diff options
Diffstat (limited to 'src/algebra')
| -rw-r--r-- | src/algebra/fraction.spad.pamphlet | 55 |
1 files changed, 30 insertions, 25 deletions
diff --git a/src/algebra/fraction.spad.pamphlet b/src/algebra/fraction.spad.pamphlet index f7d5d6e0..b16b4f77 100644 --- a/src/algebra/fraction.spad.pamphlet +++ b/src/algebra/fraction.spad.pamphlet @@ -38,41 +38,46 @@ Localize(M:Module R, ++ denom x returns the denominator of x. == add - --representation - Rep:= Record(num:M,den:S) - --declarations + Rep == Record(num:M,den:S) x,y: % n: Integer m: M r: R d: S - --definitions - 0 == [0,1] - zero? x == zero? (x.num) - -x== [-x.num,x.den] - x=y == y.den*x.num = x.den*y.num - before?(x,y) == before?(y.den*x.num, x.den*y.num) - numer x == x.num - denom x == x.den + 0 == per [0,1] + zero? x == zero? rep(x).num + -x == + per [-rep(x).num,rep(x).den] + x=y == + rep(y).den*rep(x).num = rep(x).den*rep(y).num + before?(x,y) == + before?(rep(y).den*rep(x).num, rep(x).den*rep(y).num) + numer x == rep(x).num + denom x == rep(x).den if M has OrderedAbelianGroup then x < y == --- if y.den::R < 0 then (x,y):=(y,x) --- if x.den::R < 0 then (x,y):=(y,x) - y.den*x.num < x.den*y.num - x+y == [y.den*x.num+x.den*y.num, x.den*y.den] - n*x == [n*x.num,x.den] - r*x == if r=x.den then [x.num,1] else [r*x.num,x.den] + rep(y).den*rep(x).num < rep(x).den*rep(y).num + x+y == + per [rep(y).den*rep(x).num+rep(x).den*rep(y).num, rep(x).den*rep(y).den] + n*x == + per [n*rep(x).num,rep(x).den] + r*x == + r=rep(x).den => per [rep(x).num,1] + per [r*rep(x).num,rep(x).den] x/d == - zero?(u:S:=d*x.den) => error "division by zero" - [x.num,u] - m/d == if zero? d then error "division by zero" else [m,d] + u: S := d*rep(x).den + zero? u => error "division by zero" + per [rep(x).num,u] + m/d == + zero? d => error "division by zero" + per [m,d] coerce(x:%):OutputForm == - one?(xd:=x.den) => (x.num)::OutputForm - (x.num)::OutputForm / (xd::OutputForm) + one?(xd:=rep(x).den) => rep(x).num::OutputForm + rep(x).num::OutputForm / (xd::OutputForm) latex(x:%): String == - one?(xd:=x.den) => latex(x.num) - nl : String := concat("{", concat(latex(x.num), "}")$String)$String - dl : String := concat("{", concat(latex(x.den), "}")$String)$String + one?(xd:=rep(x).den) => latex rep(x).num + nl : String := concat("{", concat(latex rep(x).num, "}")$String)$String + dl : String := concat("{", concat(latex rep(x).den, "}")$String)$String concat("{ ", concat(nl, concat(" \over ", concat(dl, " }")$String)$String)$String)$String @ |