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Subject: [Axiom-developer] alternative geometry/graphics framework
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I have written an alternative geometry/graphics framework.
I have put links to the code and documentation at the bottom of this
page here:
http://www.euclideanspace.com/maths/standards/program/mycode/graph/
It is based on a scenegraph structure which allows
lines, surfaces and higher dimensional structures to be defined and
modified by transforms, clipping boxes, material (line width, colour and
so on) which control individual nodes or whole branches in the
scenegraph. This means that, for example, transforms can be applied
continuously to a whole branch without altering the nodes in that branch,
this means that we can avoid a cumulative build up of floating point errors
when many transforms are applied.
This framework supports all the 2D and 3D draw and plotting that the
existing framework supports. Use of transforms in the scenegraph means that
many plots can be combined together, either overlayed or next to each other
and combined with various show scales, grids text annotations and so on.
The framework supports:
* Different algebras: vector, matrix, complex numbers and Clifford Algebra.
* Different geometries: Euclidean, projective, conformal (hyperbolic to be
added later)
* Different coordinate systems: Cartesian coordinates, Argand Plane,
Spherical, Cylindrical.
* Different number of dimensions: 2,3 (4 and more to be added)
The aim is not just to draw plots but also to allow experimentation with
arbitrary shapes being transformed, for instance to transform a given shape
by reflecting in a circle. To see the sort of thing I am trying to do here
see first chapter of [Dorst,Fontijne & Mann 2007] except this is not just
limited to Clifford algebra and conformal space.
Currently Axiom/FriCAS has domains that represent transforms:
(for example: dhmatrix.spad.pamphlet, moebius.spad.pamphlet and so on) but
they are just standalone domains which don't fit into a wider graphics
framework so it is more difficult to combine them with other things and
to experiment. The aim of this framework is to create a way for geometry
and graphics related entities to interwork.
This scenegraph framework currently exports to file formats like: SVG,X3D,
VRML and Wavefront(obj) but currently there is not the capability to interact
directly in a graphical way, that is, there is no xwindow support. The
existing graphics framework allows user interaction in a very limited way in
that the graphics can be displayed in an xwindow and there is then the
ability to do simple transforms like pan and zoom.
However this is not suitable for the new framework because the existing
framework builds a data structure to represent the graphics
using SPAD and then passes this to 'C' code. The 'C' code then does the pan,
zoom and so on and can then save to a file format.
Apart from being very messy trying to mix different languages, this would not
work for the new framework because:
* We want to use non-linear as well as linear transforms.
* I would like to be able to work with discontinuous (fractal) shapes.
* I want to use different algebras such as vector, matrix, complex numbers
and Clifford algebras and I would not want to implement these algebras
using 'C'.
Possible options might be:
* Implement an OpenGL canvas in SPAD which allows SPAD to directly output to
OpenGL (a thin wrapper for OpenGL calls) and also to read and process mouse
position.
* Implement Axiom/FriCAS as library code that can be called from other
languages.
* Implement some form of two-way API which allows other programs to use SPAD
algebra.
Bill Page mentioned that there is an OpenGL binding for lisp.
http://common-lisp.net/project/cl-opengl/
http://repo.or.cz/w/cl-glfw.git
Would it be possible to create a thin wrapper to allow these functions to be
called from SPAD?
OpenGL consists of a couple of hundred function calls but this would only need
a small subset of those (because transforms would be done by SPAD and not
OpenGL).
We would also need the ability to read mouse movements from SPAD to allow user
interaction.
Do you think this would be possible?
Martin
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From: Tim Daly
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To: Martin Baker
Subject: Re: [Axiom-developer] alternative geometry/graphics framework
References: <4B5B3779.4060900@axiom-developer.org> <4B6436F5.3060201@axiom-developer.org> <201001301618.50345.ax87438@martinb.com>
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I'll look into it as soon as I'm able. --Tim
Martin Baker wrote:
> I have written an alternative geometry/graphics framework.
>
> I have put links to the code and documentation at the bottom of this
> page here:
> http://www.euclideanspace.com/maths/standards/program/mycode/graph/
>
> It is based on a scenegraph structure which allows
> lines, surfaces and higher dimensional structures to be defined and
> modified by transforms, clipping boxes, material (line width, colour and
> so on) which control individual nodes or whole branches in the
> scenegraph. This means that, for example, transforms can be applied
> continuously to a whole branch without altering the nodes in that branch,
> this means that we can avoid a cumulative build up of floating point errors
> when many transforms are applied.
>
> This framework supports all the 2D and 3D draw and plotting that the
> existing framework supports. Use of transforms in the scenegraph means that
> many plots can be combined together, either overlayed or next to each other
> and combined with various show scales, grids text annotations and so on.
