They talk about it being more environmentally friendly, however how many of these ingredients that you growing, then cutting, and processing the hell out of them are you using. You "egg" is made from an acre of Soybeans, don't you feel good about yourself, with a good portion of it going to waste. While my Egg is from a chicken that has eaten 1 acre of feed and produced hundreds of eggs during its lifetime. And the chicken works as a rather efficient little factory of making eggs.
If you're going to argue that using pea protein instead of eggs is less environmentally friendly, you'll have to do better than just making up some numbers. The chicken seems rather inefficient since if all you want is the egg, doing things like growing, moving around, maintaining life, etc. all are inefficiencies in the plant to egg process.
On first glance, it would seem that it's more efficient to use the plant-based version. Hellman's Mayo is 8% eggs while Hampton Creek's mayo is
under 2% pea protein. Even if the chicken was ultra-efficient and converted 1g of feed to 1g of eggs, you'd still have to show the that process from pea to pea protein was at least four times less efficient.
Given that one of their main points / goals is to be less expensive than using eggs, it seems unlikely that the plant-based version would be less efficient.
INGREDIENTS: Non-GMO Expeller-Pressed Canola Oil, Filtered Water, Lemon Juice, White Vinegar, 2% or less of the following: Organic Sugar, Salt, Apple Cider Vinegar, Pea Protein, Spices, Garlic, Modified Food Starch, Beta-Carotene.
Relatively benign if you ask me. The key for the emulsification seems to be the pea protein.
We're talking about vegans here, though, and if they enjoy their breakfasts so much, why do they need fake eggs? What's wrong with their normal vegan breakfast that they have to eat fake animal protein?
They aren't making egg replacements to cater to vegans. Think of all of the processed food like mayo, cookies, etc. which contains eggs. If they can create a cheaper, effective replacement for eggs then it would reduce the demand for factory farm produced eggs (which is how a majority of all eggs are produced).
If you are interested in playing around with the symmetry group associated to the Rubik's cube, Sage (http://www.sagemath.org) has good support for it; the documentation can be found at http://www.sagemath.org/doc/html/ref/module-sage.groups.perm-gps.cubegroup.html . Sage also includes a number of efficient solvers for the Rubik's cube.
This article is related to Sage ( http://www.sagemath.org/ ), a free open-source math project. The article is about a computation (not using Sage) of an L-function, a computation about that L-function (using Sage), and a major new NSF-funded initiative to compute large tables of modular forms and L-functions that William Stein (director of the Sage project) is co-directing, which will have a large impact on Sage development.
Maxima, Sage and Axiom all fail to make the grade, and have infuriating names besides.
Could you elaborate a bit more on hwo you feel Sage "fails to make the grade"? We are definitely interested in feedback to help improve things.
That being said, I think a lot of it is really dependent on the type of math you are interested in doing. For me personally, using Mathematica would be a waste of my time while I've been able to be pretty productive using Sage.
The math fonts are not really necessary. Everything will run fine without them. If you do want them, there are instructions on how to install them on the jsmath website.
Octave does not come included with Sage, but Sage can make use of any installed version of Octave. There is a Sage spkg for Octave which can be installed by running the command "sage -i octave-2.1.73". With the new release of Octave, that spkg should be updated soon.
Here is how you can solve a Ax=b equation in Sage:
sage: A = random_matrix(ZZ, 3)
sage: A
[ 1 3 -1]
[-2 2 4]
[ 2 -1 -1]
sage: b = vector([3,2,1])
sage: b
(3, 2, 1)
sage: x = A \ b
sage: x
(14/11, 9/11, 8/11)
sage: A*x
(3, 2, 1)
I actually really like functional programming for a lot of things;-] But, in terms of interfacing with third party software, working with debuggers, etc. I don't think that Mathematica comes close to Python. I guess that is not totally reflective of the language itself, but instead of the "software ecosystem" that surrounds it.
We're working hard on adding R to Sage for the 2.9 release next week. With that, you'd be able to use R from the notebook interface as well. As for the interface, it is code that is unique to Sage although it was indeed modeled after the Google docs interface.
I don't think of it as a hybrid syntax since it is just Python. For all the interfaces that work via pseudo-tty, there is a standard way that the Python objects work with the underlying R objects. RPy provides a much more native Python interface to R. There are some standard Python to R function name mappings (adopted by RPy) to avoid syntax clashes with Python. You can also always do r.eval('R CODE') and it'd be just like typing into an R interpreter.
