### 5.1.141 simplify

`Syntax:`
`simplify (` poly_expression`,` int_expression `)`
`simplify (` vector_expression`,` int_expression `)`
`simplify (` ideal_expression`,` int_expression `)`
`simplify (` module_expression`,` int_expression `)`
`Type:`
the type of the first argument
`Purpose:`
returns the "simplified" first argument depending on the simplification rules specified by the second argument. The simplification rules are the following functions:
`1`
normalize (divide by leading coefficient if this is a unit of the ground field/ring).
`2`
erase zero generators/columns.
`4`
erase copies of earlier listed generators/columns.
`8`
erase generators/columns which a scalar multiples (w.r.t. ground field/ring) of earlier listed generators/columns.
`16`
erase generators/columns whose leading monomials are copies of leading monomials of earlier listed generators/columns such that the coefficients of both leading terms are units in the ground field/ring.
`32`
erase generators/columns whose leading terms are divisible by leading terms of other (not necessarily earlier) listed generators/columns.
`64`
normalize each coefficient of every monomial (of every polynomial)
`Example:`
 ```ring r=0,(x,y,z),(c,dp); ideal i=0,2x,2x,4x,3x+y,5x2; simplify(i,1); ==> _=0 ==> _=x ==> _=x ==> _=x ==> _=x+1/3y ==> _=x2 simplify(i,2); ==> _=2x ==> _=2x ==> _=4x ==> _=3x+y ==> _=5x2 simplify(i,4); ==> _=0 ==> _=2x ==> _=0 ==> _=4x ==> _=3x+y ==> _=5x2 simplify(i,8); ==> _=0 ==> _=2x ==> _=0 ==> _=0 ==> _=3x+y ==> _=5x2 simplify(i,16); ==> _=0 ==> _=2x ==> _=0 ==> _=0 ==> _=0 ==> _=5x2 simplify(i,32); ==> _=0 ==> _=2x ==> _=0 ==> _=0 ==> _=0 ==> _=0 simplify(i,32+2+1); ==> _=x matrix A=x,0,2x,y,0,2y; simplify(A,2+8); // by automatic conversion to module ==> _=[x,y] ```
See ideal; module; poly; vector.

User manual for Singular version 4.3.2, 2023, generated by texi2html.