{-# OPTIONS_GHC -Wall -fno-warn-orphans #-}
module Data.NumInstances.Tuple () where
lift2 :: (a->u) -> (b->v) -> (a,b) -> (u,v)
lift2 :: forall a u b v. (a -> u) -> (b -> v) -> (a, b) -> (u, v)
lift2 a -> u
fa b -> v
fb (a
a,b
b) = (a -> u
fa a
a, b -> v
fb b
b)
instance (Num a, Num b) => Num (a,b) where
fromInteger :: Integer -> (a, b)
fromInteger Integer
n = (forall a. Num a => Integer -> a
fromInteger Integer
n, forall a. Num a => Integer -> a
fromInteger Integer
n)
(a
a,b
b) + :: (a, b) -> (a, b) -> (a, b)
+ (a
a',b
b') = (a
aforall a. Num a => a -> a -> a
+a
a',b
bforall a. Num a => a -> a -> a
+b
b')
(a
a,b
b) - :: (a, b) -> (a, b) -> (a, b)
- (a
a',b
b') = (a
aforall a. Num a => a -> a -> a
-a
a',b
bforall a. Num a => a -> a -> a
-b
b')
(a
a,b
b) * :: (a, b) -> (a, b) -> (a, b)
* (a
a',b
b') = (a
aforall a. Num a => a -> a -> a
*a
a',b
bforall a. Num a => a -> a -> a
*b
b')
negate :: (a, b) -> (a, b)
negate = forall a u b v. (a -> u) -> (b -> v) -> (a, b) -> (u, v)
lift2 forall a. Num a => a -> a
negate forall a. Num a => a -> a
negate
abs :: (a, b) -> (a, b)
abs = forall a u b v. (a -> u) -> (b -> v) -> (a, b) -> (u, v)
lift2 forall a. Num a => a -> a
abs forall a. Num a => a -> a
abs
signum :: (a, b) -> (a, b)
signum = forall a u b v. (a -> u) -> (b -> v) -> (a, b) -> (u, v)
lift2 forall a. Num a => a -> a
signum forall a. Num a => a -> a
signum
instance (Fractional a, Fractional b) => Fractional (a,b) where
fromRational :: Rational -> (a, b)
fromRational Rational
x = (forall a. Fractional a => Rational -> a
fromRational Rational
x, forall a. Fractional a => Rational -> a
fromRational Rational
x)
recip :: (a, b) -> (a, b)
recip = forall a u b v. (a -> u) -> (b -> v) -> (a, b) -> (u, v)
lift2 forall a. Fractional a => a -> a
recip forall a. Fractional a => a -> a
recip
instance (Floating a, Floating b) => Floating (a,b) where
pi :: (a, b)
pi = (forall a. Floating a => a
pi,forall a. Floating a => a
pi)
exp :: (a, b) -> (a, b)
exp = forall a u b v. (a -> u) -> (b -> v) -> (a, b) -> (u, v)
lift2 forall a. Floating a => a -> a
exp forall a. Floating a => a -> a
exp
log :: (a, b) -> (a, b)
log = forall a u b v. (a -> u) -> (b -> v) -> (a, b) -> (u, v)
lift2 forall a. Floating a => a -> a
log forall a. Floating a => a -> a
log
sqrt :: (a, b) -> (a, b)
sqrt = forall a u b v. (a -> u) -> (b -> v) -> (a, b) -> (u, v)
lift2 forall a. Floating a => a -> a
sqrt forall a. Floating a => a -> a
sqrt
sin :: (a, b) -> (a, b)
sin = forall a u b v. (a -> u) -> (b -> v) -> (a, b) -> (u, v)
lift2 forall a. Floating a => a -> a
sin forall a. Floating a => a -> a
sin
cos :: (a, b) -> (a, b)
cos = forall a u b v. (a -> u) -> (b -> v) -> (a, b) -> (u, v)
lift2 forall a. Floating a => a -> a
cos forall a. Floating a => a -> a
cos
sinh :: (a, b) -> (a, b)
sinh = forall a u b v. (a -> u) -> (b -> v) -> (a, b) -> (u, v)
lift2 forall a. Floating a => a -> a
sinh forall a. Floating a => a -> a
sinh
cosh :: (a, b) -> (a, b)
cosh = forall a u b v. (a -> u) -> (b -> v) -> (a, b) -> (u, v)
lift2 forall a. Floating a => a -> a
cosh forall a. Floating a => a -> a
cosh
asin :: (a, b) -> (a, b)
asin = forall a u b v. (a -> u) -> (b -> v) -> (a, b) -> (u, v)
lift2 forall a. Floating a => a -> a
asin forall a. Floating a => a -> a
asin
acos :: (a, b) -> (a, b)
acos = forall a u b v. (a -> u) -> (b -> v) -> (a, b) -> (u, v)
lift2 forall a. Floating a => a -> a
acos forall a. Floating a => a -> a
acos
atan :: (a, b) -> (a, b)
atan = forall a u b v. (a -> u) -> (b -> v) -> (a, b) -> (u, v)
lift2 forall a. Floating a => a -> a
atan forall a. Floating a => a -> a
atan
asinh :: (a, b) -> (a, b)
asinh = forall a u b v. (a -> u) -> (b -> v) -> (a, b) -> (u, v)
lift2 forall a. Floating a => a -> a
asinh forall a. Floating a => a -> a
asinh
acosh :: (a, b) -> (a, b)
acosh = forall a u b v. (a -> u) -> (b -> v) -> (a, b) -> (u, v)
lift2 forall a. Floating a => a -> a
acosh forall a. Floating a => a -> a
acosh
atanh :: (a, b) -> (a, b)
atanh = forall a u b v. (a -> u) -> (b -> v) -> (a, b) -> (u, v)
lift2 forall a. Floating a => a -> a
atanh forall a. Floating a => a -> a
atanh
instance (Num a, Num b, Num c) => Num (a,b,c) where
fromInteger :: Integer -> (a, b, c)
fromInteger Integer
n = (forall a. Num a => Integer -> a
fromInteger Integer
n, forall a. Num a => Integer -> a
fromInteger Integer
n, forall a. Num a => Integer -> a
fromInteger Integer
n)
(a
a,b
b,c
c) + :: (a, b, c) -> (a, b, c) -> (a, b, c)
+ (a
a',b
b',c
c') = (a
aforall a. Num a => a -> a -> a
+a
a',b
bforall a. Num a => a -> a -> a
+b
b',c
cforall a. Num a => a -> a -> a
+c
c')
(a
a,b
b,c
c) - :: (a, b, c) -> (a, b, c) -> (a, b, c)
- (a
a',b
b',c
c') = (a
aforall a. Num a => a -> a -> a
-a
a',b
bforall a. Num a => a -> a -> a
-b
b',c
cforall a. Num a => a -> a -> a
-c
c')
(a
a,b
b,c
c) * :: (a, b, c) -> (a, b, c) -> (a, b, c)
* (a
a',b
b',c
c') = (a
aforall a. Num a => a -> a -> a
*a
a',b
bforall a. Num a => a -> a -> a
*b
b',c
cforall a. Num a => a -> a -> a
*c
c')
negate :: (a, b, c) -> (a, b, c)
negate = forall a u b v c w.
