 CAS: Hyperoblic CAS Transformations - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: HP Software Libraries (/forum-10.html) +--- Forum: HP Prime Software Library (/forum-15.html) +--- Thread: CAS: Hyperoblic CAS Transformations (/thread-14060.html) CAS: Hyperoblic CAS Transformations - Eddie W. Shore - 11-27-2019 01:58 PM sinhexp sinhexp(ϕ) = (e^(ϕ) - e^(-ϕ)) / 2 = ((e^ϕ)^2 - 1) / (2 * e^ϕ) Code: ``` #cas sinhexp(f):= BEGIN RETURN (e^(f)-e^(−f))/2 END; #end``` coshexp coshexp(ϕ) = (e^(ϕ) + e^(-ϕ)) / 2 = ((e^ϕ)^2 + 1) / (2 * e^ϕ) Code: ``` #cas coshexp(f):= BEGIN RETURN (e^(f)+e^(−f))/2 END; #end``` tanhexp tanhexp(ϕ) = (e^(ϕ) - e^(-ϕ)) / (e^(ϕ) + e^(-ϕ)) Code: ``` #cas tanhexp(f):= BEGIN RETURN (e^(f)-e^(−f))/ (e^(f)+e^(−f)) END; #end``` Adding Properties addsinh addsinh(ϕ + Ω) = sinh ϕ * cosh Ω + sinh Ω * cosh ϕ Code: ``` #cas addcosh(f,g):= BEGIN RETURN COSH(f)*COSH(g)+ SINH(f)*SINH(g); END; #end``` addcosh addcosh(ϕ + Ω) = csoh ϕ * cosh Ω + sinh Ω * sinh ϕ Code: ``` #cas addsinh(f,g):= BEGIN RETURN SINH(f)*COSH(g)+ COSH(f)*SINH(g); END; #end``` addtanh addtanh(ϕ + Ω) = (tanh ϕ + tanh Ω) / (1 + tanh ϕ * tanh Ω) Code: ``` #cas addtanh(f,g):= BEGIN RETURN (TANH(f)+TANH(g))/ (1+TANH(f)*TANH(g)); END; #end``` Squaring Properties sqsinh sqsinh(ϕ) = sinh^2 ϕ = 1/2 * cosh(2 * ϕ) - 1/2 Code: ``` #cas sqsinh(f):= BEGIN RETURN COSH(2*f)/2-1/2; END; #end``` sqcosh sqcosh(ϕ) = cosh^2 ϕ = 1/2 * cosh(2 * ϕ) + 1/2 Code: ``` #cas sqcosh(f):= BEGIN RETURN COSH(2*f)/2+1/2; END; #end``` Product Properties sinhsinh sinhsinh(ϕ, Ω) = 1/2 * (cosh(ϕ + Ω) - cosh(ϕ - Ω)) Code: ``` #cas sinhsinh(f,g):= BEGIN RETURN 1/2*(COSH(f+g)- COSH(f-g)); END; #end``` coshcosh coshcosh(ϕ, Ω) = 1/2 * (cosh(ϕ + Ω) + cosh(ϕ - Ω)) Code: ``` #cas coshcosh(f,g):= BEGIN RETURN 1/2*(COSH(f+g)+ COSH(f-g)); END; #end``` sinhcosh sinhcosh(ϕ, Ω) = 1/2 * (sinh(ϕ + Ω) + sinh(ϕ - Ω)) Code: ``` #cas sinhcosh(f,g):= BEGIN RETURN 1/2*(SINH(f+g)+ SINH(f-g)); END; #end``` Source: Spiegel, Murray R. and Seymour Lipschutz, John Liu. Schuam's Outlines: Mathematical Handbook of Formulas and Tables 5th Edition McGraw Hill: New York 2018 ISBN 978-1-260-01053-4 Blog Link: http://edspi31415.blogspot.com/2019/11/hp-prime-hyperoblic-cas-transformations.html RE: CAS: Hyperoblic CAS Transformations - compsystems - 11-27-2019 02:34 PM I hope that in a next XCAS launch they are embedded by default, that is, without the need to load libraries, almost all CASs have pre-included functions.