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 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) ```