(a -> u) -> (b -> v) -> (c -> w) -> (a, b, c) -> (u, v, w)
lift3 forall a. Num a => a -> a
negate forall a. Num a => a -> a
negate forall a. Num a => a -> a
negate
abs :: (a, b, c) -> (a, b, c)
abs = forall a u b v c w.
(a -> u) -> (b -> v) -> (c -> w) -> (a, b, c) -> (u, v, w)
lift3 forall a. Num a => a -> a
abs forall a. Num a => a -> a
abs forall a. Num a => a -> a
abs
signum :: (a, b, c) -> (a, b, c)
signum = forall a u b v c w.
(a -> u) -> (b -> v) -> (c -> w) -> (a, b, c) -> (u, v, w)
lift3 forall a. Num a => a -> a
signum forall a. Num a => a -> a
signum forall a. Num a => a -> a
signum
instance (Fractional a, Fractional b, Fractional c)
=> Fractional (a,b,c) where
fromRational :: Rational -> (a, b, c)
fromRational Rational
x = (forall a. Fractional a => Rational -> a
fromRational Rational
x, forall a. Fractional a => Rational -> a
fromRational Rational
x, forall a. Fractional a => Rational -> a
fromRational Rational
x)
recip :: (a, b, c) -> (a, b, c)
recip = forall a u b v c w.
(a -> u) -> (b -> v) -> (c -> w) -> (a, b, c) -> (u, v, w)
lift3 forall a. Fractional a => a -> a
recip forall a. Fractional a => a -> a
recip forall a. Fractional a => a -> a
recip
lift3 :: (a->u) -> (b->v) -> (c->w)
-> (a,b,c) -> (u,v,w)
lift3 :: forall a u b v c w.
(a -> u) -> (b -> v) -> (c -> w) -> (a, b, c) -> (u, v, w)
lift3 a -> u
fa b -> v
fb c -> w
fc (a
a,b
b,c
c) = (a -> u
fa a
a, b -> v
fb b
b, c -> w
fc c
c)
instance (Floating a, Floating b, Floating c)
=> Floating (a,b,c) where
pi :: (a, b, c)
pi = (forall a. Floating a => a
pi,forall a. Floating a => a
pi,forall a. Floating a => a
pi)
exp :: (a, b, c) -> (a, b, c)
exp = forall a u b v c w.
(a -> u) -> (b -> v) -> (c -> w) -> (a, b, c) -> (u, v, w)
lift3 forall a. Floating a => a -> a
exp forall a. Floating a => a -> a
exp forall a. Floating a => a -> a
exp
log :: (a, b, c) -> (a, b, c)
log = forall a u b v c w.
(a -> u) -> (b -> v) -> (c -> w) -> (a, b, c) -> (u, v, w)
lift3 forall a. Floating a => a -> a
log forall a. Floating a => a -> a
log forall a. Floating a => a -> a
log
sqrt :: (a, b, c) -> (a, b, c)
sqrt = forall a u b v c w.
(a -> u) -> (b -> v) -> (c -> w) -> (a, b, c) -> (u, v, w)
lift3 forall a. Floating a => a -> a
sqrt forall a. Floating a => a -> a
sqrt forall a. Floating a => a -> a
sqrt
sin :: (a, b, c) -> (a, b, c)
sin = forall a u b v c w.
(a -> u) -> (b -> v) -> (c -> w) -> (a, b, c) -> (u, v, w)
lift3 forall a. Floating a => a -> a
sin forall a. Floating a => a -> a
sin forall a. Floating a => a -> a
sin
cos :: (a, b, c) -> (a, b, c)
cos = forall a u b v c w.
(a -> u) -> (b -> v) -> (c -> w) -> (a, b, c) -> (u, v, w)
lift3 forall a. Floating a => a -> a
cos forall a. Floating a => a -> a
cos forall a. Floating a => a -> a
cos
sinh :: (a, b, c) -> (a, b, c)
sinh = forall a u b v c w.
(a -> u) -> (b -> v) -> (c -> w) -> (a, b, c) -> (u, v, w)
lift3 forall a. Floating a => a -> a
sinh forall a. Floating a => a -> a
sinh forall a. Floating a => a -> a
sinh
cosh :: (a, b, c) -> (a, b, c)
cosh = forall a u b v c w.
(a -> u) -> (b -> v) -> (c -> w) -> (a, b, c) -> (u, v, w)
lift3 forall a. Floating a => a -> a
cosh forall a. Floating a => a -> a
cosh forall a. Floating a => a -> a
cosh
asin :: (a, b, c) -> (a, b, c)
asin = forall a u b v c w.
(a -> u) -> (b -> v) -> (c -> w) -> (a, b, c) -> (u, v, w)
lift3 forall a. Floating a => a -> a
asin forall a. Floating a => a -> a
asin forall a. Floating a => a -> a
asin
acos :: (a, b, c) -> (a, b, c)
acos = forall a u b v c w.
(a -> u) -> (b -> v) -> (c -> w) -> (a, b, c) -> (u, v, w)
lift3 forall a. Floating a => a -> a
acos forall a. Floating a => a -> a
acos forall a. Floating a => a -> a
acos
atan :: (a, b, c) -> (a, b, c)
atan = forall a u b v c w.
(a -> u) -> (b -> v) -> (c -> w) -> (a, b, c) -> (u, v, w)
lift3 forall a. Floating a => a -> a
atan forall a. Floating a => a -> a
atan forall a. Floating a => a -> a
atan
asinh :: (a, b, c) -> (a, b, c)
asinh = forall a u b v c w.
(a -> u) -> (b -> v) -> (c -> w) -> (a, b, c) -> (u, v, w)
lift3 forall a. Floating a => a -> a
asinh forall a. Floating a => a -> a
asinh forall a. Floating a => a -> a
asinh
acosh :: (a, b, c) -> (a, b, c)
acosh = forall a u b v c w.
(a -> u) -> (b -> v) -> (c -> w) -> (a, b, c) -> (u, v, w)
lift3 forall a. Floating a => a -> a
acosh forall a. Floating a => a -> a
acosh forall a. Floating a => a -> a
acosh
atanh :: (a, b, c) -> (a, b, c)
atanh = forall a u b v c w.
(a -> u) -> (b -> v) -> (c -> w) -> (a, b, c) -> (u, v, w)
lift3 forall a. Floating a => a -> a
atanh forall a. Floating a => a -> a
atanh forall a. Floating a => a -> a
atanh
lift4 :: (a->u) -> (b->v) -> (c->w) -> (d->x)
-> (a,b,c,d) -> (u,v,w,x)
lift4 :: forall a u b v c w d x.
