## 25 Reputation

16 years, 79 days

## MaplePrimes Activity

### These are replies submitted by jfitzsimons

Thank you, radical works. Maple can not do cos(Pi/17). Maple can only do cos(n*Pi/120). Here is an example. How can I find the exact solution? > a20:=cos(Pi/17) = sqrt(sqrt(38*sqrt(17) + 170) + 3*sqrt(17) + 17)/8 + sqrt(34 - 2*sqrt(17))/16 - sqrt(17)/16 + 1/16: > evalf(a20); .9829730997 = .9829730994 > convert(a20,radical); cos(1/17*Pi) = 1/8*((38*17^(1/2)+170)^(1/2)+3*17^(1/2)+17)^(1/2)+1/16*(34-2*17^(1/2))^(1/2)-1/16*17^(1/2)+1/16 > convert(cos(Pi/15),radical); 1/8*2^(1/2)*3^(1/2)*(5+5^(1/2))^(1/2)+1/8*5^(1/2)-1/8 > convert(cos(Pi/17),radical); cos(1/17*Pi) > I can do cos(Pi/16) > a21:=convert(cos(Pi/8),radical); a21 := 1/2*(2+2^(1/2))^(1/2) > convert(cos(Pi/16),radical); cos(1/16*Pi) > a22:=cos(Pi/16)=sqrt((1+a21)/2); a22 := cos(1/16*Pi) = 1/2*(2+(2+2^(1/2))^(1/2))^(1/2) > evalf(a22); .9807852804 = .9807852805 > Regards, Jim FitzSimons

## Rpn...

A RPN language is FORTH. It is interactive and could be used on a Computer Algebra System calculator. The first CAS was Macsyma and it was programed in LISP. LISP is interactive and symbolic and could be used on a CAS calculator. The TI-92 and TI-89 are CAS calculators. The software in these calculators came from the developers of the CAS DERIVE, which was programmed in MuLISP. Jim FitzSimons

## Rpn...

A RPN language is FORTH. It is interactive and could be used on a Computer Algebra System calculator. The first CAS was Macsyma and it was programed in LISP. LISP is interactive and symbolic and could be used on a CAS calculator. The TI-92 and TI-89 are CAS calculators. The software in these calculators came from the developers of the CAS DERIVE, which was programmed in MuLISP. Jim FitzSimons

## Elliptic integral...

Georgios Kokovidis, thank you, it works. I could not find Int in the Maple help. Here is an example using Symmetric Elliptic integrals. > c12:=2*sqrt(2)*Int(sqrt(3*t^2-2*t*(sqrt(2)+2)+2*sqrt(2)+3)*sqrt(3*t^2*(17-12*sqrt(2))+2*t*(29*sqrt(2)-41)-24*sqrt(2)+34),t=0..1): > > evalf(c12,32); 1.5710166980738556513064017544217 > c26:=IHAT(e1+e2+e3+e4)=(572*SQRT(2)/2187+797/2187)*R_D(52*SQRT(2)/9+74/9,20*SQRT(2)/3+86/9,64*SQRT(2)/9+95/9)+(64*SQRT(2)/81+95/81)*R_F(64*SQRT(2)/9+95/9,52*SQRT(2)/9+74/9,20*SQRT(2)/3+86/9)+5*SQRT(2)/27+5/18: > SQRT:=proc(x) sqrt(x) end proc: > R_F:=proc(x,y,z) int(t/sqrt((t^2+x)*(t^2+y)*(t^2+z)),t=0..infinity) end proc: > R_J:=proc(x,y,z,p) 3*int(t/(sqrt((t^2+x)*(t^2+y)*(t^2+z))*(t^2+p)),t=0..infinity) end proc: > R_D:=proc(x,y,z) R_J(x,y,z,z) end proc: > c1:=length=(18*SQRT(2)-24)*IHAT(e1+e2+e3+e4): > c2:=subs(c26,c1): > evalf(c2,32); length = 1.5710166980738556513064017544222 > Regards, Jim FitzSimons

## Elliptic integral...

Georgios Kokovidis, thank you, it works. I could not find Int in the Maple help. Here is an example using Symmetric Elliptic integrals. > c12:=2*sqrt(2)*Int(sqrt(3*t^2-2*t*(sqrt(2)+2)+2*sqrt(2)+3)*sqrt(3*t^2*(17-12*sqrt(2))+2*t*(29*sqrt(2)-41)-24*sqrt(2)+34),t=0..1): > > evalf(c12,32); 1.5710166980738556513064017544217 > c26:=IHAT(e1+e2+e3+e4)=(572*SQRT(2)/2187+797/2187)*R_D(52*SQRT(2)/9+74/9,20*SQRT(2)/3+86/9,64*SQRT(2)/9+95/9)+(64*SQRT(2)/81+95/81)*R_F(64*SQRT(2)/9+95/9,52*SQRT(2)/9+74/9,20*SQRT(2)/3+86/9)+5*SQRT(2)/27+5/18: > SQRT:=proc(x) sqrt(x) end proc: > R_F:=proc(x,y,z) int(t/sqrt((t^2+x)*(t^2+y)*(t^2+z)),t=0..infinity) end proc: > R_J:=proc(x,y,z,p) 3*int(t/(sqrt((t^2+x)*(t^2+y)*(t^2+z))*(t^2+p)),t=0..infinity) end proc: > R_D:=proc(x,y,z) R_J(x,y,z,z) end proc: > c1:=length=(18*SQRT(2)-24)*IHAT(e1+e2+e3+e4): > c2:=subs(c26,c1): > evalf(c2,32); length = 1.5710166980738556513064017544222 > Regards, Jim FitzSimons

## stats...

The old package is easier to use. I can not understand the help for the new package. Here is an example. > data:=[0.0630, 0.1050, 0.1560]: > with(stats): > with(Statistics): > StandardDeviation(data); 0.04657252409 > describe[standarddeviation](data); 0.03802630668 > describe[standarddeviation](data); 0.04657252409 > describe[mean](data); 0.1080000000 > describe[median](data); 0.1050 > Jim FitzSimons

## stats...

The old package is easier to use. I can not understand the help for the new package. Here is an example. > data:=[0.0630, 0.1050, 0.1560]: > with(stats): > with(Statistics): > StandardDeviation(data); 0.04657252409 > describe[standarddeviation](data); 0.03802630668 > describe[standarddeviation](data); 0.04657252409 > describe[mean](data); 0.1080000000 > describe[median](data); 0.1050 > Jim FitzSimons

## Stats...

Use both untill you get a better answer. Both packages work at the same time. Here is an example. > data:=[0.0630, 0.1050, 0.1560]: > with(stats): > with(Statistics): > StandardDeviation(data); 0.04657252409 > describe[standarddeviation](data); 0.03802630668 > Jim FitzSimons

## Stats...

Use both untill you get a better answer. Both packages work at the same time. Here is an example. > data:=[0.0630, 0.1050, 0.1560]: > with(stats): > with(Statistics): > StandardDeviation(data); 0.04657252409 > describe[standarddeviation](data); 0.03802630668 > Jim FitzSimons

## lists...

Thank you, J. Tarr it works. Jim FitzSimons

## lists...

Thank you, J. Tarr it works. Jim FitzSimons
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