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__Function:__poly_t***poly_assign_variable***(const poly_t**`po`, int`rank`, const pkint_t*`tab`)- This function applies to the polyhedron the linear transformation
*x'_rank := \sum_{i=0}^{dim-1} a_i/d x_i + b/d*with`rank`the rank of the variable (rank 0 corresponding to the first normal variable) and

.`tab`=[d,b,[0],a_0,...,a_{dim-1}]`po`may be minimized in order to obtain its generators. Minimality is then preserved if the transformation is inversible.

__Function:__poly_t***poly_substitute_variable***(const poly_t**`po`, int`rank`, const pkint_t*`tab`)- This function applies to the polyhedron the linear substitution
*x'_rank <- \sum_{i=0}^{dim-1} a_i/d x_i + b/d*with*rank*denoting the rank of the variable (rank 0 corresponding to the first normal variable) and

.`tab`=[d,b,[0],a_0,...,a_{dim-1}]`po`may be minimized in order to obtain its constraints. Minimality is then preserved if the transformation is inversible.

The two following functions are kept for compatibility.
The variable to be assigne or substituted is not denoted by its rank,
but by its index in vectors: we have the relationship ```
index =
rank + polka_dec
```

.

__Function:__poly_t***poly_assign_variable_old***(const poly_t**`po`, int`index`, const pkint_t*`tab`)__Function:__poly_t***poly_substitute_variable_old***(const poly_t**`po`, int`index`, const pkint_t*`tab`)- Same as
`poly_assign_variable`

and`poly_substitute_variable`

, but with*index*denoting the index of the variable in vectors.

__Function:__poly_t***poly_assign_variables***(const poly_t**`po`, const equation_t*`eqn`, size_t`size`)- Computes the image of
`po`by the parallel assignment of`eqn[i].var`

by`eqn[i].expr`

, for`i`between`0`

and`size-1`

. The array`eqn`is supposed to be sorted w.r.t. the field`.var`

. You may use the function`sort_equations`

to ensure this (see``polka.h'`).

__Function:__poly_t***poly_substitute_variables***(const poly_t**`po`, const equation_t*`eqn`, size_t`size`)- Computes the image of
`poly`by the parallel substitution of`eqn[i].expr`

by`eqn[i].expr`

, for`i`between`0`

and`size-1`

. The array`eqn`is supposed to be sorted w.r.t. the field`.var`

. You may use the function`sort_equations`

to ensure this (see``polka.h'`).

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