(a -> u)
-> (b -> v) -> (c -> w) -> (d -> x) -> (a, b, c, d) -> (u, v, w, x)
lift4 a -> u
fa b -> v
fb c -> w
fc d -> x
fd (a
a,b
b,c
c,d
d) = (a -> u
fa a
a, b -> v
fb b
b, c -> w
fc c
c, d -> x
fd d
d)
instance (Num a, Num b, Num c, Num d) => Num (a,b,c,d) where
fromInteger :: Integer -> (a, b, c, d)
fromInteger Integer
n = (forall a. Num a => Integer -> a
fromInteger Integer
n, forall a. Num a => Integer -> a
fromInteger Integer
n, forall a. Num a => Integer -> a
fromInteger Integer
n, forall a. Num a => Integer -> a
fromInteger Integer
n)
(a
a,b
b,c
c,d
d) + :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d)
+ (a
a',b
b',c
c',d
d') = (a
aforall a. Num a => a -> a -> a
+a
a',b
bforall a. Num a => a -> a -> a
+b
b',c
cforall a. Num a => a -> a -> a
+c
c',d
dforall a. Num a => a -> a -> a
+d
d')
(a
a,b
b,c
c,d
d) - :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d)
- (a
a',b
b',c
c',d
d') = (a
aforall a. Num a => a -> a -> a
-a
a',b
bforall a. Num a => a -> a -> a
-b
b',c
cforall a. Num a => a -> a -> a
-c
c',d
dforall a. Num a => a -> a -> a
-d
d')
(a
a,b
b,c
c,d
d) * :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d)
* (a
a',b
b',c
c',d
d') = (a
aforall a. Num a => a -> a -> a
*a
a',b
bforall a. Num a => a -> a -> a
*b
b',c
cforall a. Num a => a -> a -> a
*c
c',d
dforall a. Num a => a -> a -> a
*d
d')
negate :: (a, b, c, d) -> (a, b, c, d)
negate = forall a u b v c w d x.
(a -> u)
-> (b -> v) -> (c -> w) -> (d -> x) -> (a, b, c, d) -> (u, v, w, x)
lift4 forall a. Num a => a -> a
negate forall a. Num a => a -> a
negate forall a. Num a => a -> a
negate forall a. Num a => a -> a
negate
abs :: (a, b, c, d) -> (a, b, c, d)
abs = forall a u b v c w d x.
(a -> u)
-> (b -> v) -> (c -> w) -> (d -> x) -> (a, b, c, d) -> (u, v, w, x)
lift4 forall a. Num a => a -> a
abs forall a. Num a => a -> a
abs forall a. Num a => a -> a
abs forall a. Num a => a -> a
abs
signum :: (a, b, c, d) -> (a, b, c, d)
signum = forall a u b v c w d x.
(a -> u)
-> (b -> v) -> (c -> w) -> (d -> x) -> (a, b, c, d) -> (u, v, w, x)
lift4 forall a. Num a => a -> a
signum forall a. Num a => a -> a
signum forall a. Num a => a -> a
signum forall a. Num a => a -> a
signum
instance (Fractional a, Fractional b, Fractional c, Fractional d)
=> Fractional (a,b,c,d) where
fromRational :: Rational -> (a, b, c, d)
fromRational Rational
x = (forall a. Fractional a => Rational -> a
fromRational Rational
x, forall a. Fractional a => Rational -> a
fromRational Rational
x, forall a. Fractional a => Rational -> a
fromRational Rational
x, forall a. Fractional a => Rational -> a
fromRational Rational
x)
recip :: (a, b, c, d) -> (a, b, c, d)
recip = forall a u b v c w d x.
(a -> u)
-> (b -> v) -> (c -> w) -> (d -> x) -> (a, b, c, d) -> (u, v, w, x)
lift4 forall a. Fractional a => a -> a
recip forall a. Fractional a => a -> a
recip forall a. Fractional a => a -> a
recip forall a. Fractional a => a -> a
recip
instance (Floating a, Floating b, Floating c, Floating d)
=> Floating (a,b,c,d) where
pi :: (a, b, c, d)
pi = (forall a. Floating a => a
pi,forall a. Floating a => a
pi,forall a. Floating a => a
pi,forall a. Floating a => a
pi)
exp :: (a, b, c, d) -> (a, b, c, d)
exp = forall a u b v c w d x.
(a -> u)
-> (b -> v) -> (c -> w) -> (d -> x) -> (a, b, c, d) -> (u, v, w, x)
lift4 forall a. Floating a => a -> a
exp forall a. Floating a => a -> a
exp forall a. Floating a => a -> a
exp forall a. Floating a => a -> a
exp
log :: (a, b, c, d) -> (a, b, c, d)
log = forall a u b v c w d x.
(a -> u)
-> (b -> v) -> (c -> w) -> (d -> x) -> (a, b, c, d) -> (u, v, w, x)
lift4 forall a. Floating a => a -> a
log forall a. Floating a => a -> a
log forall a. Floating a => a -> a
log forall a. Floating a => a -> a
log
sqrt :: (a, b, c, d) -> (a, b, c, d)
sqrt = forall a u b v c w d x.
(a -> u)
-> (b -> v) -> (c -> w) -> (d -> x) -> (a, b, c, d) -> (u, v, w, x)
lift4 forall a. Floating a => a -> a
sqrt forall a. Floating a => a -> a
sqrt forall a. Floating a => a -> a
sqrt forall a. Floating a => a -> a
sqrt
sin :: (a, b, c, d) -> (a, b, c, d)
sin = forall a u b v c w d x.
(a -> u)
-> (b -> v) -> (c -> w) -> (d -> x) -> (a, b, c, d) -> (u, v, w, x)
lift4 forall a. Floating a => a -> a
sin forall a. Floating a => a -> a
sin forall a. Floating a => a -> a
sin forall a. Floating a => a -> a
sin
cos :: (a, b, c, d) -> (a, b, c, d)
cos = forall a u b v c w d x.
(a -> u)
-> (b -> v) -> (c -> w) -> (d -> x) -> (a, b, c, d) -> (u, v, w, x)
lift4 forall a. Floating a => a -> a
cos forall a. Floating a => a -> a
cos forall a. Floating a => a -> a
cos forall a. Floating a => a -> a
cos
sinh :: (a, b, c, d) -> (a, b, c, d)
sinh = forall a u b v c w d x.
(a -> u)
-> (b -> v) -> (c -> w) -> (d -> x) -> (a, b, c, d) -> (u, v, w, x)
lift4 forall a. Floating a => a -> a
sinh forall a. Floating a => a -> a
sinh forall a. Floating a => a -> a
sinh forall a. Floating a => a -> a
sinh
cosh :: (a, b, c, d) -> (a, b, c, d)
cosh = forall a u b v c w d x.
(a -> u)
-> (b -> v) -> (c -> w) -> (d -> x) -> (a, b, c, d) -> (u, v, w, x)
lift4 forall a. Floating a => a -> a
cosh forall a. Floating a => a -> a
cosh forall a. Floating a => a -> a
cosh forall a. Floating a => a -> a
cosh
asin :: (a, b, c, d) -> (a, b, c, d)
asin = forall a u b v c w d x.
(a -> u)
-> (b -> v) -> (c -> w) -> (d -> x) -> (a, b, c, d) -> (u, v, w, x)
lift4 forall a. Floating a => a -> a
asin forall a. Floating a => a -> a
asin forall a. Floating a => a -> a
asin forall a. Floating a => a -> a
asin
acos :: (a, b, c, d) -> (a, b, c, d)
acos = forall a u b v c w d x.
(a -> u)
-> (b -> v) -> (c -> w) -> (d -> x) -> (a, b, c, d) -> (u, v, w, x)
lift4 forall a. Floating a => a -> a
acos forall a. Floating a => a -> a
acos forall a. Floating a => a -> a
acos forall a. Floating a => a -> a
acos
atan :: (a, b, c, d) -> (a, b, c, d)
atan = forall a u b v c w d x.
