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# linearize(?Expression, -Linear, -Residue)

Split and arithmetic expression into linear and nonlinear parts
*Expression*
- Arithmetic expression with constants and variables
*Linear*
- Normalized lists of monomials
*Residue*
- Residual nonlinear components in the form AuxVar=Expr

## Description

The linear component of expression is normalised into a list
(sum) of monomials of the form
[C0*1, C1*X1, C2*X2, ...]

where Ci are numbers and Xi are distinct variables.
The first (constant) term is always present, Ci (i>=1) are nonzero.
linearize/3 converts a general arithmetic expression into a
normalised linear form. The nonlinear parts are extracted using
auxiliary variables, and returned as Residue, which is a list of
Aux=NonLinExpr constraints.

linearize/3 understands all arithmetic expressions plus

lin(Lin)

where Lin is an already normalised linear expression. All variables
within Expression (which are free at linearization time) are taken
to be numerical variables. If you intend to have variables which can
be bound to symbolic expressions rather than numbers, they must be
wrapped into an eval/1 functor.
### Modules

This predicate is sensitive to its module context (tool predicate, see @/2).
## Examples

?- linearize(3*X-7*Y+2*(X+Y), L, R).
X = X
Y = Y
L = [0 * 1, 5 * X, -5 * Y]
R = []
yes.
?- linearize(12*3, L, R).
L = [36 * 1]
R = []
yes.
?- linearize(X*(3+7*Y)-X, L, R).
Y = Y
X = X
L = [0 * 1, 1 * _308, 2 * X]
R = [_308 = X * (7 * Y)]
yes.

## See Also

polynorm / 3, linrenorm / 2, delinearize / 2