leadTermValuation -- The valuation defined by leading terms

Synopsis

Usage:

v = leadTermValuation R
Inputs:
- R, a polynomial ring, the ring whose term order is used to define the valuation
Outputs:
- v, an instance of the type Valuation, the lead term valuation

Description

This function constructs a valuation which returns the negative exponent vector of the lead term of a polynomial with respect to the ring's term order. The valuation returns vectors in an ordered $\QQ$-module, which respects the monomial order of the PolynomialRing. For more details see Ordered modules.

i1 : R = QQ[a,b,c, MonomialOrder => Lex];

i2 : v = leadTermValuation R;

i3 : f = 13*a^2*b + a*c^3;

i4 : g = 5*a^2*c + b^3;

i5 : v f

o5 = | -2 |
     | -1 |
     |  0 |

o5 : Ordered QQ^3 module

i6 : v g

o6 = | -2 |
     |  0 |
     | -1 |

o6 : Ordered QQ^3 module

i7 : v f < v g

o7 = true

Ways to use leadTermValuation :

leadTermValuation(PolynomialRing)

For the programmer

The object leadTermValuation is a method function.

leadTermValuation -- The valuation defined by leading terms

Synopsis

Description

See also

Ways to use leadTermValuation :

For the programmer