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symbolic computing example with Ryacas

4 messages · Vivek Sutradhara, Bert Gunter, Gabor Grothendieck

Vivek Sutradhara
# 
Hi all,
I am trying to implement the following matlab code with Ryacas :

syms U x x0 C

d1=diff(U/(1+exp(-(x-x0)/C)),x);

pretty(d1)

d2=diff(U/(1+exp(-(x-x0)/C)),x,2);

pretty(d2)

solx2 = solve(d2 == 0, x, 'Real', true)

pretty(solx2)

slope2=subs(d1,solx2)


I have tried the following :

library(Ryacas)

x <- Sym("x");U <- Sym("U");x0 <- Sym("x0");C <- Sym("C")

my_func <- function(x,U,x0,C) {

  return (U/(1+exp(-(x-x0)/C)))}

FirstDeriv <- deriv(my_func(x,U,x0,C), x)

PrettyForm(FirstDeriv)

slope <- yacas("Subst(x,x0),deriv(my_func(x,U,x0,C), x)")

PrettyForm(slope)


I don't understand how I should use the Subst command. I want the slope of
the first derivative at x=x0. How do I implement that?

I would appreciate any help that I can get.

Thanks,

Vivek
Bert Gunter
# 
Have you studied the "Introduction to Ryacas" vignette that come with the
package?

Cheers,
Bert



Bert Gunter

"The trouble with having an open mind is that people keep coming along and
sticking things into it."
-- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )

On Tue, Sep 19, 2017 at 2:37 AM, Vivek Sutradhara <viveksutra at gmail.com>
wrote:

  
  


  


      

    

    

      
      

        


  

        

      Vivek Sutradhara
    

    

      
      #
    

  


  

      
Thanks for the response. Yes, I did study the vignette but did not
understand it fully. Anyway, I have tried once again now. I am happy to say
that I have got what I wanted.

library(Ryacas)
x <- Sym("x");U <- Sym("U");x0 <- Sym("x0");C <- Sym("C")
my_func <- function(x,U,x0,C) {
  return (U/(1+exp(-(x-x0)/C)))}
FirstDeriv <- deriv(my_func(x,U,x0,C), x)
PrettyForm(FirstDeriv)
#slope <- yacas("Subst(x,x0),deriv(my_func(x,U,x0,C), x)")
slope <- Subst(FirstDeriv,x,x0)
#PrettyForm(slope) - gives errors
PrettyForm(Simplify(slope))

I was confused by the references to the yacas command.  Now, I have chosen
to omit it. Then I get what I want.
Thanks,
Vivek

2017-09-19 16:04 GMT+02:00 Bert Gunter <bgunter.4567 at gmail.com>:

            

      
      
      
    

        

      
      
    

            

      
      
      
    

        

  
  


  


      

    

    

      
      

        


  

        

      Gabor Grothendieck
    

    

      
      #
    

  


  

      
Here are some more examples:

library(Ryacas)

x <- Sym("x")
yacas("x:=2")
Eval(x*x)
## [1] 4

# vignette has similar example
y <- Sym("y")
Eval(Subst(y*y, y, 3))
## [1] 9

# demo("Ryacas-Function") has similar example to this
f <- function(z) {}
body(f) <- yacas(expression(z*z))[[1]]
f(4)
## [1] 16

        
On Tue, Sep 19, 2017 at 2:08 PM, Vivek Sutradhara <viveksutra at gmail.com> wrote: