Dimiter Prodanov | 28 Jun 00:31 2016
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unusual behavior wrt declare

Dear all,

I want to emulate Grassmann's outer product.
So I use the following declaration:

infix("~", 135, 134);
declare("~", linear);

However, expand does not recognize the new operator

>> e[1]~ (e[2]+5),expand;

e[1]~(5+e[2])

I use the "." symbol for a Clifford multiplication so it is not an option to change the symbol.

How can I make expand recognize custom infix operators?

best regards,

Dimiter
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Pierre Cyr | 21 Jun 14:58 2016

diff behavior after loading itensor

Hi,

 

It seems that after loading itensor, the function of a constant value (thus, also a constant) derived by a variable with an index is not evaluated to the expected 0 value.

 

Maxima 5.38.1 http://maxima.sourceforge.net

using Lisp SBCL 1.3.4

Distributed under the GNU Public License. See the file COPYING.

Dedicated to the memory of William Schelter.

The function bug_report() provides bug reporting information.

(%i1) declare(beta,constant);

(%o1)                                done

(%i2) diff(beta,x);

(%o2)                                  0

(%i3) diff(beta,x[1]);

(%o3)                                  0

(%i4) diff(cos(beta),x);

(%o4)                                  0

(%i5) diff(cos(beta),x[1]);

(%o5)                                  0

(%i6) load(itensor);

WARNING: redefining MAXIMA::$NAME in DEFUN

WARNING: redefining MAXIMA::DERIV in DEFUN

WARNING: redefining MAXIMA::SDIFF in DEFUN

WARNING: redefining MAXIMA::I-$DEPENDENCIES in DEFUN

WARNING: redefining MAXIMA::$DECSYM in DEFUN

WARNING: redefining MAXIMA::$CANFORM in DEFUN

(%o6) D:/Maxima-sbcl-5.38.1/share/maxima/5.38.1/share/tensor/itensor.lisp

(%i7) diff(beta,x);

(%o7)                                  0

(%i8) diff(beta,x[1]);

(%o8)                                  0

(%i9) diff(cos(beta),x);

(%o9)                                  0

(%i10) diff(cos(beta),x[1]);

                                 d

(%o10)                          --- (cos(beta))

                                dx

                                  1

 

 

Best Regards,

 

 

Pierre Cyr

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raihaneh moti | 24 Jun 10:43 2016
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help

 I use contrib_ode package to solve differential equations. But it seems that it does nothing to nonlinear equations. Does Maxima have any other  package for solving non-linear equations like
    'diff(y,x,2)*x^2 + (1/(2*sinh(x/2)-1)*(x^2/y)*'diff(y,x,1)-(x^2/y)*'diff(y,x,1)^2+y^3+x=0


--
R. Moti
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Alex Leontiev | 19 Jun 06:43 2016
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How polynomial factorization is implemented?

Hi, all

Sorry to bother, I have a brief question. If possible, I'd like to know how factor() procedure (for *multivariable* polynomials) is implemented in Maxima.

More concretely, I'd like to know whether if factor() does not change its input, does this mean that there is no factorization, ie. that polynomial is irred over integers? Or is there any possibility that algorithm just "gives up"?

Best Regards,
Alex
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Daniel Volinski | 23 Jun 18:43 2016
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Still eigenvectors

Hi All,

I installed the latest version of Maxima (5.38.1) and I noticed the eigenvector problem has not been solved yet. Here is an example:

load(eigen)$
M:matrix([1,2,5],[2,4,10],[3,6,15]);
eigenvectors(M);

the result: it misses the last eigenvector.

Thanks,

Daniel Volinski


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Yury | 23 Jun 17:56 2016
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command-line arguments for the maxima script?

Hi all,

Is there something in modern Maxima allowing for command-line arguments
parsing in Maxima script? For the sort of use scenario which I think was
discussed here years ago:

maxima -b script.mc -- a b c

The net search seems to be of opinion there is no such thing available
(boiling down to: http://rosettacode.org/wiki/Category:Maxima/Omit), and
there seems to be nothing likely in man page and in Maxima manual.

Are there other easy ways of passing parameters into maxima script?
Environment variables?

-Yury

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Richard Fateman | 23 Jun 14:09 2016
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Fwd: computing hypergeometric functions rigorously

---------- Forwarded message ----------
From: <Paul.Zimmermann <at> loria.fr>
Date: Jun 23, 2016 1:34 AM
Subject: computing hypergeometric functions rigorously
To: <STDS-1788 <at> listserv.ieee.org>
Cc:

       Hi,

this new preprint might be interesting to the P1788 community:

Computing hypergeometric functions rigorously
by Fredrik Johansson
http://arxiv.org/abs/1606.06977

We present an efficient implementation of hypergeometric functions in arbitrary-precision interval arithmetic. The functions 0F1, 1F1, 2F1 and 2F0 (or the Kummer U-function) are supported for unrestricted complex parameters and argument, and by extension, we cover exponential and trigonometric integrals, error functions, Fresnel integrals, incomplete gamma and beta functions, Bessel functions, Airy functions, Legendre functions, Jacobi polynomials, complete elliptic integrals, and other special functions. The output can be used directly for interval computations or to generate provably correct floating-point approximations in any format. Performance is competitive with earlier arbitrary-precision software, and sometimes orders of magnitude faster. We also partially cover the generalized hypergeometric function pFq and computation of high-order parameter derivatives.

