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18 |
18 |
19 |
19 |
20 .. Author : Amit |
20 .. Author : Amit |
21 Internal Reviewer : |
21 Internal Reviewer : |
22 External Reviewer : |
22 External Reviewer : |
23 Checklist OK? : <put date stamp here, if OK> [2010-10-05] |
23 Language Reviewer : Bhanukiran |
|
24 Checklist OK? : <, if OK> [2010-10-05] |
24 |
25 |
25 Symbolics with Sage |
26 Symbolics with Sage |
26 ------------------- |
27 ------------------- |
27 |
28 |
28 Hello friends and welcome to the tutorial on Symbolics with Sage. |
29 Hello friends and welcome to the tutorial on Symbolics with Sage. |
38 * Performing Integration, differentiation using Sage. |
39 * Performing Integration, differentiation using Sage. |
39 * Defining matrices. |
40 * Defining matrices. |
40 * Defining symbolic functions. |
41 * Defining symbolic functions. |
41 * Simplifying and solving symbolic expressions and functions. |
42 * Simplifying and solving symbolic expressions and functions. |
42 |
43 |
43 Amongst a lot of other things, Sage can do Symbolic Math and we shall |
44 In addtion to a lot of other things, Sage can do Symbolic Math and we shall |
44 start with defining symbolic expressions in Sage. |
45 start with defining symbolic expressions in Sage. |
45 |
46 |
46 Hope you have your Sage notebook open. If not, pause the video and |
47 Have your Sage notebook opened. If not, pause the video and |
47 start you Sage notebook. |
48 start you Sage notebook right now. |
48 |
49 |
49 On the sage notebook type:: |
50 On the sage notebook type:: |
50 |
51 |
51 sin(y) |
52 sin(y) |
52 |
53 |
61 sin(y) |
62 sin(y) |
62 |
63 |
63 Sage simply returns the expression. |
64 Sage simply returns the expression. |
64 |
65 |
65 Sage treats ``sin(y)`` as a symbolic expression. We can use this to do |
66 Sage treats ``sin(y)`` as a symbolic expression. We can use this to do |
66 symbolic maths using Sage's built-in constants and expressions. |
67 symbolic math using Sage's built-in constants and expressions. |
67 |
68 |
68 Let us try out a few examples. :: |
69 Let us try out a few examples. :: |
69 |
70 |
70 var('x,alpha,y,beta') |
71 var('x,alpha,y,beta') |
71 x^2/alpha^2+y^2/beta^2 |
72 x^2/alpha^2+y^2/beta^2 |
284 f.substitute(phi=root) |
285 f.substitute(phi=root) |
285 |
286 |
286 as we can see when we substitute the value the answer is almost = 0 showing |
287 as we can see when we substitute the value the answer is almost = 0 showing |
287 the solution we got was correct. |
288 the solution we got was correct. |
288 |
289 |
289 Following is an (are) exercise(s) that you must do. |
290 Following are a few exercises that you must do. |
290 |
291 |
291 %% %% Differentiate the following. |
292 %% %% Differentiate the following. |
292 |
293 |
293 1. sin(x^3)+log(3x) , degree=2 |
294 1. sin(x^3)+log(3x) , degree=2 |
294 #. x^5*log(x^7) , degree=4 |
295 #. x^5*log(x^7) , degree=4 |