t1=: >: -: > +. = |
(Dyad only) The primitive >: is
identical to greater than or equal |
t2=: <. -: -@>.&- |
(Both) Lesser-of is neg on greater-of on neg; Floor is neg
on ceiling on neg |
t3=: <. -: >.&.- |
Same as t2 but uses under |
t4=: *:@>: -: *: + +: + 1: |
(Monad) Square of a+1 is square of a plus
twice a plus 1 |
t5=: *:@>: -: #.&1 2 1"0 |
Same as t4 using polynomial |
t6=: ^&3@>: -: #.&1 3 3 1"0 |
Like t5 for cube |
bc=: i.@>: ! ] |
Binomial coefficients |
t7=: (>:@]^[) -: (]#.bc@[)"0 |
Like t6 with k&t7 for kth power |
s=: 1&o. |
Sine |
c=: 2&o. |
Cosine |
t8=: s@+-:(s@[*c@])+(c@[*s@]) |
(Dyad) Addition and Subtraction |
t9=: s@--:(s@[*c@])-(c@[*s@]) |
Formulas for sine |
det=: -/ . * |
Determinant |
perm=: +/ . * |
Permanent |
sct=: 1 2&o."0@(,"0) |
Sine and cosine tables |
t10=: s@- -: det@sct |
Same as t9 but using the determinant of
the sin and cos table |
t11=: s@+ -: perm@sct |
Like t8 using the permanent |
S=: 5&o. |
Hyperbolic sine |
C=: 6&o. |
Hyperbolic cosine |
SCT=: 5 6&o."0@(,"0) |
Sinh and Cosh table |
t12=: S@+ -: perm@SCT |
Addition theorem for sinh |
SINH=: ^ .: - |
Odd part of exponential |
COSH=: ^ .. - |
Even part of exponential |
t13=: SINH -: S |
Sinh is odd part of exponential |
t14=: COSH -: C |
Cosh is the even part of exponential |
sine=: ^&.j. .: - |
Sine is the odd part of exponential |
t15=: sine -: s |
under multiplication by 0j1 |