>
> The framework supports:
> * Different algebras: vector, matrix, complex numbers and Clifford Algebra.
> * Different geometries: Euclidean, projective, conformal (hyperbolic to be
> added later)
> * Different coordinate systems: Cartesian coordinates, Argand Plane,
> Spherical, Cylindrical.
> * Different number of dimensions: 2,3 (4 and more to be added)
>
> The aim is not just to draw plots but also to allow experimentation with
> arbitrary shapes being transformed, for instance to transform a given shape
> by reflecting in a circle. To see the sort of thing I am trying to do here
> see first chapter of [Dorst,Fontijne & Mann 2007] except this is not just
> limited to Clifford algebra and conformal space.
>
> Currently Axiom/FriCAS has domains that represent transforms:
> (for example: dhmatrix.spad.pamphlet, moebius.spad.pamphlet and so on) but
> they are just standalone domains which don't fit into a wider graphics
> framework so it is more difficult to combine them with other things and
> to experiment. The aim of this framework is to create a way for geometry
> and graphics related entities to interwork.
>
> This scenegraph framework currently exports to file formats like: SVG,X3D,
> VRML and Wavefront(obj) but currently there is not the capability to interact
> directly in a graphical way, that is, there is no xwindow support. The
> existing graphics framework allows user interaction in a very limited way in
> that the graphics can be displayed in an xwindow and there is then the
> ability to do simple transforms like pan and zoom.
> However this is not suitable for the new framework because the existing
> framework builds a data structure to represent the graphics
> using SPAD and then passes this to 'C' code. The 'C' code then does the pan,
> zoom and so on and can then save to a file format.
>
> Apart from being very messy trying to mix different languages, this would not
> work for the new framework because:
> * We want to use non-linear as well as linear transforms.
> * I would like to be able to work with discontinuous (fractal) shapes.
> * I want to use different algebras such as vector, matrix, complex numbers
> and Clifford algebras and I would not want to implement these algebras
> using 'C'.
>
> Possible options might be:
> * Implement an OpenGL canvas in SPAD which allows SPAD to directly output to
> OpenGL (a thin wrapper for OpenGL calls) and also to read and process mouse
> position.
> * Implement Axiom/FriCAS as library code that can be called from other
> languages.
> * Implement some form of two-way API which allows other programs to use SPAD
> algebra.
>
> Bill Page mentioned that there is an OpenGL binding for lisp.
> http://common-lisp.net/project/cl-opengl/
> http://repo.or.cz/w/cl-glfw.git
> Would it be possible to create a thin wrapper to allow these functions to be
> called from SPAD?
> OpenGL consists of a couple of hundred function calls but this would only need
> a small subset of those (because transforms would be done by SPAD and not
> OpenGL).
> We would also need the ability to read mouse movements from SPAD to allow user
> interaction.
>
> Do you think this would be possible?
>
> Martin
>
> _______________________________________________
> Axiom-developer mailing list
> Axiom-developer@nongnu.org
> http://lists.nongnu.org/mailman/listinfo/axiom-developer
>
>
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Subject: [Axiom-developer] Axiom September 2010 Release
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Axiom has been released for September 2010.
The website has the sources and the ubuntu binary.
Other binaries are being built and will appear when they pass testing.
Tim Daly
=============================================================================
September 2010 Release
This release concentrated on treeshaking the compiler code into book volume 9.
Due to the complexity of this task it will take several releases to complete.
Additional global changes included collecting all of the Axiom-related
latex macros into axiom.sty and removing references to Aldor.
Makefile
always run help extractions in parallel
build src/input quietly
books/bookvol0
remove references to aldor
books/bookvol1
remove references to aldor
books/bookvol5
expose StreamTensor, U32Vector, U32VectorPolynomialOperations
mark pure common lisp routines
merge ptrop, varini
move latex macros to axiom.sty
remove POLYVEC
remove compile, duplicated in vol9
remove memq
remove references to aldor
treeshake
remove $useNewParser
books/bookvol7.1
move latex macros to axiom.sty
remove references to aldor
rewrite \pagehead to \pagetitle
books/bookvol9
cross-reference functions and variables
move latex macros to axiom.sty
remove memq
treeshake the compiler code
remove $useNewParser
books/bookvol10
move latex macros to axiom.sty
move GOPT0 from bookvol10.3
books/bookvol10.1
move latex macros to axiom.sty
books/bookvol10.2
move latex macros to axiom.sty
books/bookvol10.3
add U32Vector, move GOPT0 from bookvol10.4
move latex macros to axiom.sty
books/bookvol10.4
add StreamTensor, U32VectorPolynomialOperations
fix ScriptTensor regression test
move latex macros to axiom.sty
remove POLYVEC
update Chinese Remainder documentation
books/bookvol10.5
move latex macros to axiom.sty
books/bookvolbib
Parnas & Madey [PM95], Parnas & Jin [PJ10], GCL92, AS64, NIST10, RF94,
Hamdy [Ham04], Steele [Ste90], Tim Lahey's Sage Integration Test Suite
books/ps/
v103guessoptionfunctions0, v103u32vector, v104streamtensor,
v104u32vectorpolynomialoperations, v104u32vectorpolynomialoperations
src/algebra
Makefile help and test for StreamTensor
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src/interp
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*.lisp remove memq
treeshake compiler -- br-con, cattable, compiler
remove nspadaux.lisp, mark.lisp, pspad1.lisp, pspad2.lisp,
remove ptrop.lisp, wi1.lisp, wi2.lisp
add HTMLFormat code i-output.lisp, vmlisp.lisp
src/scripts/tex
axiom.sty collect all script commands
axiom.sty consolidate latex macros
src/axiom-website/
documentation.html add Knuth quote per W. Sit
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Subject: [Axiom-developer] wrong sign in limit?
