CoCoA:LT

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 <command>
   <title>LT</title>
   <short_description>the leading term of an object</short_description>
   <description>

If E is a polynomial this function returns the leading term of the polynomial E with respect to the term-ordering of the polynomial ring of E. For the leading monomial, which includes the coefficient, use <ttref>LM</ttref>.

<example>

 Use R ::= Q[x,y,z];  -- the default term-ordering is DegRevLex
 LT(y^2-xz);

y^2


 Use R ::= Q[x,y,z], Lex;
 LT(y^2-xz);

xz


</example>

If E is a vector, LT(E) gives the leading term of E with respect to the module term-ordering of the polynomial ring of E. For the leading monomial, which includes the coefficient, use <ttref>LM</ttref>.

<example>

 Use R ::= Q[x,y];
 V := Vector(0,x,y^2);
 LT(V); -- the leading term of V w.r.t. the default term-ordering, ToPos

Vector(0, 0, y^2)


 Use R ::= Q[x,y], PosTo;
 V := Vector(0,x,y^2);
 LT(V); -- the leading term of V w.r.t. PosTo

Vector(0, x, 0)


</example>

If E is an ideal or module, LT(E) returns the ideal or module generated by the leading terms of all elements of E, sometimes called the initial ideal or module.

<example>

 Use R ::= Q[x,y,z];
 I := Ideal(x-y,x-z^2);
 LT(I);

Ideal(x, z^2)


</example>

   </description>
   <syntax>

LT(E):same type as E

where E has type IDEAL, MODULE, POLY, or VECTOR. </syntax>

   <see>LC</see>
   <see>LM</see>
   <see>LPP</see>
   <see>Module Orderings</see>
   <see>Orderings</see>
   <see>GBasis5, and more</see>
   <type>ideal</type>
   <type>module</type>
   <type>polynomial</type>
   <type>vector</type>
   <type>cocoaserver</type>
   <key>leading term</key>
   <key>lt</key>
 </command>