CoCoA:Elim

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 <command>
   <title>Elim</title>
   <short_description>eliminate variables</short_description>
   <description>

This function returns the ideal or module obtained by eliminating the indeterminates X from M. The coefficient ring needs to be a field. <par/> As opposed to this function, there is also the *modifier*, Elim, used when constructing a ring (see <ttref>Orderings</ttref> and <ref>Predefined Term-Orderings</ref>).

<example>

 Use R ::= Q[t,x,y,z];
 Set Indentation;
 Elim(t,Ideal(t^15+t^6+t-x,t^5-y,t^3-z));

Ideal(

 -z^5 + y^3,
 -y^4 - yz^2 + xy - z^2,
 -xy^3z - y^2z^3 - xz^3 + x^2z - y^2 - y,
 -y^2z^4 - x^2y^3 - xy^2z^2 - yz^4 - x^2z^2 + x^3 - y^2z - 2yz - z,
 -y^3z^3 + xz^3 - y^3 - y^2)

 Use R ::= Q[t,s,x,y,z,w];
 t..x;

[t, s, x]


 Elim(t..x,Ideal(t-x^2zw,x^2-t,y^2t-w)); -- Note the use of t..x.

Ideal(-zw^2 + w)


 Use R ::= Q[t[1..2],x[1..4]];
 I := Ideal(x[1]-t[1]^4,x[2]-t[1]^2t[2],x[3]-t[1]t[2]^3,x[4]-t[2]^4);
 t;

[t[1], t[2]]


 Elim(t,I);                         -- Note the use t.

Ideal(x[3]^4 - x[1]x[4]^3, x[2]^4 - x[1]^2x[4])


</example>

   </description>
   <syntax>

Elim(X:INDETS,M:IDEAL):IDEAL Elim(X:INDETS,M:MODULE):MODULE

where X is an indeterminate or a list of indeterminates. </syntax>

   <see>Orderings</see>
   <see>Predefined Term-Orderings</see>
   <type>groebner</type>
   <type>groebner-basic</type>
   <type>ideal</type>
   <type>module</type>
   <key>elim</key>
   <key>elimination</key>
 </command>