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Hello,
perhaps i have found a bug in the limit operation. I am using
AXIOM Computer Algebra System
Version: Axiom (July 2010)
Timestamp: Wednesday August 18, 2010 at 11:16:49
on a x86_64 with linux. There seems to be an error in the sign, if you
compare the limit result with the de L'Hospital one.
>>>>Example
-- problem with limit
)clear
Z:=sqrt(a^2+h^2)-a
N:=a*sqrt(a^2+h^2) - a^2 - h^2
limit( Z/N, h=0 )
-- this seems to be wrong!
-- because de L'Hospital says
dZ:=differentiate( Z, h, 2 )
dN:=differentiate( N, h, 2 )
eval(dZ/dN,h=0)
-- which seems to be right (see graph): opposite sign!
>>>>EndExample
which generates the output:
AXIOM Computer Algebra System
Version: Axiom (July 2010)
Timestamp: Wednesday August 18, 2010 at 11:16:49
-----------------------------------------------------------------------------
Issue )copyright to view copyright notices.
Issue )summary for a summary of useful system commands.
Issue )quit to leave AXIOM and return to shell.
Visit http://axiom-developer.org for more information
-----------------------------------------------------------------------------
Re-reading compress.daase Re-reading interp.daase
Re-reading operation.daase
Re-reading category.daase
Re-reading browse.daase
(1) ->
(1) -> )read hos.input
-- problem with limit
)clear
Use )clear all to clear everything in the workspace. Use )clear
completely to clear everything in the workspace and internal
tables. Other )clear keyword arguments are
modes
operations
properties
types
values
or abbreviations thereof. Issue )clear? for more information.
Z:=sqrt(a^2+h^2)-a
+-------+
| 2 2
(1) \|h + a - a
Type: Expression
Integer
N:=a*sqrt(a^2+h^2) - a^2 - h^2
+-------+
| 2 2 2 2
(2) a\|h + a - h - a
Type: Expression
Integer
limit( Z/N, h=0 )
1
(3) -
a
Type: Union(OrderedCompletion Expression
Integer,...)
-- this seems to be wrong!
-- because de L'Hospital says
dZ:=differentiate( Z, h, 2 )
2
a
(4) -------------------
+-------+
2 2 | 2 2
(h + a )\|h + a
Type: Expression
Integer
dN:=differentiate( N, h, 2 )
+-------+
2 2 | 2 2 3
(- 2h - 2a )\|h + a + a
(5) ----------------------------
+-------+
2 2 | 2 2
(h + a )\|h + a
Type: Expression
Integer
eval(dZ/dN,h=0)
1
(6) - ----------
+--+
| 2
2\|a - a
Type: Expression
Integer
(7) ->
(7) ->
(see sign)
Thanks
Ingo
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Date: Sun, 26 Sep 2010 14:46:31 -0400
From: Tim Daly
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Subject: Re: [Axiom-developer] wrong sign in limit?
References: <4C9CF1ED.7020806@uni-bremen.de>
In-Reply-To: <4C9CF1ED.7020806@uni-bremen.de>
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Interesting. I'll look at it further. --Tim
On 9/24/2010 2:46 PM, Dr.-Ing. Ingo D. Rullhusen wrote:
> Hello,
>
> perhaps i have found a bug in the limit operation. I am using
>
> AXIOM Computer Algebra System
> Version: Axiom (July 2010)
> Timestamp: Wednesday August 18, 2010 at 11:16:49
>
> on a x86_64 with linux. There seems to be an error in the sign, if you
> compare the limit result with the de L'Hospital one.
>
>>>>> Example
> -- problem with limit
>
> )clear
>
> Z:=sqrt(a^2+h^2)-a
> N:=a*sqrt(a^2+h^2) - a^2 - h^2
>
> limit( Z/N, h=0 )
>
> -- this seems to be wrong!
