lowestTermValuation -- The valuation defined by lowest terms

Usage:

v = lowestTermValuation
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 lowest term valuation

Description

This function builds a valuation which returns the 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 : vR = lowestTermValuation R;

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

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

i5 : vR f

o5 = | 1 |
     | 0 |
     | 3 |

o5 : Ordered QQ^3 module

i6 : vR f < vR g

o6 = false

i7 : S = QQ[a,b,c, MonomialOrder => RevLex, Global => false];

i8 : vS = lowestTermValuation S;

i9 : f = 13*a^2*b + a*c^3;

i10 : g = 5*a^2*c + b^3;

i11 : vS f

o11 = | 2 |
      | 1 |
      | 0 |

o11 : Ordered QQ^3 module

i12 : vS f < vS g

o12 = true

Ways to use lowestTermValuation:

lowestTermValuation(PolynomialRing)

For the programmer

The object lowestTermValuation is a method function.

The source of this document is in Valuations.m2:568:0.

lowestTermValuation -- The valuation defined by lowest terms

Description

See also

Ways to use lowestTermValuation:

For the programmer