by two unequations and unbounded variables will be replaced by two new variables.

Internally the tableau returned consists of more information than viewable on the screen. Therefore `linopt::Transparent::convert` is provided to perform the transduction into the structure of the screen-tableau. (This can be necessary if the returned tableau shall serve as an input-parameter for another function — e.g. a user defined procedure for the selection of pivot elements.) If an ordinary simplex with two phases is wished, the next step should be the call of `linopt::Transparent::phaseI_tableau`.

All functions of the linopt library using the tableau returned by `linopt::Transparent` try to minimize the problem! Therefore it can be necessary to multiply the objective function with -1 first.

In the simplex tableau returned a special notation is used. "linopt" stands for the tableau them self, "obj" describes the linear objective function, "restr" stands for the vector of restrictions, slk, slk, ... are the slack variables and the names of the other variables stand for themselves. Variables which are given as row labels indicate that they are part of the base.

## Examples

### Example 1

First a small example, returning the ordinary simplex tableau of the given linear program. One can see that the slack variables are forming the basis:

```k := [{x + y >= -1, x + y <= 3}, x + 2*y, NonNegative]: linopt::Transparent(k)```
` `

It follows a little bit larger example:

```k := [{3*x + 4*y - 3*z <= 23, 5*x - 4*y - 3*z <= 10, 7*x + 4*y + 11*z <= 30}, -x + y + 2*z, NonNegative]: linopt::Transparent(k)```
` `

The result of `linopt::Transparent` is of domain type `linopt::Transparent`. So it can be used as input for other `linopt::Transparent::*` function, e.g. for `linopt::Transparent::suggest`:

```k := [{x + y >= -1, x + y <= 3}, x + 2*y, NonNegative]: t := linopt::Transparent(k): domtype(t), linopt::Transparent::suggest(t)```
` `
`delete k, t:`

## Parameters

 `constr` A set or list of linear constraints `obj` A linear expression `seti` A set which contains identifiers interpreted as indeterminates `setn` A set which contains identifiers interpreted as indeterminates

## Options

 `All` All variables are constrained to be integer `NonNegative` All variables are constrained to be nonnegative

## Return Values

Simplex tableau of domain type `linopt::Transparent`.

## References

Papadimitriou, Christos H; Steiglitz, Kenneth: Combinatorial Optimization; Algorithms and Complexity. Prentice-Hall, 1982.

Nemhauser, George L; Wolsey, Laurence A: Integer and Combinatorial Optimization. New York, Wiley, 1988.

Salkin, Harvey M; Mathur, Kamlesh: Foundations of Integer Programming. North-Holland, 1989.

Neumann, Klaus; Morlock, Martin: Operations-Research. Munich, Hanser, 1993.

Duerr, Walter; Kleibohm, Klaus: Operations Research; Lineare Modelle und ihre Anwendungen. Munich, Hanser, 1992.

Suhl, Uwe H: MOPS - Mathematical OPtimization System. European Journal of Operational Research 72(1994)312-322. North-Holland, 1994.

Suhl, Uwe H; Szymanski, Ralf: Supernode Processing of Mixed Integer Models. Boston, Kluwer Academic Publishers, 1994.

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