(a -> u)
-> (b -> v) -> (c -> w) -> (d -> x) -> (a, b, c, d) -> (u, v, w, x)
lift4 forall a. Floating a => a -> a
atan forall a. Floating a => a -> a
atan forall a. Floating a => a -> a
atan forall a. Floating a => a -> a
atan
asinh :: (a, b, c, d) -> (a, b, c, d)
asinh = forall a u b v c w d x.
(a -> u)
-> (b -> v) -> (c -> w) -> (d -> x) -> (a, b, c, d) -> (u, v, w, x)
lift4 forall a. Floating a => a -> a
asinh forall a. Floating a => a -> a
asinh forall a. Floating a => a -> a
asinh forall a. Floating a => a -> a
asinh
acosh :: (a, b, c, d) -> (a, b, c, d)
acosh = forall a u b v c w d x.
(a -> u)
-> (b -> v) -> (c -> w) -> (d -> x) -> (a, b, c, d) -> (u, v, w, x)
lift4 forall a. Floating a => a -> a
acosh forall a. Floating a => a -> a
acosh forall a. Floating a => a -> a
acosh forall a. Floating a => a -> a
acosh
atanh :: (a, b, c, d) -> (a, b, c, d)
atanh = forall a u b v c w d x.
(a -> u)
-> (b -> v) -> (c -> w) -> (d -> x) -> (a, b, c, d) -> (u, v, w, x)
lift4 forall a. Floating a => a -> a
atanh forall a. Floating a => a -> a
atanh forall a. Floating a => a -> a
atanh forall a. Floating a => a -> a
atanh
lift5 :: (a->u) -> (b->v) -> (c->w) -> (d->x) -> (e->y)
-> (a,b,c,d,e) -> (u,v,w,x,y)
lift5 :: forall a u b v c w d x e y.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (a, b, c, d, e)
-> (u, v, w, x, y)
lift5 a -> u
fa b -> v
fb c -> w
fc d -> x
fd e -> y
fe (a
a,b
b,c
c,d
d,e
e) =
(a -> u
fa a
a, b -> v
fb b
b, c -> w
fc c
c, d -> x
fd d
d, e -> y
fe e
e)
instance (Num a, Num b, Num c, Num d, Num e) => Num (a,b,c,d,e) where
fromInteger :: Integer -> (a, b, c, d, e)
fromInteger Integer
n = (forall a. Num a => Integer -> a
fromInteger Integer
n, forall a. Num a => Integer -> a
fromInteger Integer
n, forall a. Num a => Integer -> a
fromInteger Integer
n, forall a. Num a => Integer -> a
fromInteger Integer
n, forall a. Num a => Integer -> a
fromInteger Integer
n)
(a
a,b
b,c
c,d
d,e
e) + :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e)
+ (a
a',b
b',c
c',d
d',e
e') = (a
aforall a. Num a => a -> a -> a
+a
a',b
bforall a. Num a => a -> a -> a
+b
b',c
cforall a. Num a => a -> a -> a
+c
c',d
dforall a. Num a => a -> a -> a
+d
d',e
eforall a. Num a => a -> a -> a
+e
e')
(a
a,b
b,c
c,d
d,e
e) - :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e)
- (a
a',b
b',c
c',d
d',e
e') = (a
aforall a. Num a => a -> a -> a
-a
a',b
bforall a. Num a => a -> a -> a
-b
b',c
cforall a. Num a => a -> a -> a
-c
c',d
dforall a. Num a => a -> a -> a
-d
d',e
eforall a. Num a => a -> a -> a
-e
e')
(a
a,b
b,c
c,d
d,e
e) * :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e)
* (a
a',b
b',c
c',d
d',e
e') = (a
aforall a. Num a => a -> a -> a
*a
a',b
bforall a. Num a => a -> a -> a
*b
b',c
cforall a. Num a => a -> a -> a
*c
c',d
dforall a. Num a => a -> a -> a
*d
d',e
eforall a. Num a => a -> a -> a
*e
e')
negate :: (a, b, c, d, e) -> (a, b, c, d, e)
negate = forall a u b v c w d x e y.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (a, b, c, d, e)
-> (u, v, w, x, y)
lift5 forall a. Num a => a -> a
negate forall a. Num a => a -> a
negate forall a. Num a => a -> a
negate forall a. Num a => a -> a
negate forall a. Num a => a -> a
negate
abs :: (a, b, c, d, e) -> (a, b, c, d, e)
abs = forall a u b v c w d x e y.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (a, b, c, d, e)
-> (u, v, w, x, y)
lift5 forall a. Num a => a -> a
abs forall a. Num a => a -> a
abs forall a. Num a => a -> a
abs forall a. Num a => a -> a
abs forall a. Num a => a -> a
abs
signum :: (a, b, c, d, e) -> (a, b, c, d, e)
signum = forall a u b v c w d x e y.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (a, b, c, d, e)
-> (u, v, w, x, y)
lift5 forall a. Num a => a -> a
signum forall a. Num a => a -> a
signum forall a. Num a => a -> a
signum forall a. Num a => a -> a
signum forall a. Num a => a -> a
signum
instance (Fractional a, Fractional b, Fractional c, Fractional d, Fractional e)
=> Fractional (a,b,c,d,e) where
fromRational :: Rational -> (a, b, c, d, e)
fromRational Rational
x = (forall a. Fractional a => Rational -> a
fromRational Rational
x, forall a. Fractional a => Rational -> a
fromRational Rational
x, forall a. Fractional a => Rational -> a
fromRational Rational
x, forall a. Fractional a => Rational -> a
fromRational Rational
x, forall a. Fractional a => Rational -> a
fromRational Rational
x)
recip :: (a, b, c, d, e) -> (a, b, c, d, e)
recip = forall a u b v c w d x e y.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (a, b, c, d, e)
-> (u, v, w, x, y)
lift5 forall a. Fractional a => a -> a
recip forall a. Fractional a => a -> a
recip forall a. Fractional a => a -> a
recip forall a. Fractional a => a -> a
recip forall a. Fractional a => a -> a
recip
instance (Floating a, Floating b, Floating c, Floating d, Floating e)
=> Floating (a,b,c,d,e) where
pi :: (a, b, c, d, e)
pi = (forall a. Floating a => a
pi,forall a. Floating a => a
pi,forall a. Floating a => a
pi,forall a. Floating a => a
pi,forall a. Floating a => a
pi)
exp :: (a, b, c, d, e) -> (a, b, c, d, e)
exp = forall a u b v c w d x e y.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (a, b, c, d, e)
-> (u, v, w, x, y)
lift5 forall a. Floating a => a -> a
exp forall a. Floating a => a -> a
exp forall a. Floating a => a -> a
exp forall a. Floating a => a -> a
exp forall a. Floating a => a -> a
exp
log :: (a, b, c, d, e) -> (a, b, c, d, e)
log = forall a u b v c w d x e y.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (a, b, c, d, e)
-> (u, v, w, x, y)
lift5 forall a. Floating a => a -> a
log forall a. Floating a => a -> a
log forall a. Floating a => a -> a
log forall a. Floating a => a -> a
log forall a. Floating a => a -> a
log
sqrt :: (a, b, c, d, e) -> (a, b, c, d, e)
sqrt = forall a u b v c w d x e y.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (a, b, c, d, e)
-> (u, v, w, x, y)
lift5 forall a. Floating a => a -> a
sqrt forall a. Floating a => a -> a
sqrt forall a. Floating a => a -> a
sqrt forall a. Floating a => a -> a
sqrt forall a. Floating a => a -> a
sqrt
sin :: (a, b, c, d, e) -> (a, b, c, d, e)