Sage already has arbitrary precision floating point arithmetic provided by MPFR as well as interval arithmetic. I'm not quite sure what you mean by "symbolic editor", but Sage uses maxima behind the scenes for its symbolic integration and differentiation. Sage also include sympy so you could use that if you prefer. Sage can do ODEs as well. I think maxima has some support for PDEs as well -- I'm not sure; those aren't really the areas of math that I'm interested in. More of Sage's functionality can be found by glancing over http://www.msri.org/about/computing/docs/sage/ref/ref.html .
Yes, it's pretty much completely separated from the code. Eventually, the web interface will get split off into it's own separate project. Since Sage is just a (C)Python library, you can use any GUI that Python supports.
When I meant not good at linear algebra, I meant that it is slow. For example, Sage is over 30x faster at computing the characteristic polynomial of a matrix over the integers. Regarding number theory, there isn't really any support in Mathematica for working with number fields, modular forms, or elliptic curves. What I meant by "real" programming language was that there is a lot of software out there that can be taken advantage of. Say for instance I need to work with data stored in an relational database. How easy is that to do with Mathematica? It is trivial with Sage since Sage uses Python. When Sage needs to do things fast, it uses Cython ( http://www.cython.org/ ) which is almost a superset of Python and compiles down to C.
When I said "include R in Sage", I meant to include R as part of the Sage distribution (so that it gets installed when Sage is installed) as well as provide interfaces to R from Sage. One such interface is RPy ( http://rpy.sourceforge.net/ ) which is a library level interface that allows R to be used from Python. Another interface will communicate with R via a pseudo-tty. Here is how such a session will look:
sage: a = r([1,2,3,4])
sage: a = r([1,2,3,4]); a
1 2 3 4
sage: a.length()
4
sage: a.dim = (2,2)
sage: a
[,1] [,2]
[1,] 1 3
[2,] 2 4
sage: r.t_test(range(100))
One Sample t-test
data: sage106
t = 17.0622, df = 99, p-value
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
43.74349 55.25651
sample estimates:
mean of x
49.5
Well, in addition to including existing software, Sage contains about 200,000 lines of new code implementing functionality not found in the other packages. Many packages have C library interfaces which provides something much different that you'd get with a BASH shell; for example, GMP, GSL, and MPFR come to mind. Even the pexpect interfaces which use a psuedo-tty do more than you can do with a BASH shell. For example, look at the following Sage session which mixes Sage, Maxima (behind the scenes), and Maple:
sage: f = x^2 + x
sage: df = diff(f, x); df
2*x + 1
sage: a = maple(df).integrate(x); a
x^2+x
sage: a+2
x^2+x+2
Math software, like Sage, is incredibly useful for coming up with and testing conjectures. Before you can prove something, you need to know what you want to prove. For example, in some of my research, the direction we went was primarily driven by computational results, which led to conjectures, which in turn led to theorems and proofs. I've looked at Isabelle, and it looks to be a long way off from being able to help with the math that I'm interested in.
Slashdot Mirror
They talk about it being more environmentally friendly, however how many of these ingredients that you growing, then cutting, and processing the hell out of them are you using. You "egg" is made from an acre of Soybeans, don't you feel good about yourself, with a good portion of it going to waste. While my Egg is from a chicken that has eaten 1 acre of feed and produced hundreds of eggs during its lifetime. And the chicken works as a rather efficient little factory of making eggs.
If you're going to argue that using pea protein instead of eggs is less environmentally friendly, you'll have to do better than just making up some numbers. The chicken seems rather inefficient since if all you want is the egg, doing things like growing, moving around, maintaining life, etc. all are inefficiencies in the plant to egg process.
On first glance, it would seem that it's more efficient to use the plant-based version. Hellman's Mayo is 8% eggs while Hampton Creek's mayo is under 2% pea protein. Even if the chicken was ultra-efficient and converted 1g of feed to 1g of eggs, you'd still have to show the that process from pea to pea protein was at least four times less efficient.
Given that one of their main points / goals is to be less expensive than using eggs, it seems unlikely that the plant-based version would be less efficient.
From https://hamptoncreekfoods.com/justmayo/:
INGREDIENTS: Non-GMO Expeller-Pressed Canola Oil, Filtered Water, Lemon Juice, White Vinegar, 2% or less of the following: Organic Sugar, Salt, Apple Cider Vinegar, Pea Protein, Spices, Garlic, Modified Food Starch, Beta-Carotene.
Relatively benign if you ask me. The key for the emulsification seems to be the pea protein.
We're talking about vegans here, though, and if they enjoy their breakfasts so much, why do they need fake eggs? What's wrong with their normal vegan breakfast that they have to eat fake animal protein?
They aren't making egg replacements to cater to vegans. Think of all of the processed food like mayo, cookies, etc. which contains eggs. If they can create a cheaper, effective replacement for eggs then it would reduce the demand for factory farm produced eggs (which is how a majority of all eggs are produced).
