LT

the leading term of an object

Syntax

LT(I: RINGELEM):   RINGELEM
LT(I: IDEAL):      IDEAL
LT(I: MODULEELEM): MODULEELEM
LT(I: MODULE):     MODULE

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-x*z);
y^2

/**/  Use R ::= QQ[x,y,z], Lex;
/**/  LT(y^2-x*z);
x*z

If E is a MODULEELEM, LT(E) gives the leading term of E with respect to the module term-ordering of E . For the leading monomial, which includes the coefficient, use LM .

Example

/**/  R3 := NewFreeModule(R,3);
/**/  LT(ModuleElem(R3, [0, x, y^2]));
[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