-- -- -- Algebra -- -- -- -- Root -- rt n x := if isInteger n then match x as mathExpr with | #0 -> 0 | ?isMonomial -> rtMonomial n x | (poly \$xs) / (poly \$ys) -> let xd := reduce gcd xs yd := reduce gcd ys d := rtMonomial n (xd / yd) in d *' rt'' n (sum' (map (/' xd) xs) /' sum' (map (/' yd) ys)) | _ -> rt'' n x else rt'' n x rtMonomial n x := rtTerm n (numerator x * denominator x ^ (n - 1)) / denominator x rtTerm n x := match x as termExpr with | term \$a _ -> if a < 0 then rtm1 n *' rtPositiveTerm n (- x) else rtPositiveTerm n x rtPositiveTerm n x := match (n, x) as (mathExpr, mathExpr) with | (#3, \$a * #i * \$r) -> (- i) * rt 3 (a *' r) | (_, \$a * #sqrt \$b * \$r) -> rt (n * 2) (a ^' 2 *' b) *' rt n r | (_, \$a * #rt \$n' \$b * \$r) -> rt (n * n') (a ^' n' *' b) *' rt n r | (_, _) -> rtPositiveTerm1 n x rtPositiveTerm1 n x := let f xs := match xs as assocMultiset mathExpr with | [] -> (1, 1) | ncons \$p \$k \$rs -> let (a, b) := f rs in (p ^' quotient k n *' a, p ^' (k % n) *' b) g n x := let d := match x as termExpr with | term \$m \$xs -> gcd n (reduce gcd (map 2#%2 (toAssoc (pF m) ++ xs))) in rt'' (n / d) (rt d x) in match x as termExpr with | term \$m \$xs -> match f (toAssoc (pF (abs m)) ++ xs) as (integer, integer) with | (\$a, #1) -> a | (\$a, \$b) -> a *' g n b rt'' n x := match (n, x) as (integer, integer) with | (#2, _) -> `sqrt x | (_, _) -> `rt n x rtm1 n := match n as integer with | #1 -> -1 | #2 -> i | ?isOdd -> -1 | _ -> undefined sqrt x := if isScalar x then let m := numerator x n := denominator x in rt 2 (m * n) / n else b.sqrt x rtOfUnity := rtu rtu n := rtu' n rtu' n := if isInteger n then match n as integer with | #1 -> 1 | #2 -> -1 | #3 -> w | #4 -> i | _ -> `rtu n else `rtu n