### 5.1.143 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);
      ==> _[1]=0
      ==> _[2]=x
      ==> _[3]=x
      ==> _[4]=x
      ==> _[5]=x+1/3y
      ==> _[6]=x2
      simplify(i,2);
      ==> _[1]=2x
      ==> _[2]=2x
      ==> _[3]=4x
      ==> _[4]=3x+y
      ==> _[5]=5x2
      simplify(i,4);
      ==> _[1]=0
      ==> _[2]=2x
      ==> _[3]=0
      ==> _[4]=4x
      ==> _[5]=3x+y
      ==> _[6]=5x2
      simplify(i,8);
      ==> _[1]=0
      ==> _[2]=2x
      ==> _[3]=0
      ==> _[4]=0
      ==> _[5]=3x+y
      ==> _[6]=5x2
      simplify(i,16);
      ==> _[1]=0
      ==> _[2]=2x
      ==> _[3]=0
      ==> _[4]=0
      ==> _[5]=0
      ==> _[6]=5x2
      simplify(i,32);
      ==> _[1]=0
      ==> _[2]=2x
      ==> _[3]=0
      ==> _[4]=0
      ==> _[5]=0
      ==> _[6]=0
      simplify(i,32+2+1);
      ==> _[1]=x
      matrix A[2][3]=x,0,2x,y,0,2y;
      simplify(A,2+8); // by automatic conversion to module
      ==> _[1]=[x,y]

See ideal; module; poly; vector.

User manual for Singular version 4.4.1, 2025, generated by texi2html.