diff options
Diffstat (limited to 'src/algebra/free.spad.pamphlet')
| -rw-r--r-- | src/algebra/free.spad.pamphlet | 42 |
1 files changed, 21 insertions, 21 deletions
diff --git a/src/algebra/free.spad.pamphlet b/src/algebra/free.spad.pamphlet index 25f04f87..90588505 100644 --- a/src/algebra/free.spad.pamphlet +++ b/src/algebra/free.spad.pamphlet @@ -55,7 +55,7 @@ ListMonoidOps(S, E, un): Exports == Implementation where ++ reverse(l) reverses the list of monomials forming l. This ++ has some effect if the monoid is non-abelian, i.e. ++ \spad{reverse(a1\^e1 ... an\^en) = an\^en ... a1\^e1} which is different. - reverse_! : $ -> $ + reverse! : $ -> $ ++ reverse!(l) reverses the list of monomials forming l, destroying ++ the element l. size : $ -> NonNegativeInteger @@ -102,14 +102,14 @@ ListMonoidOps(S, E, un): Exports == Implementation where nthExpon(f, i) == f.(i-1+minIndex f).exp nthFactor(f, i) == f.(i-1+minIndex f).gen reverse l == reverse(l)$Rep - reverse_! l == reverse_!(l)$Rep + reverse! l == reverse!(l)$Rep mapGen(f, l) == [[f(x.gen), x.exp] for x in l] mapExpon(f, l) == ans:List(REC) := empty() for x in l repeat if (a := f(x.exp)) ~= 0 then ans := concat([x.gen, a], ans) - reverse_! ans + reverse! ans outputForm(l, op, opexp, id) == empty? l => id::OutputForm @@ -123,7 +123,7 @@ ListMonoidOps(S, E, un): Exports == Implementation where rightMult(f, s) == empty? f => s::$ - s = f.last.gen => (setlast_!(h := copy f, [s, f.last.exp + un]); h) + s = f.last.gen => (setlast!(h := copy f, [s, f.last.exp + un]); h) concat(f, [s, un]) leftMult(s, f) == @@ -137,7 +137,7 @@ ListMonoidOps(S, E, un): Exports == Implementation where if not member?(t1,s2) then return false true - plus_!(s:S, n:E, f:$):$ == + plus!(s:S, n:E, f:$):$ == h := g := concat([s, n], f) h1 := rest h while not empty? h1 repeat @@ -145,13 +145,13 @@ ListMonoidOps(S, E, un): Exports == Implementation where l := zero?(m := n + h1.first.exp) => rest h1 concat([s, m], rest h1) - setrest_!(h, l) + setrest!(h, l) return rest g h := h1 h1 := rest h1 g - plus(s, n, f) == plus_!(s,n,copy f) + plus(s, n, f) == plus!(s,n,copy f) plus(f, g) == #f < #g => localplus(f, g) @@ -229,7 +229,7 @@ FreeMonoid(S: SetCategory): FMcategory == FMdefinition where 1 == makeUnit() one? f == empty? listOfMonoms f coerce(f:$): Ex == outputForm(f, "*", "**", 1) - hcrf(f, g) == reverse_! hclf(reverse f, reverse g) + hcrf(f, g) == reverse! hclf(reverse f, reverse g) f:$ * s:S == rightMult(f, s) s:S * f:$ == leftMult(s, f) factors f == copy listOfMonoms f @@ -243,7 +243,7 @@ FreeMonoid(S: SetCategory): FMcategory == FMdefinition where lg := listOfMonoms g ls := last(lf := listOfMonoms f) ls.gen = lg.first.gen => - setlast_!(h := copy lf,[lg.first.gen,lg.first.exp+ls.exp]) + setlast!(h := copy lf,[lg.first.gen,lg.first.exp+ls.exp]) makeMulti concat(h, rest lg) makeMulti concat(lf, lg) @@ -264,13 +264,13 @@ FreeMonoid(S: SetCategory): FMcategory == FMdefinition where if (ru:= lquo(makeMulti rest lar, makeMulti rest lla)) case $ then if lla.first.exp > lar.first.exp then - l := concat_!(l, [lla.first.gen, + l := concat!(l, [lla.first.gen, (lla.first.exp - lar.first.exp)::NNI]) m := concat([lla.first.gen, lar.first.exp], rest lla) else m := lla return [makeMulti l, makeMulti m, ru::$] - l := concat_!(l, lla.first) + l := concat!(l, lla.first) lla := rest lla [makeMulti la0, 1, makeMulti lar] @@ -286,10 +286,10 @@ FreeMonoid(S: SetCategory): FMcategory == FMdefinition where -- Now match tail. (q:=lquo(makeMulti rest llar,makeMulti rest la))case $ => if llar.first.exp > la.first.exp then - l := concat_!(l, [la.first.gen, + l := concat!(l, [la.first.gen, (llar.first.exp - la.first.exp)::NNI]) return [makeMulti l, q::$] - l := concat_!(l, first llar) + l := concat!(l, first llar) llar := rest llar Nlar := Nlar - 1 "failed" @@ -298,7 +298,7 @@ FreeMonoid(S: SetCategory): FMcategory == FMdefinition where h:List(REC) := empty() for f0 in listOfMonoms f for g0 in listOfMonoms g repeat f0.gen ~= g0.gen => return makeMulti h - h := concat_!(h, [f0.gen, min(f0.exp, g0.exp)]) + h := concat!(h, [f0.gen, min(f0.exp, g0.exp)]) f0.exp ~= g0.exp => return makeMulti h makeMulti h @@ -308,13 +308,13 @@ FreeMonoid(S: SetCategory): FMcategory == FMdefinition where a0.gen ~= laq.first.gen or a0.exp > laq.first.exp => return "failed" if a0.exp = laq.first.exp then laq := rest laq - else setfirst_!(laq, [laq.first.gen, + else setfirst!(laq, [laq.first.gen, (laq.first.exp - a0.exp)::NNI]) makeMulti laq rquo(qa, a) == (u := lquo(reverse qa, reverse a)) case "failed" => "failed" - reverse_!(u::$) + reverse!(u::$) if S has OrderedSet then a < b == @@ -381,7 +381,7 @@ FreeGroup(S: SetCategory): Join(Group, RetractableTo S) with s:S ** n:Integer == makeTerm(s, n) f:$ * s:S == rightMult(f, s) s:S * f:$ == leftMult(s, f) - inv f == reverse_! mapExpon("-", f) + inv f == reverse! mapExpon("-", f) factors f == copy listOfMonoms f mapExpon(f, x) == mapExpon(f, x)$Rep mapGen(f, x) == mapGen(f, x)$Rep @@ -397,12 +397,12 @@ FreeGroup(S: SetCategory): Join(Group, RetractableTo S) with r := rest r q := rest q empty? r => makeMulti q - empty? q => makeMulti reverse_! r + empty? q => makeMulti reverse! r r.first.gen = q.first.gen => - setlast_!(h := reverse_! r, + setlast!(h := reverse! r, [q.first.gen, q.first.exp + r.first.exp]) - makeMulti concat_!(h, rest q) - makeMulti concat_!(reverse_! r, q) + makeMulti concat!(h, rest q) + makeMulti concat!(reverse! r, q) @ \section{category FAMONC FreeAbelianMonoidCategory} |