sin = forall a u b v c w d x e y.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (a, b, c, d, e)
-> (u, v, w, x, y)
lift5 forall a. Floating a => a -> a
sin forall a. Floating a => a -> a
sin forall a. Floating a => a -> a
sin forall a. Floating a => a -> a
sin forall a. Floating a => a -> a
sin
cos :: (a, b, c, d, e) -> (a, b, c, d, e)
cos = forall a u b v c w d x e y.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (a, b, c, d, e)
-> (u, v, w, x, y)
lift5 forall a. Floating a => a -> a
cos forall a. Floating a => a -> a
cos forall a. Floating a => a -> a
cos forall a. Floating a => a -> a
cos forall a. Floating a => a -> a
cos
sinh :: (a, b, c, d, e) -> (a, b, c, d, e)
sinh = forall a u b v c w d x e y.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (a, b, c, d, e)
-> (u, v, w, x, y)
lift5 forall a. Floating a => a -> a
sinh forall a. Floating a => a -> a
sinh forall a. Floating a => a -> a
sinh forall a. Floating a => a -> a
sinh forall a. Floating a => a -> a
sinh
cosh :: (a, b, c, d, e) -> (a, b, c, d, e)
cosh = forall a u b v c w d x e y.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (a, b, c, d, e)
-> (u, v, w, x, y)
lift5 forall a. Floating a => a -> a
cosh forall a. Floating a => a -> a
cosh forall a. Floating a => a -> a
cosh forall a. Floating a => a -> a
cosh forall a. Floating a => a -> a
cosh
asin :: (a, b, c, d, e) -> (a, b, c, d, e)
asin = forall a u b v c w d x e y.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (a, b, c, d, e)
-> (u, v, w, x, y)
lift5 forall a. Floating a => a -> a
asin forall a. Floating a => a -> a
asin forall a. Floating a => a -> a
asin forall a. Floating a => a -> a
asin forall a. Floating a => a -> a
asin
acos :: (a, b, c, d, e) -> (a, b, c, d, e)
acos = forall a u b v c w d x e y.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (a, b, c, d, e)
-> (u, v, w, x, y)
lift5 forall a. Floating a => a -> a
acos forall a. Floating a => a -> a
acos forall a. Floating a => a -> a
acos forall a. Floating a => a -> a
acos forall a. Floating a => a -> a
acos
atan :: (a, b, c, d, e) -> (a, b, c, d, e)
atan = forall a u b v c w d x e y.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (a, b, c, d, e)
-> (u, v, w, x, y)
lift5 forall a. Floating a => a -> a
atan forall a. Floating a => a -> a
atan forall a. Floating a => a -> a
atan forall a. Floating a => a -> a
atan forall a. Floating a => a -> a
atan
asinh :: (a, b, c, d, e) -> (a, b, c, d, e)
asinh = forall a u b v c w d x e y.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (a, b, c, d, e)
-> (u, v, w, x, y)
lift5 forall a. Floating a => a -> a
asinh forall a. Floating a => a -> a
asinh forall a. Floating a => a -> a
asinh forall a. Floating a => a -> a
asinh forall a. Floating a => a -> a
asinh
acosh :: (a, b, c, d, e) -> (a, b, c, d, e)
acosh = forall a u b v c w d x e y.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (a, b, c, d, e)
-> (u, v, w, x, y)
lift5 forall a. Floating a => a -> a
acosh forall a. Floating a => a -> a
acosh forall a. Floating a => a -> a
acosh forall a. Floating a => a -> a
acosh forall a. Floating a => a -> a
acosh
atanh :: (a, b, c, d, e) -> (a, b, c, d, e)
atanh = forall a u b v c w d x e y.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (a, b, c, d, e)
-> (u, v, w, x, y)
lift5 forall a. Floating a => a -> a
atanh forall a. Floating a => a -> a
atanh forall a. Floating a => a -> a
atanh forall a. Floating a => a -> a
atanh forall a. Floating a => a -> a
atanh
lift6 :: (a->u) -> (b->v) -> (c->w) -> (d->x) -> (e->y) -> (f->t)
-> (a,b,c,d,e,f) -> (u,v,w,x,y,t)
lift6 :: forall a u b v c w d x e y f t.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (a, b, c, d, e, f)
-> (u, v, w, x, y, t)
lift6 a -> u
fa b -> v
fb c -> w
fc d -> x
fd e -> y
fe f -> t
ff (a
a,b
b,c
c,d
d,e
e,f
f) =
(a -> u
fa a
a, b -> v
fb b
b, c -> w
fc c
c, d -> x
fd d
d, e -> y
fe e
e, f -> t
ff f
f)
instance (Num a, Num b, Num c, Num d, Num e, Num f) => Num (a,b,c,d,e,f) where
fromInteger :: Integer -> (a, b, c, d, e, f)
fromInteger Integer
n = (forall a. Num a => Integer -> a
fromInteger Integer
n, forall a. Num a => Integer -> a
fromInteger Integer
n, forall a. Num a => Integer -> a
fromInteger Integer
n, forall a. Num a => Integer -> a
fromInteger Integer
n, forall a. Num a => Integer -> a
fromInteger Integer
n, forall a. Num a => Integer -> a
fromInteger Integer
n)
(a
a,b
b,c
c,d
d,e
e,f
f) + :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f)
+ (a
a',b
b',c
c',d
d',e
e',f
f') = (a
aforall a. Num a => a -> a -> a
+a
a',b
bforall a. Num a => a -> a -> a
+b
b',c
cforall a. Num a => a -> a -> a
+c
c',d
dforall a. Num a => a -> a -> a
+d
d',e
eforall a. Num a => a -> a -> a
+e
e',f
fforall a. Num a => a -> a -> a
+f
f')
(a
a,b
b,c
c,d
d,e
e,f
f) - :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f)
- (a
a',b
b',c
c',d
d',e
e',f
f') = (a
aforall a. Num a => a -> a -> a
-a
a',b
bforall a. Num a => a -> a -> a
-b
b',c
cforall a. Num a => a -> a -> a
-c
c',d
dforall a. Num a => a -> a -> a
-d
d',e
eforall a. Num a => a -> a -> a
-e
e',f
fforall a. Num a => a -> a -> a
-f
f')
(a
a,b
b,c
c,d
d,e
e,f
f) * :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f)
* (a
a',b
b',c
c',d
d',e
e',f
f') = (a
aforall a. Num a => a -> a -> a
*a
a',b
bforall a. Num a => a -> a -> a
*b
b',c
cforall a. Num a => a -> a -> a
*c
c',d
dforall a. Num a => a -> a -> a
*d
d',e
eforall a. Num a => a -> a -> a
*e
e',f
fforall a. Num a => a -> a -> a
*f
f')
negate :: (a, b, c, d, e, f) -> (a, b, c, d, e, f)
negate = forall a u b v c w d x e y f t.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (a, b, c, d, e, f)
-> (u, v, w, x, y, t)
lift6 forall a. Num a => a -> a
negate forall a. Num a => a -> a
negate forall a. Num a => a -> a
negate forall a. Num a => a -> a
negate forall a. Num a => a -> a
negate forall a. Num a => a -> a
negate
abs :: (a, b, c, d, e, f) -> (a, b, c, d, e, f)
abs = forall a u b v c w d x e y f t.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (a, b, c, d, e, f)
-> (u, v, w, x, y, t)
lift6 forall a. Num a => a -> a
abs forall a. Num a => a -> a
abs forall a. Num a => a -> a
abs forall a. Num a => a -> a
abs forall a. Num a => a -> a
