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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 | )abbrev category DIVCAT DivisorCategory
++ Authors: Gaetan Hache
++ Date Created: may 1997
++ Date Last Updated: April 2010, by Tim Daly
++ Description: This category exports the function for domains
DivisorCategory(S) : Category == SIG where
S : SetCategory
INT ==> Integer
BOOLEAN ==> Boolean
LIST ==> List
AB ==> AbelianGroup
MI ==> Module(Integer)
FAMC ==> FreeAbelianMonoidCategory(S,Integer)
SIG ==> Join(AB,MI,FAMC) with
degree : % -> INT
++ degree(d) returns the degree of the divisor d
split : % -> List %
++ split(d) splits the divisor d. For example,
++ \spad{split( 2 p1 + 3p2 )} returns the list \spad{[ 2 p1, 3 p2 ]}.
"<=" : (%,%) -> BOOLEAN
collect : % -> %
++ collect collects the duplicative points in the divisor.
concat : (%,%) -> %
++ concat(a,b) concats the divisor a and b
++ without collecting the duplicative points.
effective? : % -> BOOLEAN
++ effective?(d) returns true if d >= 0.
supp: % -> LIST(S)
++ supp(d) returns the support of the divisor d.
suppOfZero : % -> LIST(S)
++ suppOfZero(d) returns the elements of the support of d that
++ have a positive coefficient.
suppOfPole : % -> LIST(S)
++ suppOfPole(d) returns the elements of the support of d that
++ have a negative coefficient.
divOfZero : % -> %
++ divOfZero(d) returns the positive part of d.
divOfPole : % -> %
++ divOfPole(d) returns the negative part of d.
incr : % -> %
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