> -- because de L'Hospital says
>
> dZ:=differentiate( Z, h, 2 )
> dN:=differentiate( N, h, 2 )
>
> eval(dZ/dN,h=0)
>
> -- which seems to be right (see graph): opposite sign!
>
>>>>> EndExample
> which generates the output:
>
> AXIOM Computer Algebra System
> Version: Axiom (July 2010)
> Timestamp: Wednesday August 18, 2010 at 11:16:49
> -----------------------------------------------------------------------------
> Issue )copyright to view copyright notices.
> Issue )summary for a summary of useful system commands.
> Issue )quit to leave AXIOM and return to shell.
> Visit http://axiom-developer.org for more information
> -----------------------------------------------------------------------------
>
> Re-reading compress.daase Re-reading interp.daase
> Re-reading operation.daase
> Re-reading category.daase
> Re-reading browse.daase
> (1) ->
> (1) -> )read hos.input
>
> -- problem with limit
>
> )clear
>
> Use )clear all to clear everything in the workspace. Use )clear
> completely to clear everything in the workspace and internal
> tables. Other )clear keyword arguments are
> modes
> operations
> properties
> types
> values
> or abbreviations thereof. Issue )clear? for more information.
>
> Z:=sqrt(a^2+h^2)-a
>
>
> +-------+
> | 2 2
> (1) \|h + a - a
> Type: Expression
> Integer
> N:=a*sqrt(a^2+h^2) - a^2 - h^2
>
>
> +-------+
> | 2 2 2 2
> (2) a\|h + a - h - a
> Type: Expression
> Integer
>
> limit( Z/N, h=0 )
>
>
> 1
> (3) -
> a
> Type: Union(OrderedCompletion Expression
> Integer,...)
>
> -- this seems to be wrong!
> -- because de L'Hospital says
>
> dZ:=differentiate( Z, h, 2 )
>
>
> 2
> a
> (4) -------------------
> +-------+
> 2 2 | 2 2
> (h + a )\|h + a
> Type: Expression
> Integer
> dN:=differentiate( N, h, 2 )
>
>
> +-------+
> 2 2 | 2 2 3
> (- 2h - 2a )\|h + a + a
> (5) ----------------------------
> +-------+
> 2 2 | 2 2
> (h + a )\|h + a
> Type: Expression
> Integer
>
> eval(dZ/dN,h=0)
>
>
> 1
> (6) - ----------
> +--+
> | 2
> 2\|a - a
> Type: Expression
> Integer
> (7) ->
> (7) ->
>
> (see sign)
>
> Thanks
> Ingo
>
>
> _______________________________________________
> Axiom-developer mailing list
> Axiom-developer@nongnu.org
> http://lists.nongnu.org/mailman/listinfo/axiom-developer
>
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From: Ralf Hemmecke
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To: axiom-developer@nongnu.org
Subject: Re: [Axiom-developer] wrong sign in limit?
References: <4C9CF1ED.7020806@uni-bremen.de>
<4C9F9507.4010108@axiom-developer.org>
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I agree that the result is questionable, but what result do you expect?
This one is perhaps better
(0) -> limit(sqrt(a^2+x), x=0)
+--+
| 2
(0) \|a
Type:
Union(OrderedCompletion(Expression(Integer)),...)
As long as nothing is known about a, that expression cannot be
simplified further. In fact sqrt stands for *two* solutions.
Look into trigcat.spad.pamphlet.
RadicalCategory(): Category == with
sqrt : % -> %
++ sqrt(x) returns the square root of x. The branch cut lies
++ along the negative real axis, continuous with quadrant II.
Even if we agree on the common convention that the root symbol for
positive real arguments denotes a positive value, simplifying the above
to just a would be wrong, as then plugging in a=-1 would violate the
convention.
It's a quite subtle result. But it is wrong in the sense that the result
should be as AXIOM says below.
Maple and Mathematica seem to use similar algorithms as they come up
with the same questionable result. But look at what FullSimplify gives.
Mathematica is just not trying hard enough.
I guess, if AXIOM could simplify Z/N, then the result would be better.
Ralf
(1) -> W := sqrt(a^2+h^2)
+-------+
| 2 2
(1) \|h + a
Type: Expression(Integer)
(2) -> Z := W -a
+-------+
| 2 2
(2) \|h + a - a
Type: Expression(Integer)
(3) -> N := a*W -W^2
+-------+
| 2 2 2 2
(3) a\|h + a - h - a
Type: Expression(Integer)
(4) -> W*Z/N
(4) - 1
Type: Expression(Integer)
(5) -> Z/N + 1/W
(5) 0
Type: Expression(Integer)
(6) -> limit(-1/W, h=0)
1
(6) - -----
+--+
| 2
\|a
Type: Union(OrderedCompletion(Expression(Integer)),...)
