On Mon, Aug 2, 2010 at 4:59 PM, cousteau <cousteaulecommand...@gmail.com> wrote:
> 1. ENGINEERING MODE
> Ok, I didn't think about the problems that using real numbers where
> indexes are required would cause. Doesn't look easy to workaround, so
> better forget about this one.
>
> 2. UNITS
> Good to know that Sage already supports units, when were they
> implemented?
I finished them off and got them into Sage not so long ago. David
Ackerman (a UW undergraduate) did most of the actual work last summer
(2009).
> Apparently not in 4.1.2 at least.
> It would still be useful to have an easy way to access units. If
> adding a syntax like "9.8 'units' " involves messing too much with
> Python's syntax, another solution is to make a function that returns
> units from a string, something like "units('kg m/s2')".
That's a great idea.
> 3. BODE DIAGRAMS
> Well, ok, maybe when I tried to plot a bode diagram I didn't research
> much on the graphics array point, but there's still missing a way to
> make the X axis have a logarithmic scale (without replacing x with
> exp(x), which would work graphically but would write the wrong numbers
> on the axis). Also, it would be nice to be able to make the Y axis
> have divisions each 15, 45 or 90 degrees for the phase diagram, but it
> will use 10, 20, 50 or 100 instead.
I agree -- we definitely need log scale for sage's default plotting.
> 4. MATRIX INPUT
> If the "[...]m" syntax is messing too much with Python's syntax, don't
> implement it then, but I keep thinking there should be an easier way
> than the one right now to input matrices. It's just not comfortable
> for people who does an intensive usage of matrices.
> (Another alternate syntax would be using a semicolon inside a list:
> "[1,2;3,4]", or "[1,2,3;]" for row matrices; it's more Matlab-like but
> it still has the same problem... although there are already some cases
> such as "list(1..10)" that don't look like valid Python)
What about something like this:
sage: m = lambda x: matrix([sage_eval(y,globals()) for y in x.split(';')])
sage: m('1,2; 3,4')
[1 2]
[3 4]
sage: m('1,2,3,5/8; 3,4,7,1.5')
[ 1.00000000000000 2.00000000000000 3.00000000000000 0.625000000000000]
[ 3.00000000000000 4.00000000000000 7.00000000000000 1.50000000000000]
sage: a = 10
sage: m('a,0;1,2')
[10 0]
[ 1 2]
> 6. TRANSPOSE/CONJUGATE
> It seems that implementing this would just involve modifying the
> __pos__(self) method for complexes, matrices and complex matrices, and
> I think that both conjugating and transposing are common enough
> operations to deserve its own operator.
-1 to making +A = A.transpose().
>
>
> On 2 ago, 22:47, William Stein <wst...@gmail.com> wrote:
>> On Mon, Aug 2, 2010 at 1:38 PM, cousteau <cousteaulecommand...@gmail.com>
>> wrote:
>> > I'm studying engineering, and I'm used to some programs such as
>> > Matlab, Maple, etc. When I knew about SAGE I found it very powerful,
>> > simple and well structured, but I quickly found out that it wouldn't
>> > be very useful in engineering, which is more oriented to numerical
>> > analysis and simple math operations than to abstract algebra. Although
>> > I could just use Octave for this, I'd like to be able to use SAGE for
>> > some engineering-oriented tasks. Here are some proposed features:
>>
>> > 1. ENGINEERING MODE
>> > Since SAGE is oriented to mathematics, all numbers are considered
>> > Integer unless otherwise specified (an integer is converted using
>> > Integer() to SAGE's inner type). This isn't practical for engineers,
>> > who normally use real numbers.
>> > Solution: There should be a variable that caused all numbers to be
>> > converted to RealNumber by default instead of Integer, even if an
>> > integer was entered.
>>
>> You can make this happen as follows:
>>
>> sage: RealNumber=float; Integer=float
>> sage: 2 + 3
>> 5.0
>> sage: 4/7
>> 0.5714285714285714
>>
>> Note that this will screw many things up big-time, e.g., list indexing
>> is broken:
>>
>> sage: v = [1,2,3]
>> sage: v[2]
>> ---------------------------------------------------------------------------
>> TypeError Traceback (most recent call last)
>>
>> /Users/was/build/sage-4.5.1/<ipython console> in <module>()
>>
>> TypeError: list indices must be integers, not float
>>
>> > 2. UNITS
>> > It would be nice to make SAGE capable of handling units and do unit
>> > conversion.
