/usr/share/axiom-20170501/src/algebra/HYPCAT.spad is in axiom-source 20170501-3.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 | )abbrev category HYPCAT HyperbolicFunctionCategory
++ Date Last Updated: 14 May 1991
++ Category for the hyperbolic trigonometric functions;
HyperbolicFunctionCategory() : Category == SIG where
SIG ==> with
cosh : $ -> $
++ cosh(x) returns the hyperbolic cosine of x.
coth : $ -> $
++ coth(x) returns the hyperbolic cotangent of x.
csch : $ -> $
++ csch(x) returns the hyperbolic cosecant of x.
sech : $ -> $
++ sech(x) returns the hyperbolic secant of x.
sinh : $ -> $
++ sinh(x) returns the hyperbolic sine of x.
tanh : $ -> $
++ tanh(x) returns the hyperbolic tangent of x.
add
if $ has Ring then
csch x ==
(a := recip(sinh x)) case "failed" => error "csch: no reciprocal"
a::$
sech x ==
(a := recip(cosh x)) case "failed" => error "sech: no reciprocal"
a::$
tanh x == sinh x * sech x
coth x == cosh x * csch x
if $ has ElementaryFunctionCategory then
cosh x ==
e := exp x
(e + recip(e)::$) * recip(2::$)::$
sinh(x):$ ==
e := exp x
(e - recip(e)::$) * recip(2::$)::$
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