up previous next

2.2.15 Substitutions

To substitute a list of numbers or polynomials for the indeterminates (in the order specified by the definition of the ring), one may use the function Eval. To substitute out of order, use the function Subst.

example

    
Use R ::= Q[x,y,z];
F := x^2+y^2+z^2;
Eval(F,[1]);  -- substitute x=1
y^2 + z^2 + 1
-------------------------------
Eval(F,[1,2,3]);  -- substitute x=1, y=2, z=3
14
-------------------------------
Subst(F,y,2);  -- substitute y=2
x^2 + z^2 + 4
-------------------------------
Eval(F,[x,2,z]); -- same as above
x^2 + z^2 + 4
-------------------------------
Subst(F,[[y,y^2],[z,z^2]]);  -- substitute y^2 for y, z^2 for z
y^4 + z^4 + x^2
-------------------------------
Eval(Ideal(F),[x^2,z]); -- substitute x^2 for x, z for y
Ideal(x^4 + 2z^2)
-------------------------------