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5.1.115 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 rule given as the second argument. The simplification rules are the sum of the following functions:
1
normalize (make leading coefficients 1).
2
erase zero generators/columns.
4
keep only the first one of identical generators/columns.
8
keep only the first one of generators/columns which differ only by a factor in the ground field.
16
keep only those generators/columns whose leading monomials differ.
32
keep only those generators/columns whose leading monomials are not divisible by other ones.
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]=4x
==> _[4]=3x+y
==> _[5]=5x2
simplify(i,8);
==> _[1]=0
==> _[2]=2x
==> _[3]=3x+y
==> _[4]=5x2
simplify(i,16);
==> _[1]=0
==> _[2]=2x
==> _[3]=5x2
simplify(i,32);
==> _[1]=0
==> _[2]=2x
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.

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