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5.1.115 simplify
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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
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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:
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1 normalize (make leading coefficients 1).
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2 erase zero generators/columns.
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4 keep only the first one of identical generators/columns.
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8 keep only the first one of generators/columns which differ only by a factor in the ground field.
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16 keep only those generators/columns whose leading monomials differ.
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32 keep only those generators/columns whose leading monomials are not divisible by other ones.
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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]