David Joyner has a book which explores some of the math behind the Rubik's cube: http://www.amazon.com/Adventures-Group-Theory-Merlins-Mathematical/dp/0801869471
If you are interested in playing around with the symmetry group associated to the Rubik's cube, Sage (http://www.sagemath.org) has good support for it; the documentation can be found at http://www.sagemath.org/doc/html/ref/module-sage.groups.perm-gps.cubegroup.html . Sage also includes a number of efficient solvers for the Rubik's cube.
This article is related to Sage ( http://www.sagemath.org/ ), a free open-source math project. The article is about a computation (not using Sage) of an L-function, a computation about that L-function (using Sage), and a major new NSF-funded initiative to compute large tables of modular forms and L-functions that William Stein (director of the Sage project) is co-directing, which will have a large impact on Sage development.
Could you elaborate a bit more on hwo you feel Sage "fails to make the grade"? We are definitely interested in feedback to help improve things.
That being said, I think a lot of it is really dependent on the type of math you are interested in doing. For me personally, using Mathematica would be a waste of my time while I've been able to be pretty productive using Sage.
The math fonts are not really necessary. Everything will run fine without them. If you do want them, there are instructions on how to install them on the jsmath website.
Octave does not come included with Sage, but Sage can make use of any installed version of Octave. There is a Sage spkg for Octave which can be installed by running the command "sage -i octave-2.1.73". With the new release of Octave, that spkg should be updated soon.
For an interesting post by the lead developer of Sage (William Stein) on the relationship between Sage and Octave in terms of overall goals, see this http://sagemath.blogspot.com/2007/12/why-isnt-sage-just-part-of-octave.html
--Mike (a Sage developer)
To evaluate a cell, you press shift-enter.
Here is how you can solve a Ax=b equation in Sage:
sage: A = random_matrix(ZZ, 3)
sage: A
[ 1 3 -1]
[-2 2 4]
[ 2 -1 -1]
sage: b = vector([3,2,1])
sage: b
(3, 2, 1)
sage: x = A \ b
sage: x
(14/11, 9/11, 8/11)
sage: A*x
(3, 2, 1)
--Mike
Actually, that reference manual is _way_ out of date. Use this instead: http://modular.fas.harvard.edu/sage/doc/html/ref/index.html
I actually really like functional programming for a lot of things ;-] But, in terms of interfacing with third party software, working with debuggers, etc. I don't think that Mathematica comes close to Python. I guess that is not totally reflective of the language itself, but instead of the "software ecosystem" that surrounds it.
Hello,
We're working hard on adding R to Sage for the 2.9 release next week. With that, you'd be able to use R from the notebook interface as well. As for the interface, it is code that is unique to Sage although it was indeed modeled after the Google docs interface.
--Mike (a Sage developer)
I don't think of it as a hybrid syntax since it is just Python. For all the interfaces that work via pseudo-tty, there is a standard way that the Python objects work with the underlying R objects. RPy provides a much more native Python interface to R. There are some standard Python to R function name mappings (adopted by RPy) to avoid syntax clashes with Python. You can also always do r.eval('R CODE') and it'd be just like typing into an R interpreter.
Sage already has arbitrary precision floating point arithmetic provided by MPFR as well as interval arithmetic. I'm not quite sure what you mean by "symbolic editor", but Sage uses maxima behind the scenes for its symbolic integration and differentiation. Sage also include sympy so you could use that if you prefer. Sage can do ODEs as well. I think maxima has some support for PDEs as well -- I'm not sure; those aren't really the areas of math that I'm interested in. More of Sage's functionality can be found by glancing over http://www.msri.org/about/computing/docs/sage/ref/ref.html .
--Mike
http://www.mwhansen.org/sage-2.8.13-use_this_on_sage_dot_math-x86_64-Linux.tar.gz.torrent
http://www.mwhansen.org/sage-2.8.13-x86_64-Linux-debian.tar.gz.torrent
http://www.mwhansen.org/sage-2.8.15-debian32-i686-Linux.tar.gz.torrent
http://www.mwhansen.org/sage-2.8.15-debian64-x86_64-Linux.tar.gz.torrent
http://www.mwhansen.org/sage-2.8.15-osx10.4-intel-i386-Darwin.tar.gz.torrent
http://www.mwhansen.org/sage-2.8.15-osx10.4-ppc-PowerMacintosh-Darwin.tar.gz.torrent
http://www.mwhansen.org/sage-2.8.15-osx10.5-intel-i386-Darwin.tar.gz.torrent
http://www.mwhansen.org/sage-2.8.15-rhel-32bit-i686-Linux.tar.gz.torrent
http://www.mwhansen.org/sage-2.8.15.tar.torrent
http://www.mwhansen.org/sage-2.8.15-ubuntu32bit-i686-Linux.tar.gz.torrent
http://www.mwhansen.org/sage-vmware-2.8.15.zip.torrent
Also, see http://www.mwhansen.org/sage-torrents.html .
