lowestTermValuation -- The valuation defined by lowest terms

Synopsis

• 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

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

See also

• valuation -- User-defined valuation object
• Valuation -- The type of all valuations
• leadTermValuation -- The valuation defined by leading terms
• localRingValuation -- The valuation defined by a local ring.
• padicValuation -- The p-adic valuation
• trivialValuation -- The trivial valuation