HP Forums - Wronskian of a matrix

hi,
with this program one can calculate wronskian of a matrix.
The CAS program produce the determinant or the matrix of wronskian.

Thanks to Han to have reviewed the program for me!

Syntax:
wronskm([f1,f2,...,fn])
wronskf(fun)

Salvo

Code:

#cas

// Salvo and Han, 2015

wronskm(f):=

BEGIN

  local s,v,m;

  s:=SIZE(f);

  IF s==0 OR TYPE(f)<>6 THEN RETURN("wronskm([f1,f2,...,fn])"); END;

  IF TYPE(s) THEN RETURN("wronskm: expecting vector of functions"); END;

  v:=lname(f);

  IF SIZE(v)<>1 THEN RETURN("wronskm: expecting single-variable functions"); END; 

  v:=v(1);

  m:=makemat((r,c)->diff(f(c),v$(r-1)),s,s);

  return m;

END;

wronsk(f):=

BEGIN

  local m;

  m:=wronskm(f);

  IF TYPE(m)==2 THEN

    return m;

  ELSE

    return det(m);

  END;

END;

#end

(06-15-2015 12:35 PM)compsystems Wrote: [ -> ]Good
+1

thank you!
it helped me very much.
Thanks also to Han that improved it for me!
Salvo

I have installed the program and can not get it to run. It shows no errors. Any help please.

(10-24-2016 02:48 PM)JB1414 Wrote: [ -> ]I have installed the program and can not get it to run. It shows no errors. Any help please.

you must operate in CAS mode.
Use the program from Vars -> CAS -> (both "All" or "Programs" list are ok).
i.e
wronsk([3*x,x^2]) -> 3*x^2
wronskm([3*x,x^2]) -> a matrix [3*x,x^2; 3,2*x]
No other.
Try and let me know.

Salvo

(06-03-2015 02:36 PM)salvomic Wrote: [ -> ]hi,
with this program one can calculate wronskian of a matrix.
The CAS program produce the determinant or the matrix of wronskian.

Thanks to Han to have reviewed the program for me!

Syntax:
wronskm([f1,f2,...,fn])
wronskf(fun)

Salvo

Code:

#cas // Salvo and Han, 2015 wronskm(f):= BEGIN local s,v,m; s:=SIZE(f); IF s==0 OR TYPE(f)<>6 THEN RETURN("wronskm([f1,f2,...,fn])"); END; IF TYPE(s) THEN RETURN("wronskm: expecting vector of functions"); END; v:=lname(f); IF SIZE(v)<>1 THEN RETURN("wronskm: expecting single-variable functions"); END; v:=v(1); m:=makemat((r,c)->diff(f(c),v$(r-1)),s,s); return m; END; wronsk(f):= BEGIN local m; m:=wronskm(f); IF TYPE(m)==2 THEN return m; ELSE return det(m); END; END; #end

Hi, thanks for the program, but I have a question.

How can I enter trigonometric values in the "f" functions?

Wronskm ([sin (x), cos (x)])

thx

(05-06-2017 01:34 AM)Fernando Wrote: [ -> ]Hi, thanks for the program, but I have a question.

How can I enter trigonometric values in the "f" functions?

Wronskm ([sin (x), cos (x)])

thx

hi Fernando,
sorry for the delay in reply...
You can simply do so:
• type wronskm() or choose it from Vars/Programs
• wronskm([])
•wronskm([SIN(x), COS(x)])
using the functions SIN, COS in the key H and I, insert x via the key D in both, and separate them with the comma (key O).
You'll get a matrix:
\[
\begin{bmatrix}
SIN(x) & COS(x) \\
COS(x) & -SIN(x)
\end{bmatrix}
\]

Please, let me know if it helps.

Salvo

Great program salvomic and Han!

(11-04-2017 02:20 PM)Eddie W. Shore Wrote: [ -> ]Great program salvomic and Han!

thanks, Eddie! :-)