--Mike
Sorry to reply to myself, I forgot the one for the VMWare image:
http://www.mwhansen.org/sage-vmware-2.8.15.zip.torrent
See also: http://www.mwhansen.org/sage-torrents.html
--Mike
Since the Sage servers are being hit pretty hard, here are torrents for the files.
http://www.mwhansen.org/sage-2.8.13-use_this_on_sage_dot_math-x86_64-Linux.tar.gz.torrent
http://www.mwhansen.org/sage-2.8.13-x86_64-Linux-debian.tar.gz.torrent
http://www.mwhansen.org/sage-2.8.15-debian32-i686-Linux.tar.gz.torrent
http://www.mwhansen.org/sage-2.8.15-debian64-x86_64-Linux.tar.gz.torrent
http://www.mwhansen.org/sage-2.8.15-osx10.4-intel-i386-Darwin.tar.gz.torrent
http://www.mwhansen.org/sage-2.8.15-osx10.4-ppc-PowerMacintosh-Darwin.tar.gz.torrent
http://www.mwhansen.org/sage-2.8.15-osx10.5-intel-i386-Darwin.tar.gz.torrent
http://www.mwhansen.org/sage-2.8.15-rhel-32bit-i686-Linux.tar.gz.torrent
http://www.mwhansen.org/sage-2.8.15.tar.torrent
http://www.mwhansen.org/sage-2.8.15-ubuntu32bit-i686-Linux.tar.gz.torrent
--Mike
Yes, it's pretty much completely separated from the code. Eventually, the web interface will get split off into it's own separate project. Since Sage is just a (C)Python library, you can use any GUI that Python supports.
--Mike
There is even a Sage plug for TeXmacs ;-]
--Mike
When I meant not good at linear algebra, I meant that it is slow. For example, Sage is over 30x faster at computing the characteristic polynomial of a matrix over the integers. Regarding number theory, there isn't really any support in Mathematica for working with number fields, modular forms, or elliptic curves. What I meant by "real" programming language was that there is a lot of software out there that can be taken advantage of. Say for instance I need to work with data stored in an relational database. How easy is that to do with Mathematica? It is trivial with Sage since Sage uses Python. When Sage needs to do things fast, it uses Cython ( http://www.cython.org/ ) which is almost a superset of Python and compiles down to C.
--Mike
When I said "include R in Sage", I meant to include R as part of the Sage distribution (so that it gets installed when Sage is installed) as well as provide interfaces to R from Sage. One such interface is RPy ( http://rpy.sourceforge.net/ ) which is a library level interface that allows R to be used from Python. Another interface will communicate with R via a pseudo-tty. Here is how such a session will look:
sage: a = r([1,2,3,4])
sage: a = r([1,2,3,4]); a
1 2 3 4
sage: a.length()
4
sage: a.dim = (2,2)
sage: a
[,1] [,2]
[1,] 1 3
[2,] 2 4
sage: r.t_test(range(100))
One Sample t-test
data: sage106
t = 17.0622, df = 99, p-value alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
43.74349 55.25651
sample estimates:
mean of x
49.5
--Mike
Well, in addition to including existing software, Sage contains about 200,000 lines of new code implementing functionality not found in the other packages. Many packages have C library interfaces which provides something much different that you'd get with a BASH shell; for example, GMP, GSL, and MPFR come to mind. Even the pexpect interfaces which use a psuedo-tty do more than you can do with a BASH shell. For example, look at the following Sage session which mixes Sage, Maxima (behind the scenes), and Maple:
sage: f = x^2 + x
sage: df = diff(f, x); df
2*x + 1
sage: a = maple(df).integrate(x); a
x^2+x
sage: a+2
x^2+x+2
--Mike
Math software, like Sage, is incredibly useful for coming up with and testing conjectures. Before you can prove something, you need to know what you want to prove. For example, in some of my research, the direction we went was primarily driven by computational results, which led to conjectures, which in turn led to theorems and proofs. I've looked at Isabelle, and it looks to be a long way off from being able to help with the math that I'm interested in.
--Mike
There's nothing official, but some ideas are here: http://groups.google.com/group/sage-devel/browse_thread/thread/98d90d3378dcf1fa The HTML and CSS could probably cleaned up as well too.
You may want to look into Sage then. It comes with SciPy and matplotlib and has an interface to Octave.
--Mike