Ask Your Question
2

Working with complex symbolic expressions

asked 2012-02-13 08:07:47 -0500

russ_hensel gravatar image

I am a beginner at Sage so my questions may not be well informed, so bear with me.

The context: I am trying to use sage to explore the exponential function assuming all I know about it is that it is its own derivative and has the value 1 at z = 0. It is then easy to develop the Taylor series to any degree using formula like:

expp2( z ) = 1 + ( 1/ factorial( 1 ) )* z + ( 1/ factorial( 2 ) ) * ( z ^ 2 )

You can take 2 of these for z = a and z = b and multiply them together in Sage. Getting something like:

1/4(b^2 + 2b + 2)(a^2 + 2a + 2)

Now I have done the algebra by hand and know this reduces to the Taylor expansion for z = a + b.

What I do not get is how to show this part in Sage in a nice clean way ( I have some ways I do not like so much ).

Here I have 2 questions one specific, and one general ( I am interested in the answer to either one or both):

1) If this exponential question interests anyone, could you offer some tips? I have tried various ( but not all ) applications of expand and simplify. I am still plugging away.

2) Is there a guide that would help me learn how to carry out algebraic operations over complex expressions. I have looked at several basic tutorials, but they do not have much detail. The most useful single resource I have found is

http://www.sagemath.org/doc/reference...

and the pages linking from it.

edit retag flag offensive close merge delete

1 answer

Sort by ยป oldest newest most voted
0

answered 2014-07-01 10:51:21 -0500

updated 2014-07-01 10:52:30 -0500

It is quite possible to get what you want with formal power series:

sage: R.<a,b> = PowerSeriesRing(QQ); R
Multivariate Power Series Ring in a, b over Rational Field
sage: exp(a+b)==exp(a)*exp(b)
True
sage: exp(a-b)==exp(a)/exp(b)
True

Read

edit flag offensive delete link more

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

Question Tools

1 follower

Stats

Asked: 2012-02-13 08:07:47 -0500

Seen: 169 times

Last updated: Jul 01 '14