LT

the leading term of an object

Syntax


LT(E):same type as E

where E has type IDEAL, MODULE, POLY, or VECTOR.

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 LM .

Example

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

Example

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

See Also