--- a/symbolics.rst Thu Sep 23 13:14:31 2010 +0530
+++ b/symbolics.rst Thu Sep 23 13:55:35 2010 +0530
@@ -4,11 +4,19 @@
This tutorial on using Sage for symbolic calculation is brought to you
by Fossee group.
+.. #[Madhu: Sounds more or less like an ad!]
+
{{{ Part of Notebook with title }}}
+.. #[Madhu: Please make your instructions, instructional. While
+ recording if I have to read this, think what you are actually
+ meaning it will take a lot of time]
+
We would be using simple mathematical functions on the sage notebook
for this tutorial.
+.. #[Madhu: What is this line doing here. I don't see much use of it]
+
During the course of the tutorial we will learn
{{{ Part of Notebook with outline }}}
@@ -21,16 +29,27 @@
.. #[Nishanth]: The formatting is all messed up
First fix the formatting and compile the rst
The I shall review
+.. #[Madhu: Please make the above items full english sentences, not
+ the slides like points. The person recording should be able to
+ read your script as is. It can read something like "we will learn
+ how to define symbolic expressions in Sage, using built-in ..."]
-Using sage we can perform mathematical operations on symbols .
+Using sage we can perform mathematical operations on symbols.
+
+.. #[Madhu: Same mistake with period symbols! Please get the
+ punctuation right. Also you may have to rephrase the above
+ sentence as "We can use Sage to perform sybmolic mathematical
+ operations" or such]
On the sage notebook type::
sin(y)
-It raises a name error saying that y is not defined . But in sage we
-can declare y as a symbol using var function. ::
-
+It raises a name error saying that y is not defined. But in sage we
+can declare y as a symbol using var function.
+
+.. #[Madhu: But is not required]
+::
var('y')
Now if you type::
@@ -39,17 +58,30 @@
sage simply returns the expression .
+.. #[Madhu: Why is this line indented? Also full stop. When will you
+ learn? Yes we can correct you. But corrections are for you to
+ learn. If you don't learn from your mistakes, I don't know what
+ to say]
+
thus now sage treats sin(y) as a symbolic expression . You can use
this to do a lot of symbolic maths using sage's built-in constants and
expressions .
-Try out ::
+.. #[Madhu: "Thus now"? It sounds like Dus and Nou, i.e 10 and 9 in
+ Hindi! Full stop again. "a lot" doesn't mean anything until you
+ quantify it or give examples.]
+
+Try out
+
+.. #[Madhu: "So let us try" sounds better]
+ ::
var('x,alpha,y,beta') x^2/alpha^2+y^2/beta^2
Similarly , we can define many algebraic and trigonometric expressions
using sage .
+.. #[Madhu: comma again. Show some more examples?]
Sage also provides a few built-in constants which are commonly used in
@@ -58,6 +90,11 @@
example : pi,e,oo , Function n gives the numerical values of all these
constants.
+.. #[Madhu: This doesn't sound like scripts. How will I read this
+ while recording. Also if I were recording I would have read your
+ third constant as Oh-Oh i.e. double O. It took me at least 30
+ seconds to figure out it is infinity]
+
For instance::
n(e)
@@ -66,22 +103,33 @@
gives numerical value of e.
-If you look into the documentation of n by doing ::
+If you look into the documentation of n by doing
+.. #[Madhu: "documentation of the function "n"?]
+
+::
n(<Tab>
You will see what all arguments it can take etc .. It will be very
helpful if you look at the documentation of all functions introduced
-
+
+.. #[Madhu: What does etc .. mean in a script?]
Also we can define the no of digits we wish to use in the numerical
-value . For this we have to pass an argument digits. Type::
-
+value . For this we have to pass an argument digits. Type
+
+.. #[Madhu: "no of digits"? Also "We wish to obtain" than "we wish to
+ use"?]
+::
+
n(pi, digits = 10)
Apart from the constants sage also has a lot of builtin functions like
sin,cos,sinh,cosh,log,factorial,gamma,exp,arcsin,arccos,arctan etc ...
-lets try some out on the sage notebook. ::
+lets try some out on the sage notebook.
+
+.. #[Madhu: Here "a lot" makes sense]
+::
sin(pi/2)
@@ -96,6 +144,10 @@
var('x') function(<tab> {{{ Just to show the documentation
extend this line }}} function('f',x)
+.. #[Madhu: What will the person recording show in the documentation
+ without a script for it? Please don't assume recorder can cook up
+ things while recording. It is impractical]
+
Here f is the name of the function and x is the independent variable .