==========================================================
BTW, why do you complain? ;-)
Mathematica 7.0 for Linux x86 (32-bit)
Copyright 1988-2008 Wolfram Research, Inc.
In[1]:= w = Sqrt[a^2+h^2]
2 2
Out[1]= Sqrt[a + h ]
In[2]:= z = w - a
2 2
Out[2]= -a + Sqrt[a + h ]
In[3]:= n = a*w-w^2
2 2 2 2
Out[3]= -a - h + a Sqrt[a + h ]
In[4]:= Limit[z/n,h->0]
1
Out[4]= -
a
In[5]:= Limit[-1/w,h->0]
2
Sqrt[a ]
Out[5]= -(--------)
2
a
In[6]:= Simplify[z/n]
2 2
a - Sqrt[a + h ]
Out[6]= -------------------------
2 2 2 2
a + h - a Sqrt[a + h ]
In[7]:= FullSimplify[z/n]
1
Out[7]= -(-------------)
2 2
Sqrt[a + h ]
==============================
|\^/| Maple 11 (IBM INTEL LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc.
2007
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
| Type ? for help.
> w := sqrt(a^2+h^2);
2 2 1/2
w := (a + h )
> z:=w-a;
2 2 1/2
z := (a + h ) - a
> n:=a*w-w^2;
2 2 1/2 2 2
n := a (a + h ) - a - h
> limit(z/n,h=0);
1/a
> limit(-1/w,h=0);
1
- -------
2 1/2
(a )
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To: daly@axiom-developer.org
Subject: Re: [Axiom-developer] Axiom September 2010 Release
References: <201009250647.o8P6lcFO022778@axiom-developer.org>
From: Camm Maguire
Date: Tue, 28 Sep 2010 17:55:20 -0400
In-Reply-To: <201009250647.o8P6lcFO022778@axiom-developer.org>
(daly@axiom-developer.org's message of "Sat\,
25 Sep 2010 01\:47\:38 -0500")
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Greetings!
Please consider this patch, as gcl has a file_exists function and this
prevents image linking when native object relocatin is absent.
--- ./src/lib/pixmap.c.pamphlet.orig 2010-09-25 05:29:00.000000000 +0000
+++ ./src/lib/pixmap.c.pamphlet 2010-09-28 14:54:03.000000000 +0000
@@ -81,7 +81,7 @@
/* returns true if the file exists */
int
-file_exists(char *file)
+ax_file_exists(char *file)
{
FILE *f;
@@ -96,10 +96,10 @@
{
char com[512], zfile[512];
- if (file_exists(file))
+ if (ax_file_exists(file))
return fopen(file, mode);
sprintf(zfile, "%s.Z", file);
- if (file_exists(zfile)) {
+ if (ax_file_exists(zfile)) {
sprintf(com, "gunzip -c %s.Z 2>/dev/null", file);
return popen(com, mode);
}
(Also unclear on how -lXpm gets into the link, but it appears to
somehow, so all else is good. Uploaded into Debian unstable.)
Take care,
daly@axiom-developer.org writes:
> Axiom has been released for September 2010.
> The website has the sources and the ubuntu binary.
> Other binaries are being built and will appear when they pass testing.
>
> Tim Daly
>
> =============================================================================
>
> September 2010 Release
>
> This release concentrated on treeshaking the compiler code into book volume 9.
> Due to the complexity of this task it will take several releases to complete.
>
> Additional global changes included collecting all of the Axiom-related
> latex macros into axiom.sty and removing references to Aldor.
