(old draft mail but I will have to resurrect it)
Hello,
I need to implement the function in a Julia object but I'm not sure
how FriCAS implemented it,
or, at least conceptually, how it should be implemented.
>From the description FiniteAbelianMonoidRing where it is declared:
++ Description: This category is
++ similar to AbelianMonoidRing, except that the sum is assumed to be finite.
++ It is a useful model for polynomials,
++ but is somewhat more general.
The only documentation of this function is:
minimumDegree : % -> E
++ minimumDegree(p) gives the least exponent of a non-zero term
of polynomial p.
But, here is an interpreter session:
(10) -> ppp :MPOLY(['x,'y],INT):=x^7*y^3+3*x^17+y^11
17 3 7 11
(10) 3 x + y x + y
Type: MultivariatePolynomial([x,y],Integer)
(11) -> minimumDegree %
11
(11) y
Type: IndexedExponents(OrderedVariableList([x,y]))
(12) -> pp:=x^7*y^3+3*x^17+y^11
11 7 3 17
(12) y + x y + 3 x
Type: Polynomial(Integer)
(13) -> minimumDegree %
17
(13) x
Type: IndexedExponents(Symbol)
So, the documentation should be more precise, no?, variable ordering
(?) to choose a variable (?) or ?
Any thoughts? How should I code it? I have a vector of (term,
exponent) or a listOfTerms.
(19) -> pp:=x^7*y^3+3*x^17+y^11
(19) 3*x^17 + x^7*y^3 + y^11
Type: NemoMultivariatePolynomial(NemoRational,[x,y,z],:lex)
(20) -> jlApply("collect", jlApply("terms",pp))
(20)
3-element Vector{QQMPolyRingElem}:
3*x^17
x^7*y^3
y^11
Type: JuliaObject
(21) -> listOfTerms pp
17 7 3 11
(21) [[k = x , c = 3], [k = x y , c = 1], [k = y , c = 1]]
Type: List(Record(k: IndexedExponents(OrderedVariableList([x,y,z])),c:
NemoRational))
And if I change the ordering of MPOLY,
(22) -> ppp :MPOLY(['yy,'xx],INT):=xx^7*yy^3+3*xx^17+yy^11
11 7 3 17
(22) yy + xx yy + 3 xx
Type: MultivariatePolynomial([yy,xx],Integer)
(23) -> minimumDegree %
17
(23) xx
- Greg
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