CoCoA:LT
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LT
the leading term of an object
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 -------------------------------
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) -------------------------------
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) -------------------------------
Syntax
LT(E):same type as E where E has type IDEAL, MODULE, POLY, or VECTOR.
<type>ideal</type> <type>module</type> <type>polynomial</type> <type>vector</type> <type>cocoaserver</type>