>
> Makefile
> always run help extractions in parallel
> build src/input quietly
>
> books/bookvol0
> remove references to aldor
>
> books/bookvol1
> remove references to aldor
>
> books/bookvol5
> expose StreamTensor, U32Vector, U32VectorPolynomialOperations
> mark pure common lisp routines
> merge ptrop, varini
> move latex macros to axiom.sty
> remove POLYVEC
> remove compile, duplicated in vol9
> remove memq
> remove references to aldor
> treeshake
> remove $useNewParser
>
> books/bookvol7.1
> move latex macros to axiom.sty
> remove references to aldor
> rewrite \pagehead to \pagetitle
>
> books/bookvol9
> cross-reference functions and variables
> move latex macros to axiom.sty
> remove memq
> treeshake the compiler code
> remove $useNewParser
>
> books/bookvol10
> move latex macros to axiom.sty
> move GOPT0 from bookvol10.3
>
> books/bookvol10.1
> move latex macros to axiom.sty
>
> books/bookvol10.2
> move latex macros to axiom.sty
>
> books/bookvol10.3
> add U32Vector, move GOPT0 from bookvol10.4
> move latex macros to axiom.sty
>
> books/bookvol10.4
> add StreamTensor, U32VectorPolynomialOperations
> fix ScriptTensor regression test
> move latex macros to axiom.sty
> remove POLYVEC
> update Chinese Remainder documentation
>
> books/bookvol10.5
> move latex macros to axiom.sty
>
> books/bookvolbib
> Parnas & Madey [PM95], Parnas & Jin [PJ10], GCL92, AS64, NIST10, RF94,
> Hamdy [Ham04], Steele [Ste90], Tim Lahey's Sage Integration Test Suite
>
> books/ps/
> v103guessoptionfunctions0, v103u32vector, v104streamtensor,
> v104u32vectorpolynomialoperations, v104u32vectorpolynomialoperations
>
> src/algebra
> Makefile help and test for StreamTensor
> Makefile help and test for U32Vector
> Makefile remove references to aldor
> Makefile test and help for POLYVEC
> Makefile remove POLYVEC
> Makefile add help and test for new algebra
> Makefile handle case-insensitive MAC filesystem
> Makefile remove new algebra scaffolding code
>
> src/doc
> axiom.sty collect all script commands in one place
> axiom.sty consolidate latex macros
>
> src/input
> Makefile add guess.input, manuel.input, risch.input
> guess.input test examples of the GUESS package
> kamke3.input clean up broken tests
> manuel.input add Manuel's integral to test suite
> richlog300-391.input clean up broken tests
> richtrig800-899.input clean up broken tests
> risch.input illustrate the Risch algorithm
> setcmd.input clean up broken tests
> test.input clean up broken tests
>
> src/interp
> Makefile merge varini
> Makefile remove nspadaux, mark, pspad1, pspad2, ptrop, wi1, wi2
> *.lisp remove memq
> treeshake compiler -- br-con, cattable, compiler
> remove nspadaux.lisp, mark.lisp, pspad1.lisp, pspad2.lisp,
> remove ptrop.lisp, wi1.lisp, wi2.lisp
> add HTMLFormat code i-output.lisp, vmlisp.lisp
>
> src/scripts/tex
> axiom.sty collect all script commands
> axiom.sty consolidate latex macros
>
> src/axiom-website/
> documentation.html add Knuth quote per W. Sit
> download.html add debian, fedora, mandriva, opensuse, slackware, vector
> download.html update ubuntu yum advice
>
>
>
>
> _______________________________________________
> Axiom-developer mailing list
> Axiom-developer@nongnu.org
> http://lists.nongnu.org/mailman/listinfo/axiom-developer
>
>
>
>
--
Camm Maguire camm@maguirefamily.org
==========================================================================
"The earth is but one country, and mankind its citizens." -- Baha'u'llah
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To: daly@axiom-developer.org
Subject: Re: [Axiom-developer] Axiom September 2010 Release
References: <201009250647.o8P6lcFO022778@axiom-developer.org>
From: Camm Maguire
Date: Wed, 29 Sep 2010 11:49:31 -0400
In-Reply-To: <201009250647.o8P6lcFO022778@axiom-developer.org>
(daly@axiom-developer.org's message of "Sat\,
25 Sep 2010 01\:47\:38 -0500")
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Greetings! How do I enable lisp breaks on error?
Take care,
daly@axiom-developer.org writes:
> Axiom has been released for September 2010.
> The website has the sources and the ubuntu binary.
> Other binaries are being built and will appear when they pass testing.
>
> Tim Daly
>
> =============================================================================
>
> September 2010 Release
>
> This release concentrated on treeshaking the compiler code into book volume 9.
> Due to the complexity of this task it will take several releases to complete.
>
> Additional global changes included collecting all of the Axiom-related
> latex macros into axiom.sty and removing references to Aldor.
