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); ==> _[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]