abs forall a. Num a => a -> a
abs
signum :: (a, b, c, d, e, f) -> (a, b, c, d, e, f)
signum = forall a u b v c w d x e y f t.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (a, b, c, d, e, f)
-> (u, v, w, x, y, t)
lift6 forall a. Num a => a -> a
signum forall a. Num a => a -> a
signum forall a. Num a => a -> a
signum forall a. Num a => a -> a
signum forall a. Num a => a -> a
signum forall a. Num a => a -> a
signum
instance (Fractional a, Fractional b, Fractional c, Fractional d, Fractional e, Fractional f)
=> Fractional (a,b,c,d,e,f) where
fromRational :: Rational -> (a, b, c, d, e, f)
fromRational Rational
x = (forall a. Fractional a => Rational -> a
fromRational Rational
x, forall a. Fractional a => Rational -> a
fromRational Rational
x, forall a. Fractional a => Rational -> a
fromRational Rational
x, forall a. Fractional a => Rational -> a
fromRational Rational
x, forall a. Fractional a => Rational -> a
fromRational Rational
x, forall a. Fractional a => Rational -> a
fromRational Rational
x)
recip :: (a, b, c, d, e, f) -> (a, b, c, d, e, f)
recip = forall a u b v c w d x e y f t.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (a, b, c, d, e, f)
-> (u, v, w, x, y, t)
lift6 forall a. Fractional a => a -> a
recip forall a. Fractional a => a -> a
recip forall a. Fractional a => a -> a
recip forall a. Fractional a => a -> a
recip forall a. Fractional a => a -> a
recip forall a. Fractional a => a -> a
recip
instance (Floating a, Floating b, Floating c, Floating d, Floating e, Floating f)
=> Floating (a,b,c,d,e,f) where
pi :: (a, b, c, d, e, f)
pi = (forall a. Floating a => a
pi,forall a. Floating a => a
pi,forall a. Floating a => a
pi,forall a. Floating a => a
pi,forall a. Floating a => a
pi,forall a. Floating a => a
pi)
exp :: (a, b, c, d, e, f) -> (a, b, c, d, e, f)
exp = forall a u b v c w d x e y f t.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (a, b, c, d, e, f)
-> (u, v, w, x, y, t)
lift6 forall a. Floating a => a -> a
exp forall a. Floating a => a -> a
exp forall a. Floating a => a -> a
exp forall a. Floating a => a -> a
exp forall a. Floating a => a -> a
exp forall a. Floating a => a -> a
exp
log :: (a, b, c, d, e, f) -> (a, b, c, d, e, f)
log = forall a u b v c w d x e y f t.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (a, b, c, d, e, f)
-> (u, v, w, x, y, t)
lift6 forall a. Floating a => a -> a
log forall a. Floating a => a -> a
log forall a. Floating a => a -> a
log forall a. Floating a => a -> a
log forall a. Floating a => a -> a
log forall a. Floating a => a -> a
log
sqrt :: (a, b, c, d, e, f) -> (a, b, c, d, e, f)
sqrt = forall a u b v c w d x e y f t.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (a, b, c, d, e, f)
-> (u, v, w, x, y, t)
lift6 forall a. Floating a => a -> a
sqrt forall a. Floating a => a -> a
sqrt forall a. Floating a => a -> a
sqrt forall a. Floating a => a -> a
sqrt forall a. Floating a => a -> a
sqrt forall a. Floating a => a -> a
sqrt
sin :: (a, b, c, d, e, f) -> (a, b, c, d, e, f)
sin = forall a u b v c w d x e y f t.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (a, b, c, d, e, f)
-> (u, v, w, x, y, t)
lift6 forall a. Floating a => a -> a
sin forall a. Floating a => a -> a
sin forall a. Floating a => a -> a
sin forall a. Floating a => a -> a
sin forall a. Floating a => a -> a
sin forall a. Floating a => a -> a
sin
cos :: (a, b, c, d, e, f) -> (a, b, c, d, e, f)
cos = forall a u b v c w d x e y f t.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (a, b, c, d, e, f)
-> (u, v, w, x, y, t)
lift6 forall a. Floating a => a -> a
cos forall a. Floating a => a -> a
cos forall a. Floating a => a -> a
cos forall a. Floating a => a -> a
cos forall a. Floating a => a -> a
cos forall a. Floating a => a -> a
cos
sinh :: (a, b, c, d, e, f) -> (a, b, c, d, e, f)
sinh = forall a u b v c w d x e y f t.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (a, b, c, d, e, f)
-> (u, v, w, x, y, t)
lift6 forall a. Floating a => a -> a
sinh forall a. Floating a => a -> a
sinh forall a. Floating a => a -> a
sinh forall a. Floating a => a -> a
sinh forall a. Floating a => a -> a
sinh forall a. Floating a => a -> a
sinh
cosh :: (a, b, c, d, e, f) -> (a, b, c, d, e, f)
cosh = forall a u b v c w d x e y f t.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (a, b, c, d, e, f)
-> (u, v, w, x, y, t)
lift6 forall a. Floating a => a -> a
cosh forall a. Floating a => a -> a
cosh forall a. Floating a => a -> a
cosh forall a. Floating a => a -> a
cosh forall a. Floating a => a -> a
cosh forall a. Floating a => a -> a
cosh
asin :: (a, b, c, d, e, f) -> (a, b, c, d, e, f)
asin = forall a u b v c w d x e y f t.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (a, b, c, d, e, f)
-> (u, v, w, x, y, t)
lift6 forall a. Floating a => a -> a
asin forall a. Floating a => a -> a
asin forall a. Floating a => a -> a
asin forall a. Floating a => a -> a
asin forall a. Floating a => a -> a
asin forall a. Floating a => a -> a
asin
acos :: (a, b, c, d, e, f) -> (a, b, c, d, e, f)
acos = forall a u b v c w d x e y f t.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (a, b, c, d, e, f)
-> (u, v, w, x, y, t)
lift6 forall a. Floating a => a -> a
acos forall a. Floating a => a -> a
acos forall a. Floating a => a -> a
acos forall a. Floating a => a -> a
acos forall a. Floating a => a -> a
acos forall a. Floating a => a -> a
acos
atan :: (a, b, c, d, e, f) -> (a, b, c, d, e, f)
atan = forall a u b v c w d x e y f t.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (a, b, c, d, e, f)
-> (u, v, w, x, y, t)
lift6 forall a. Floating a => a -> a
atan forall a. Floating a => a -> a
atan forall a. Floating a => a -> a
atan forall a. Floating a => a -> a
atan forall a. Floating a => a -> a
atan forall a. Floating a => a -> a
atan
asinh :: (a, b, c, d, e, f) -> (a, b, c, d, e, f)
asinh = forall a u b v c w d x e y f t.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (a, b, c, d, e, f)
-> (u, v, w, x, y, t)
lift6 forall a. Floating a => a -> a
asinh forall a. Floating a => a -> a
asinh forall a. Floating a => a -> a
asinh forall a. Floating a => a -> a
asinh forall a. Floating a => a -> a