>
> Makefile
> always run help extractions in parallel
> build src/input quietly
>
> books/bookvol0
> remove references to aldor
>
> books/bookvol1
> remove references to aldor
>
> books/bookvol5
> expose StreamTensor, U32Vector, U32VectorPolynomialOperations
> mark pure common lisp routines
> merge ptrop, varini
> move latex macros to axiom.sty
> remove POLYVEC
> remove compile, duplicated in vol9
> remove memq
> remove references to aldor
> treeshake
> remove $useNewParser
>
> books/bookvol7.1
> move latex macros to axiom.sty
> remove references to aldor
> rewrite \pagehead to \pagetitle
>
> books/bookvol9
> cross-reference functions and variables
> move latex macros to axiom.sty
> remove memq
> treeshake the compiler code
> remove $useNewParser
>
> books/bookvol10
> move latex macros to axiom.sty
> move GOPT0 from bookvol10.3
>
> books/bookvol10.1
> move latex macros to axiom.sty
>
> books/bookvol10.2
> move latex macros to axiom.sty
>
> books/bookvol10.3
> add U32Vector, move GOPT0 from bookvol10.4
> move latex macros to axiom.sty
>
> books/bookvol10.4
> add StreamTensor, U32VectorPolynomialOperations
> fix ScriptTensor regression test
> move latex macros to axiom.sty
> remove POLYVEC
> update Chinese Remainder documentation
>
> books/bookvol10.5
> move latex macros to axiom.sty
>
> books/bookvolbib
> Parnas & Madey [PM95], Parnas & Jin [PJ10], GCL92, AS64, NIST10, RF94,
> Hamdy [Ham04], Steele [Ste90], Tim Lahey's Sage Integration Test Suite
>
> books/ps/
> v103guessoptionfunctions0, v103u32vector, v104streamtensor,
> v104u32vectorpolynomialoperations, v104u32vectorpolynomialoperations
>
> src/algebra
> Makefile help and test for StreamTensor
> Makefile help and test for U32Vector
> Makefile remove references to aldor
> Makefile test and help for POLYVEC
> Makefile remove POLYVEC
> Makefile add help and test for new algebra
> Makefile handle case-insensitive MAC filesystem
> Makefile remove new algebra scaffolding code
>
> src/doc
> axiom.sty collect all script commands in one place
> axiom.sty consolidate latex macros
>
> src/input
> Makefile add guess.input, manuel.input, risch.input
> guess.input test examples of the GUESS package
> kamke3.input clean up broken tests
> manuel.input add Manuel's integral to test suite
> richlog300-391.input clean up broken tests
> richtrig800-899.input clean up broken tests
> risch.input illustrate the Risch algorithm
> setcmd.input clean up broken tests
> test.input clean up broken tests
>
> src/interp
> Makefile merge varini
> Makefile remove nspadaux, mark, pspad1, pspad2, ptrop, wi1, wi2
> *.lisp remove memq
> treeshake compiler -- br-con, cattable, compiler
> remove nspadaux.lisp, mark.lisp, pspad1.lisp, pspad2.lisp,
> remove ptrop.lisp, wi1.lisp, wi2.lisp
> add HTMLFormat code i-output.lisp, vmlisp.lisp
>
> src/scripts/tex
> axiom.sty collect all script commands
> axiom.sty consolidate latex macros
>
> src/axiom-website/
> documentation.html add Knuth quote per W. Sit
> download.html add debian, fedora, mandriva, opensuse, slackware, vector
> download.html update ubuntu yum advice
>
>
>
>
> _______________________________________________
> Axiom-developer mailing list
> Axiom-developer@nongnu.org
> http://lists.nongnu.org/mailman/listinfo/axiom-developer
>
>
>
>
--
Camm Maguire camm@maguirefamily.org
==========================================================================
"The earth is but one country, and mankind its citizens." -- Baha'u'llah
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Date: Wed, 29 Sep 2010 14:57:26 -0400
From: Tim Daly
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To: Camm Maguire
Subject: Re: [Axiom-developer] Axiom September 2010 Release
References: <201009250647.o8P6lcFO022778@axiom-developer.org>
<87iq1opn1w.fsf@maguirefamily.org>
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)set break break
On 9/29/2010 11:49 AM, Camm Maguire wrote:
> Greetings! How do I enable lisp breaks on error?
>
> Take care,
>
> daly@axiom-developer.org writes:
>
>> Axiom has been released for September 2010.
>> The website has the sources and the ubuntu binary.
>> Other binaries are being built and will appear when they pass testing.
>>
>> Tim Daly
>>
>> =============================================================================
>>
>> September 2010 Release
>>
>> This release concentrated on treeshaking the compiler code into book volume 9.
>> Due to the complexity of this task it will take several releases to complete.
>>
>> Additional global changes included collecting all of the Axiom-related
>> latex macros into axiom.sty and removing references to Aldor.