>> > Solution: There are already some Python modules that allow the "1 m"
>> > syntax for a value with units. For some more complex units, I'd use a
>> > syntax like "9.8 'kg*m/s^2' " (a literal number followed by a string),
>> > or "9.8 [kg*m/s^2]" (a literal number followed by the units between
>> > brackets).
>>
>> Sage already has extensive support for units.
>>
>> sage: kg = units.mass.kilogram; m = units.length.meter; s = units.time.second
>> sage: a = (9.8 * kg * m / s^2); a
>> 9.8000000000000007*kilogram*meter/second^2.0
>> sage: a.convert(units.mass.gram * m / s^2)
>> 9800.0*gram*meter/second^2.0
>>
>> > 3. BODE DIAGRAMS
>> > I didn't find it easy to plot a Bode diagram of a function. The plot()
>> > function doesn't appear to have a "logarithmic" option, and it doesn't
>> > look easy to put 2 parallel plots on the same image, one on the upper
>> > half and another on the lower half.
>> > Solution: have a bode() function that does all the work (along with
>> > nyquist() and maybe root_locus()). Extending the options on the plot()
>> > function would also be nice (at least, add logarithmic_x and
>> > logarithmic_y options).
>>
>> Parallel plots? Do you mean like this:
>>
>> sage: graphics_array([plot(sin(x), 0, 3), plot(cos(x),0,3)],2,1)
>>
>> > 4. MATRIX INPUT
>> > SAGE lacks an easy way to enter matrices. The easiest one is to do
>> > something like "matrix([[1,2],[3,4]])", but that's uncomfortable,
>> > specially for people who are used to Matlab's (or Octave's) "[1 2; 3
>> > 4]".
>> > Solution: My proposed syntax is "[[1,2],[3,4]]m", this is, a literal
>> > list followed by an "m", as an alias to "matrix([[1,2],[3,4]])". Same
>> > for "v" (vectors), "c" (complex numbers), maybe "q" (quaternions),
>> > "p" (polynomials)...
>>
>> I think this is pretty easy:
>>
>> sage: matrix(2, [1,2, 3,4])
>> [1 2]
>> [3 4]
>>
>> I don't like your suggestion to introduce something that isn't valid
>> Python to enter matrices.
>>
>> > 5. MATRIX INDEXES
>> > I had written a long paragraph about how easy is to get slices of
>> > matrices on Matlab/Octave and how good it would be to implement
>> > something similar on SAGE with some examples, just to realize that it
>> > was already implemented. :(
>> > (some examples: mat[3], mat[1,2], mat[0:3], mat[[3,2,1,0]], mat[:,
>> > 0]...)
>>
>> Moreover, if you use numpy arrays you get extremely powerful and
>> efficient slicing into n-dimensional arrays. This is very useful,
>> e.g., when dealing with 3d scientific data.
>>
>>
>>
>> > 6. TRANSPOSE/CONJUGATE
>> > If I want to get the transposed of a matrix, I have to write
>> > "mat.transpose()", while on Matlab it's as easy as "mat' ". Same for
>> > conjugating complex numbers or transposing+conjugating complex
>> > matrices.
>> > Solution: The solutions are to have a .T (or .H, .C...) attribute, or
>> > to have a custom operator that conjugates and transposes, such as
>> > "*mat" or "+mat" (the latter might be easier to implement since
>> > there's already an unary "+" operator in Python that doesn't do
>> > anything useful).
>>
>> Why don't you do this:
>>
>> sage: T = lambda x: x.transpose()
>> sage: A = matrix(3, [1,2, 3,4, 5,6]); A
>> [1 2]
>> [3 4]
>> [5 6]
>> sage: T(A)
>> [1 3 5]
>> [2 4 6]
>>
>>
>>
>> > --
>> > To post to this group, send an email to sage-devel@googlegroups.com
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>> > URL:http://www.sagemath.org
>>
>> --
>> William Stein
>> Professor of Mathematics
>> University of Washingtonhttp://wstein.org
>
> --
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>
--
William Stein
Professor of Mathematics
University of Washington
http://wstein.org
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