asinh forall a. Floating a => a -> a
asinh
acosh :: (a, b, c, d, e, f) -> (a, b, c, d, e, f)
acosh = forall a u b v c w d x e y f t.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (a, b, c, d, e, f)
-> (u, v, w, x, y, t)
lift6 forall a. Floating a => a -> a
acosh forall a. Floating a => a -> a
acosh forall a. Floating a => a -> a
acosh forall a. Floating a => a -> a
acosh forall a. Floating a => a -> a
acosh forall a. Floating a => a -> a
acosh
atanh :: (a, b, c, d, e, f) -> (a, b, c, d, e, f)
atanh = forall a u b v c w d x e y f t.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (a, b, c, d, e, f)
-> (u, v, w, x, y, t)
lift6 forall a. Floating a => a -> a
atanh forall a. Floating a => a -> a
atanh forall a. Floating a => a -> a
atanh forall a. Floating a => a -> a
atanh forall a. Floating a => a -> a
atanh forall a. Floating a => a -> a
atanh
lift7 :: (a->u) -> (b->v) -> (c->w) -> (d->x) -> (e->y) -> (f->t) -> (g->z)
-> (a,b,c,d,e,f,g) -> (u,v,w,x,y,t,z)
lift7 :: forall a u b v c w d x e y f t g z.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (g -> z)
-> (a, b, c, d, e, f, g)
-> (u, v, w, x, y, t, z)
lift7 a -> u
fa b -> v
fb c -> w
fc d -> x
fd e -> y
fe f -> t
ff g -> z
fg (a
a,b
b,c
c,d
d,e
e,f
f,g
g) =
(a -> u
fa a
a, b -> v
fb b
b, c -> w
fc c
c, d -> x
fd d
d, e -> y
fe e
e, f -> t
ff f
f, g -> z
fg g
g)
instance (Num a, Num b, Num c, Num d, Num e, Num f, Num g) => Num (a,b,c,d,e,f,g) where
fromInteger :: Integer -> (a, b, c, d, e, f, g)
fromInteger Integer
n = (forall a. Num a => Integer -> a
fromInteger Integer
n, forall a. Num a => Integer -> a
fromInteger Integer
n, forall a. Num a => Integer -> a
fromInteger Integer
n, forall a. Num a => Integer -> a
fromInteger Integer
n, forall a. Num a => Integer -> a
fromInteger Integer
n, forall a. Num a => Integer -> a
fromInteger Integer
n, forall a. Num a => Integer -> a
fromInteger Integer
n)
(a
a,b
b,c
c,d
d,e
e,f
f,g
g) + :: (a, b, c, d, e, f, g)
-> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g)
+ (a
a',b
b',c
c',d
d',e
e',f
f',g
g') = (a
aforall a. Num a => a -> a -> a
+a
a',b
bforall a. Num a => a -> a -> a
+b
b',c
cforall a. Num a => a -> a -> a
+c
c',d
dforall a. Num a => a -> a -> a
+d
d',e
eforall a. Num a => a -> a -> a
+e
e',f
fforall a. Num a => a -> a -> a
+f
f',g
gforall a. Num a => a -> a -> a
+g
g')
(a
a,b
b,c
c,d
d,e
e,f
f,g
g) - :: (a, b, c, d, e, f, g)
-> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g)
- (a
a',b
b',c
c',d
d',e
e',f
f',g
g') = (a
aforall a. Num a => a -> a -> a
-a
a',b
bforall a. Num a => a -> a -> a
-b
b',c
cforall a. Num a => a -> a -> a
-c
c',d
dforall a. Num a => a -> a -> a
-d
d',e
eforall a. Num a => a -> a -> a
-e
e',f
fforall a. Num a => a -> a -> a
-f
f',g
gforall a. Num a => a -> a -> a
-g
g')
(a
a,b
b,c
c,d
d,e
e,f
f,g
g) * :: (a, b, c, d, e, f, g)
-> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g)
* (a
a',b
b',c
c',d
d',e
e',f
f',g
g') = (a
aforall a. Num a => a -> a -> a
*a
a',b
bforall a. Num a => a -> a -> a
*b
b',c
cforall a. Num a => a -> a -> a
*c
c',d
dforall a. Num a => a -> a -> a
*d
d',e
eforall a. Num a => a -> a -> a
*e
e',f
fforall a. Num a => a -> a -> a
*f
f',g
gforall a. Num a => a -> a -> a
*g
g')
negate :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g)
negate = forall a u b v c w d x e y f t g z.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (g -> z)
-> (a, b, c, d, e, f, g)
-> (u, v, w, x, y, t, z)
lift7 forall a. Num a => a -> a
negate forall a. Num a => a -> a
negate forall a. Num a => a -> a
negate forall a. Num a => a -> a
negate forall a. Num a => a -> a
negate forall a. Num a => a -> a
negate forall a. Num a => a -> a
negate
abs :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g)
abs = forall a u b v c w d x e y f t g z.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (g -> z)
-> (a, b, c, d, e, f, g)
-> (u, v, w, x, y, t, z)
lift7 forall a. Num a => a -> a
abs forall a. Num a => a -> a
abs forall a. Num a => a -> a
abs forall a. Num a => a -> a
abs forall a. Num a => a -> a
abs forall a. Num a => a -> a
abs forall a. Num a => a -> a
abs
signum :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g)
signum = forall a u b v c w d x e y f t g z.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (g -> z)
-> (a, b, c, d, e, f, g)
-> (u, v, w, x, y, t, z)
lift7 forall a. Num a => a -> a
signum forall a. Num a => a -> a
signum forall a. Num a => a -> a
signum forall a. Num a => a -> a
signum forall a. Num a => a -> a
signum forall a. Num a => a -> a
signum forall a. Num a => a -> a
signum
instance (Fractional a, Fractional b, Fractional c, Fractional d, Fractional e, Fractional f, Fractional g)
=> Fractional (a,b,c,d,e,f,g) where
fromRational :: Rational -> (a, b, c, d, e, f, g)
fromRational Rational
x = (forall a. Fractional a => Rational -> a
fromRational Rational
x, forall a. Fractional a => Rational -> a
fromRational Rational
x, forall a. Fractional a => Rational -> a
fromRational Rational
x, forall a. Fractional a => Rational -> a
fromRational Rational
x, forall a. Fractional a => Rational -> a
fromRational Rational
x, forall a. Fractional a => Rational -> a
fromRational Rational
x, forall a. Fractional a => Rational -> a
fromRational Rational
x)
recip :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g)
recip = forall a u b v c w d x e y f t g z.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (g -> z)
-> (a, b, c, d, e, f, g)
-> (u, v, w, x, y, t, z)
lift7 forall a. Fractional a => a -> a
recip forall a. Fractional a => a -> a
recip forall a. Fractional a => a -> a
recip forall a. Fractional a => a -> a
recip forall a. Fractional a => a -> a
recip forall a. Fractional a => a -> a
recip forall a. Fractional a => a -> a
recip
instance (Floating a, Floating b, Floating c, Floating d, Floating e, Floating f, Floating g)
=> Floating (a,b,c,d,e,f,g) where
pi :: (a, b, c, d, e, f, g)
pi = (forall a. Floating a => a
pi,forall a. Floating a => a
pi,forall a. Floating a => a
pi,forall a. Floating a => a
pi,forall a. Floating a => a
pi,forall a. Floating a => a
pi,forall a. Floating a => a
pi)
exp :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g)