>>
>> Makefile
>> always run help extractions in parallel
>> build src/input quietly
>>
>> books/bookvol0
>> remove references to aldor
>>
>> books/bookvol1
>> remove references to aldor
>>
>> books/bookvol5
>> expose StreamTensor, U32Vector, U32VectorPolynomialOperations
>> mark pure common lisp routines
>> merge ptrop, varini
>> move latex macros to axiom.sty
>> remove POLYVEC
>> remove compile, duplicated in vol9
>> remove memq
>> remove references to aldor
>> treeshake
>> remove $useNewParser
>>
>> books/bookvol7.1
>> move latex macros to axiom.sty
>> remove references to aldor
>> rewrite \pagehead to \pagetitle
>>
>> books/bookvol9
>> cross-reference functions and variables
>> move latex macros to axiom.sty
>> remove memq
>> treeshake the compiler code
>> remove $useNewParser
>>
>> books/bookvol10
>> move latex macros to axiom.sty
>> move GOPT0 from bookvol10.3
>>
>> books/bookvol10.1
>> move latex macros to axiom.sty
>>
>> books/bookvol10.2
>> move latex macros to axiom.sty
>>
>> books/bookvol10.3
>> add U32Vector, move GOPT0 from bookvol10.4
>> move latex macros to axiom.sty
>>
>> books/bookvol10.4
>> add StreamTensor, U32VectorPolynomialOperations
>> fix ScriptTensor regression test
>> move latex macros to axiom.sty
>> remove POLYVEC
>> update Chinese Remainder documentation
>>
>> books/bookvol10.5
>> move latex macros to axiom.sty
>>
>> books/bookvolbib
>> Parnas& Madey [PM95], Parnas& Jin [PJ10], GCL92, AS64, NIST10, RF94,
>> Hamdy [Ham04], Steele [Ste90], Tim Lahey's Sage Integration Test Suite
>>
>> books/ps/
>> v103guessoptionfunctions0, v103u32vector, v104streamtensor,
>> v104u32vectorpolynomialoperations, v104u32vectorpolynomialoperations
>>
>> src/algebra
>> Makefile help and test for StreamTensor
>> Makefile help and test for U32Vector
>> Makefile remove references to aldor
>> Makefile test and help for POLYVEC
>> Makefile remove POLYVEC
>> Makefile add help and test for new algebra
>> Makefile handle case-insensitive MAC filesystem
>> Makefile remove new algebra scaffolding code
>>
>> src/doc
>> axiom.sty collect all script commands in one place
>> axiom.sty consolidate latex macros
>>
>> src/input
>> Makefile add guess.input, manuel.input, risch.input
>> guess.input test examples of the GUESS package
>> kamke3.input clean up broken tests
>> manuel.input add Manuel's integral to test suite
>> richlog300-391.input clean up broken tests
>> richtrig800-899.input clean up broken tests
>> risch.input illustrate the Risch algorithm
>> setcmd.input clean up broken tests
>> test.input clean up broken tests
>>
>> src/interp
>> Makefile merge varini
>> Makefile remove nspadaux, mark, pspad1, pspad2, ptrop, wi1, wi2
>> *.lisp remove memq
>> treeshake compiler -- br-con, cattable, compiler
>> remove nspadaux.lisp, mark.lisp, pspad1.lisp, pspad2.lisp,
>> remove ptrop.lisp, wi1.lisp, wi2.lisp
>> add HTMLFormat code i-output.lisp, vmlisp.lisp
>>
>> src/scripts/tex
>> axiom.sty collect all script commands
>> axiom.sty consolidate latex macros
>>
>> src/axiom-website/
>> documentation.html add Knuth quote per W. Sit
>> download.html add debian, fedora, mandriva, opensuse, slackware, vector
>> download.html update ubuntu yum advice
>>
>>
>>
>>
>> _______________________________________________
>> Axiom-developer mailing list
>> Axiom-developer@nongnu.org
>> http://lists.nongnu.org/mailman/listinfo/axiom-developer
>>
>>
>>
>>
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Subject: Re: [Axiom-developer] wrong sign in limit?
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From: Waldek Hebisch
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Dr.-Ing. Ingo D. Rullhusen wrote:
>
> Hello,
>
> perhaps i have found a bug in the limit operation. I am using
>
> AXIOM Computer Algebra System
> Version: Axiom (July 2010)
> Timestamp: Wednesday August 18, 2010 at 11:16:49
>
> on a x86_64 with linux. There seems to be an error in the sign, if you
> compare the limit result with the de L'Hospital one.
>
>
> Z:=sqrt(a^2+h^2)-a
>
> N:=a*sqrt(a^2+h^2) - a^2 - h^2
>
> limit( Z/N, h=0 )
>
>
> 1
> (3) -
> a
> Type: Union(OrderedCompletion Expression
> Integer,...)
>
> -- this seems to be wrong!
> -- because de L'Hospital says
>
> dZ:=differentiate( Z, h, 2 )
>
> dN:=differentiate( N, h, 2 )
>
> eval(dZ/dN,h=0)
>
>
> 1
> (6) - ----------
> +--+
> | 2
> 2\|a - a
>
> (see sign)
Square root has two branches, the result depends on which branch
you choose. Limit decided that sqrt(a^2) = -a and the result
is correct for this branch (and wrong for the other branch).
de L'Hospital rule can be used only when limit on N is 0, which
hold when sqrt(a^2) = a, but the result is wrong for the other
branch. If you want result which is correct for both branches
you need something like:
-sqrt(a^2)/a^2
but such expressions cause trouble so limit decided just to pick
one branch...
--
Waldek Hebisch
hebisch@math.uni.wroc.pl