CoCoA:Subst

Subst

substitute values for indeterminates

Description

The first form of this function substitutes F_i for X_i in the

expression E. The second form is a shorthand for the first in the

case of a single indeterminate. When substituting for the indeterminates in order, it is easier to use <ttref>Eval</ttref>.

Example

  Use R ::= Q[x,y,z,t];
  F := x+y+z+t^2;
  Subst(F,x,-2);
t^2 + y + z - 2
-------------------------------
  Subst(F,x,z/y);
(yt^2 + y^2 + yz + z)/y
-------------------------------
  Subst(F,[[x,x^2],[y,y^3],[z,t^5]]);
t^5 + y^3 + x^2 + t^2
-------------------------------
  Eval(F,[x^2,y^3,t^5]); -- the same thing as above
t^5 + y^3 + x^2 + t^2
-------------------------------
  MySubst := [[y,1],[t,3z-x]];
  Subst(xyzt,MySubst);  -- substitute into the function xyzt
-x^2z + 3xz^2
-------------------------------

Syntax

Subst(E:OBJECT,X,F):OBJECT
Subst(E:OBJECT,[[X_1,F_1],...,[X_r,F_r]]):OBJECT

where each X or X_i is an indeterminate and each F or F_i is a number,
polynomial, or rational function.

Eval

Evaluation of Polynomials

Image

QZP

ZPQ

Substitutions

   <type>polynomial</type>
   <type>ratfun</type>