exp = forall a u b v c w d x e y f t g z.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (g -> z)
-> (a, b, c, d, e, f, g)
-> (u, v, w, x, y, t, z)
lift7 forall a. Floating a => a -> a
exp forall a. Floating a => a -> a
exp forall a. Floating a => a -> a
exp forall a. Floating a => a -> a
exp forall a. Floating a => a -> a
exp forall a. Floating a => a -> a
exp forall a. Floating a => a -> a
exp
log :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g)
log = forall a u b v c w d x e y f t g z.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (g -> z)
-> (a, b, c, d, e, f, g)
-> (u, v, w, x, y, t, z)
lift7 forall a. Floating a => a -> a
log forall a. Floating a => a -> a
log forall a. Floating a => a -> a
log forall a. Floating a => a -> a
log forall a. Floating a => a -> a
log forall a. Floating a => a -> a
log forall a. Floating a => a -> a
log
sqrt :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g)
sqrt = forall a u b v c w d x e y f t g z.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (g -> z)
-> (a, b, c, d, e, f, g)
-> (u, v, w, x, y, t, z)
lift7 forall a. Floating a => a -> a
sqrt forall a. Floating a => a -> a
sqrt forall a. Floating a => a -> a
sqrt forall a. Floating a => a -> a
sqrt forall a. Floating a => a -> a
sqrt forall a. Floating a => a -> a
sqrt forall a. Floating a => a -> a
sqrt
sin :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g)
sin = forall a u b v c w d x e y f t g z.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (g -> z)
-> (a, b, c, d, e, f, g)
-> (u, v, w, x, y, t, z)
lift7 forall a. Floating a => a -> a
sin forall a. Floating a => a -> a
sin forall a. Floating a => a -> a
sin forall a. Floating a => a -> a
sin forall a. Floating a => a -> a
sin forall a. Floating a => a -> a
sin forall a. Floating a => a -> a
sin
cos :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g)
cos = forall a u b v c w d x e y f t g z.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (g -> z)
-> (a, b, c, d, e, f, g)
-> (u, v, w, x, y, t, z)
lift7 forall a. Floating a => a -> a
cos forall a. Floating a => a -> a
cos forall a. Floating a => a -> a
cos forall a. Floating a => a -> a
cos forall a. Floating a => a -> a
cos forall a. Floating a => a -> a
cos forall a. Floating a => a -> a
cos
sinh :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g)
sinh = forall a u b v c w d x e y f t g z.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (g -> z)
-> (a, b, c, d, e, f, g)
-> (u, v, w, x, y, t, z)
lift7 forall a. Floating a => a -> a
sinh forall a. Floating a => a -> a
sinh forall a. Floating a => a -> a
sinh forall a. Floating a => a -> a
sinh forall a. Floating a => a -> a
sinh forall a. Floating a => a -> a
sinh forall a. Floating a => a -> a
sinh
cosh :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g)
cosh = forall a u b v c w d x e y f t g z.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (g -> z)
-> (a, b, c, d, e, f, g)
-> (u, v, w, x, y, t, z)
lift7 forall a. Floating a => a -> a
cosh forall a. Floating a => a -> a
cosh forall a. Floating a => a -> a
cosh forall a. Floating a => a -> a
cosh forall a. Floating a => a -> a
cosh forall a. Floating a => a -> a
cosh forall a. Floating a => a -> a
cosh
asin :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g)
asin = forall a u b v c w d x e y f t g z.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (g -> z)
-> (a, b, c, d, e, f, g)
-> (u, v, w, x, y, t, z)
lift7 forall a. Floating a => a -> a
asin forall a. Floating a => a -> a
asin forall a. Floating a => a -> a
asin forall a. Floating a => a -> a
asin forall a. Floating a => a -> a
asin forall a. Floating a => a -> a
asin forall a. Floating a => a -> a
asin
acos :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g)
acos = forall a u b v c w d x e y f t g z.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (g -> z)
-> (a, b, c, d, e, f, g)
-> (u, v, w, x, y, t, z)
lift7 forall a. Floating a => a -> a
acos forall a. Floating a => a -> a
acos forall a. Floating a => a -> a
acos forall a. Floating a => a -> a
acos forall a. Floating a => a -> a
acos forall a. Floating a => a -> a
acos forall a. Floating a => a -> a
acos
atan :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g)
atan = forall a u b v c w d x e y f t g z.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (g -> z)
-> (a, b, c, d, e, f, g)
-> (u, v, w, x, y, t, z)
lift7 forall a. Floating a => a -> a
atan forall a. Floating a => a -> a
atan forall a. Floating a => a -> a
atan forall a. Floating a => a -> a
atan forall a. Floating a => a -> a
atan forall a. Floating a => a -> a
atan forall a. Floating a => a -> a
atan
asinh :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g)
asinh = forall a u b v c w d x e y f t g z.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (g -> z)
-> (a, b, c, d, e, f, g)
-> (u, v, w, x, y, t, z)
lift7 forall a. Floating a => a -> a
asinh forall a. Floating a => a -> a
asinh forall a. Floating a => a -> a
asinh forall a. Floating a => a -> a
asinh forall a. Floating a => a -> a
asinh forall a. Floating a => a -> a
asinh forall a. Floating a => a -> a
asinh
acosh :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g)
acosh = forall a u b v c w d x e y f t g z.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (g -> z)
-> (a, b, c, d, e, f, g)
-> (u, v, w, x, y, t, z)
lift7 forall a. Floating a => a -> a
acosh forall a. Floating a => a -> a
acosh forall a. Floating a => a -> a
acosh forall a. Floating a => a -> a
acosh forall a. Floating a => a -> a
acosh forall a. Floating a => a -> a
acosh forall a. Floating a => a -> a
acosh
atanh :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g)
atanh = forall a u b v c w d x e y f t g z.
(a -> u)
-> (b -> v)
-> (c -> w)
-> (d -> x)
-> (e -> y)
-> (f -> t)
-> (g -> z)
-> (a, b, c, d, e, f, g)
-> (u, v, w, x, y, t, z)
lift7 forall a. Floating a => a -> a
atanh forall a. Floating a => a -> a
atanh forall a. Floating a => a -> a
atanh forall a. Floating a => a -> a
atanh forall a. Floating a => a -> a
atanh forall a. Floating a => a -> a
atanh forall a. Floating a => a -> a
atanh