Paul Zimmermann
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Gunter Königsmann | 22 Jun 09:04 2016
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abs() and cabs()

Dear all,

Just for interest:

wxMaxima from time to time gets bug reports that can be solved by
replacing abs() by cabs(). One example is the following one:

f(x):=abs(x+%i)^2;
plot2d(realpart(f(x)),[x,-1,1]);

As f(x) is >0 realpart(f(x)) should be >0, as well and the documentation
tells abs() to be able to cope with complex numbers.

Is this a bug?

What I did about it just now was adding a cross-reference from abs() to
cabs to the manual.

Kind regards,

  Gunter.

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José A. Vallejo Rodríguez | 21 Jun 05:00 2016
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load(lapack) fails

Hi all:
This is my setting:

Maxima 5.38.0
SBCL 1.3.5
Slackware 14.1 64bits

When doing load(lapack) I get the error

(%i1) load(lapack);

;; loading #P"/home/jvallejo/.maxima/binary/5_38_0/sbcl/1_3_5/share/lapack/lapack-package.fasl"
;; loading #P"/home/jvallejo/.maxima/binary/5_38_0/sbcl/1_3_5/share/lapack/blas/daxpy.fasl"
;; loading #P"/home/jvallejo/.maxima/binary/5_38_0/sbcl/1_3_5/share/lapack/blas/dcopy.fasl"
(several similar lines)
;; loading #P"/home/jvallejo/.maxima/binary/5_38_0/sbcl/1_3_5/share/lapack/lapack/dlasq2.fasl"
;; loading #P"/home/jvallejo/.maxima/binary/5_38_0/sbcl/1_3_5/share/lapack/lapack/dlasq1.fasl"
;; loading #P"/home/jvallejo/.maxima/binary/5_38_0/sbcl/1_3_5/share/lapack/lapack/dlasv2.fasl"
;; loading #P"/home/jvallejo/.maxima/binary/5_38_0/sbcl/1_3_5/share/lapack/lapack/dbdsqr.fasl"
While evaluating the form starting at line 13, column 0
  of #P"/usr/share/maxima/5.38.0/share/lapack/load-lapack.lisp":;
                                                                ; compilation unit aborted
                                                                ;   caught 1 fatal ERROR condition
;
; compilation unit aborted
;   caught 1 fatal ERROR condition
;
; compilation unit aborted
;   caught 1 fatal ERROR condition
loadfile: failed to load /usr/share/maxima/5.38.0/share/lapack/load-lapack.lisp
 -- an error. To debug this try: debugmode(true);

Looking at line 13 of load-lapack.lisp i see

(mk:oos "lapack-interface" :compile)

But lapack-interface is absent from the /usr/share/maxima/5.38.0/share/lapack/ directory.
How can I fix this?
All the best,
--
_______________________________
José Antonio Vallejo

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sholman | 20 Jun 23:49 2016
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implicit function and its Taylor series by hand

Hello All, I wasn't able to get impdiff to work - I didn't try very hard
because I, at first, want to see it being done step by step (sort of).

My toy model equation is;

eq(x,y):=y+x+3+x*y+x^2*y+x*y^2+x^2*y^2+x^2*y^3;

/*and I want to find y(x) near one of the points (say the first one);*/

bp: solve([eq(x,y)=0,y=1],[x,y]);

/*So after having scanned Ch.6 of Ted Woolet's pdf, I did this;*/

depends(y,x)$
gradef(y(x),dydx)$

/*Then to calculate the first derivative:*/

diff(eq(x,y(x)),x);
at(%,x=rhs(bp[1][1]));
at(%,y(rhs(bp[1][1]))=rhs(bp[1][2]));
firstCoef: solve(%,dydx); /* a number */

/*Then the second derivative;*/

diff(eq(x,y(x)),x,2);

/*yielding;*/

2*y(x)^3+12*dydx*x*y(x)^2+2*y(x)^2+6*dydx^2*x^2*y(x)+8*dydx*x*y(x)+4*dydx*y(x)+2*y(x)+2*dydx^2*x^2+2*dydx^2*x+4*dydx*x+2*dydx

/*then,*/

at(%,x=rhs(bp[1][1]));
at(%,y(rhs(bp[1][1]))=rhs(bp[1][2]));

/*which yields;*/

out:(2*(sqrt(39)*%i+3)^2*dydx^2)/9-((sqrt(39)*%i+3)*dydx^2)/3-4*(sqrt(39)*%i+3)*dydx+6*dydx+6

I know that dydx (the first derivative by gradef()) is just the number
above, but if I subst() in that value for dydx, the dydx^2 terms will
become a number too, when in fact these are supposed to be the second
derivatives at this spot.

How can I set dydx to the above number, firstCoef, without setting the
second derivative to this number squared?

Thank you!

Maybe there is an even better way...?

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Richard Fateman | 15 Jun 19:04 2016
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if you want to do fractional derivatives etc

Here's a start ...

matchdeclare(r,notint,[ff,vv],true);
notint(z):=is  not(integerp(z));

tellsimpafter('diff(ff,vv,r) ,  general_diff(ff,vv,r));

then define  general_diff  etc.
(you might wish to modify the definition of notint)

There seem to be several different models for fractional derivatives in the
literature, and even after choosing one, I suspect that one would be 
faced with many decisions
about the "best" representation of expressions by traditional special 
functions
or fractional derivatives.  So the naive approach -- to drop in a definition
for general_diff chosen from some reference  as the program
for general_diff -- is unlikely to be of much use.  But there's no 
particular
problem in inserting this kind of stuff into Maxima.
So we could easily define  diff(sin(x),x,1/2)   or even diff(sin(x),x,%pi),
if that's of interest.

RJF

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