valuation -- User-defined valuation object

Synopsis

Usage:

v = valuation(f)

v = valuation(f, S, T)
Inputs:
- f, a function, the valuation function.
- S, a ring, a local ring, or an instance of the type Subring, the source
- T, a ring, a local ring, or an instance of the type Subring, the target
Outputs:
- v, an instance of the type Valuation, user-defined valuation function

Description

Construct a user defined valuation function. User-defined functions are not checked for satisfying the properties of a valuation. It is not necessary to specify a source or target, but if they are provided, then the input is checked to be in the source (or either promotable to the source or in the fraction field of the source). For common use cases, it is suggested to use the provided valuations.

i1 : v = valuation(x -> if x == 0 then infinity else 0)

o1 = valuation with unspecified source and target

o1 : Valuation

i2 : v = valuation(x -> if x == 0 then infinity else 0, ZZ, ZZ)

o2 = valuation from ZZ to ZZ

o2 : Valuation

Ways to use valuation :

valuation(Function)
valuation(Function,LocalRing,LocalRing)
valuation(Function,LocalRing,OrderedQQn)
valuation(Function,LocalRing,Ring)
valuation(Function,LocalRing,RingOfInvariants)
valuation(Function,LocalRing,Subring)
valuation(Function,Ring,LocalRing)
valuation(Function,Ring,OrderedQQn)
valuation(Function,Ring,Ring)
valuation(Function,Ring,RingOfInvariants)
valuation(Function,Ring,Subring)
valuation(Function,RingOfInvariants,LocalRing)
valuation(Function,RingOfInvariants,OrderedQQn)
valuation(Function,RingOfInvariants,Ring)
valuation(Function,RingOfInvariants,RingOfInvariants)
valuation(Function,RingOfInvariants,Subring)
valuation(Function,Subring,LocalRing)
valuation(Function,Subring,OrderedQQn)
valuation(Function,Subring,Ring)
valuation(Function,Subring,RingOfInvariants)
valuation(Function,Subring,Subring)

For the programmer

The object valuation is a method function.

valuation -- User-defined valuation object

Synopsis

Description

See also

Ways to use valuation :

For the programmer