Now we can define f(x) to be ::
@@ -105,10 +157,14 @@
f(pi)
-We can also define function that are not continuous but defined
+We can also define functions that are not continuous but defined
piecewise. We will be using a function which is a parabola between 0
to 1 and a constant from 1 to 2 . type the following as given on the
-screen::
+screen
+
+.. #[Madhu: Instead of "We will be using ..." how about "Let us define
+ a function ..."]
+::
var('x') h(x)=x^2 g(x)=1 f=Piecewise(<Tab> {{{ Just to show the
@@ -117,21 +173,27 @@
Checking f at 0.4, 1.4 and 3 :: f(0.4) f(1.4) f(3)
+.. #[Madhu: Again this doesn't sound like a script]
+
for f(3) it raises a value not defined in domain error .
Apart from operations on expressions and functions one can also use
them for series .
+.. #[Madhu: I am not able to understand this line. "Use them as
+.. series". Use what as series?]
+
We first define a function f(n) in the way discussed above.::
var('n') function('f', n)
+.. #[Madhu: Shouldn't this be on 2 separate lines?]
To sum the function for a range of discrete values of n, we use the
sage function sum.
- For a convergent series , f(n)=1/n^2 we can say ::
+For a convergent series , f(n)=1/n^2 we can say ::
var('n') function('f', n)
@@ -141,11 +203,18 @@
For the famous Madhava series :: var('n') function('f', n)
+.. #[Madhu: What is this? your double colon says it must be code block
+ but where is the indentation and other things. How will the
+ recorder know about it?]
+
f(n) = (-1)^(n-1)*1/(2*n - 1)
This series converges to pi/4. It was used by ancient Indians to
interpret pi.
+.. #[Madhu: I am losing the context. Please add something to bring
+ this thing to the context]
+
For a divergent series, sum would raise a an error 'Sum is
divergent' ::
@@ -158,6 +227,10 @@
We can perform simple calculus operation using sage
+.. #[Madhu: When you switch to irrelevant topics make sure you use
+ some connectors in English like "Moving on let us see how to
+ perform simple calculus operations using Sage" or something like
+ that]
For example lets try an expression first ::
diff(x**2+sin(x),x) 2x+cos(x)
@@ -166,6 +239,8 @@
first argument is expression or function and second argument is the
independent variable .
+.. #[Madhu: Full stop, Full stop, Full stop]
+
We have already tried an expression now lets try a function ::
f=exp(x^2)+arcsin(x) diff(f(x),x)
@@ -175,6 +250,7 @@
diff(<tab> diff(f(x),x,3)
+.. #[Madhu: Please try to be more explicit saying third argument]
in this case it is 3.
@@ -183,10 +259,13 @@
x = var('x') s = integral(1/(1 + (tan(x))**2),x) s
+.. #[Madhu: Two separate lines.]
+To find the factors of an expression use the "factor" function
-To find factors of an expression use the function factor
+.. #[Madhu: See the diff]
+::
factor(<tab> y = (x^100 - x^70)*(cos(x)^2 + cos(x)^2*tan(x)^2) f =
factor(y)
@@ -198,20 +277,25 @@
f.simplify_exp() f.simplify_trig()
+.. #[Madhu: Separate lines?]
One can also find roots of an equation by using find_root function::
phi = var('phi') find_root(cos(phi)==sin(phi),0,pi/2)
+.. #[Madhu: Separate lines?]
+
Lets substitute this solution into the equation and see we were
correct ::
var('phi') f(phi)=cos(phi)-sin(phi)
root=find_root(f(phi)==0,0,pi/2) f.substitute(phi=root)
+.. #[Madhu: Separate lines?]
as we can see the solution is almost equal to zero .
+.. #[Madhu: So what?]
We can also define symbolic matrices ::
@@ -219,11 +303,16 @@
var('a,b,c,d') A=matrix([[a,1,0],[0,b,0],[0,c,d]]) A
+.. #[Madhu: Why don't you break the lines?]
-Now lets do some of the matrix operations on this matrix ::
+Now lets do some of the matrix operations on this matrix
+.. #[Madhu: Why don't you break the lines? Also how do you connect
+ this up? Use some transformation keywords in English]
+::
+ A.det() A.inverse()
- A.det() A.inverse()
+.. #[Madhu: Why don't you break the lines?]
You can do ::
@@ -231,6 +320,7 @@
To see what all operations are available
+.. #[Madhu: Sounds very abrupt]
{{{ Part of the notebook with summary }}}
@@ -247,3 +337,7 @@
factor() , simplify_full, simplify_exp , simplify_trig .
Substituting values in expression using substitute function.
And finally creating symbolic matrices and performing operation on them .
+
+.. #[Madhu: See what Nishanth is doing. He has written this as
+ points. So easy to read out while recording. You may want to
+ reorganize like that]