Euler's Identity in 3
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So, I'm trying to learn Rust. And in thinking about the ontological status of mathematical representations of waves (https://arxiv.org/abs/2101.10873), I figured I'd validate Euler's identity:
fn main() { let e = num::complex::Complex::new(std::f32::consts::E,0.); let e2ip = e.powc(num::complex::Complex::new(0.,std::f32::consts::PI)); let i = num::complex::Complex::new(0.,1.); println!("ln(e^iπ) = {}",e2ip.ln()); println!("ln(-1) = {}", i.powi(2).ln()); } $ cargo run ln(e^iπ) = 0+3.1415925i ln(-1) = 0+3.141592653589793i I don't have any idea if that's a reasonable way to do that, since I'm ignorant of Rust. But it's interesting to contrast it with R and Sage: $ Rscript -e "log(exp(1)^((0+1i)*pi));log((0+1i)^2)" [1] 0+3.141593i [1] 0+3.141593i sage: numerical_approx(ln(e^(i*pi)));numerical_approx(ln(i^2)) 3.14159265358979*I 3.14159265358979*I The precision difference between the 2 results in Rust is interesting. It's the same if I use powf() instead of powi(). Any clues? Or should I simply RTFM? -- ↙↙↙ uǝlƃ - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ archives: http://friam.471366.n2.nabble.com/
uǝʃƃ ⊥ glen
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Bah! I'm an idiot. If I use f64, I get:
ln(e^iπ) = 0+3.141592653589793i ln(-1) = 0+3.141592653589793i On 3/9/21 12:54 PM, uǝlƃ ↙↙↙ wrote: > So, I'm trying to learn Rust. And in thinking about the ontological status of mathematical representations of waves (https://arxiv.org/abs/2101.10873), I figured I'd validate Euler's identity: > > fn main() { > let e = num::complex::Complex::new(std::f32::consts::E,0.); > let e2ip = e.powc(num::complex::Complex::new(0.,std::f32::consts::PI)); > let i = num::complex::Complex::new(0.,1.); > println!("ln(e^iπ) = {}",e2ip.ln()); > println!("ln(-1) = {}", i.powi(2).ln()); > } > $ cargo run > ln(e^iπ) = 0+3.1415925i > ln(-1) = 0+3.141592653589793i > > I don't have any idea if that's a reasonable way to do that, since I'm ignorant of Rust. But it's interesting to contrast it with R and Sage: > > $ Rscript -e "log(exp(1)^((0+1i)*pi));log((0+1i)^2)" > [1] 0+3.141593i > [1] 0+3.141593i > > sage: numerical_approx(ln(e^(i*pi)));numerical_approx(ln(i^2)) > 3.14159265358979*I > 3.14159265358979*I > > The precision difference between the 2 results in Rust is interesting. It's the same if I use powf() instead of powi(). Any clues? Or should I simply RTFM? > -- ↙↙↙ uǝlƃ - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ archives: http://friam.471366.n2.nabble.com/
uǝʃƃ ⊥ glen
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In reply to this post by gepr
Or,
$ ginsh ginsh - GiNaC Interactive Shell (GiNaC V1.7.11) __, _______ Copyright (C) 1999-2020 Johannes Gutenberg University Mainz, (__) * | Germany. This is free software with ABSOLUTELY NO WARRANTY. ._) i N a C | You are welcome to redistribute it under certain conditions. <-------------' For details type `warranty;'. Type ?? for a list of help topics. > exp(Pi*I); -1 > -----Original Message----- From: Friam <[hidden email]> On Behalf Of u?l? ??? Sent: Tuesday, March 9, 2021 12:55 PM To: FriAM <[hidden email]> Subject: [FRIAM] Euler's Identity in 3 So, I'm trying to learn Rust. And in thinking about the ontological status of mathematical representations of waves (https://arxiv.org/abs/2101.10873), I figured I'd validate Euler's identity: fn main() { let e = num::complex::Complex::new(std::f32::consts::E,0.); let e2ip = e.powc(num::complex::Complex::new(0.,std::f32::consts::PI)); let i = num::complex::Complex::new(0.,1.); println!("ln(e^iπ) = {}",e2ip.ln()); println!("ln(-1) = {}", i.powi(2).ln()); } $ cargo run ln(e^iπ) = 0+3.1415925i ln(-1) = 0+3.141592653589793i I don't have any idea if that's a reasonable way to do that, since I'm ignorant of Rust. But it's interesting to contrast it with R and Sage: $ Rscript -e "log(exp(1)^((0+1i)*pi));log((0+1i)^2)" [1] 0+3.141593i [1] 0+3.141593i sage: numerical_approx(ln(e^(i*pi)));numerical_approx(ln(i^2)) 3.14159265358979*I 3.14159265358979*I The precision difference between the 2 results in Rust is interesting. It's the same if I use powf() instead of powi(). Any clues? Or should I simply RTFM? -- ↙↙↙ uǝlƃ - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ archives: http://friam.471366.n2.nabble.com/ - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ archives: http://friam.471366.n2.nabble.com/ |
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From the (hilarious) FAQ:
$ for i in `seq 1 100`; do echo "a = x; b = y; x-y;"|ginsh; done |sort -n |uniq x x-y y -y+x I think I'm in love! On 3/9/21 2:20 PM, Marcus Daniels wrote: > Or, > > $ ginsh > ginsh - GiNaC Interactive Shell (GiNaC V1.7.11) > __, _______ Copyright (C) 1999-2020 Johannes Gutenberg University Mainz, > (__) * | Germany. This is free software with ABSOLUTELY NO WARRANTY. > ._) i N a C | You are welcome to redistribute it under certain conditions. > <-------------' For details type `warranty;'. > > Type ?? for a list of help topics. >> exp(Pi*I); > -1 >> > -- ↙↙↙ uǝlƃ - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ archives: http://friam.471366.n2.nabble.com/
uǝʃƃ ⊥ glen
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