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2012-11-12 07:05:55 -0600 asked a question Rotational 3d

How can I rotate a function like f(x)=sqrt(x) (from 0 to3) around the x-axis? I would like to have a 3D picture of the rotational.

Thanks. Thomas

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2011-08-29 22:07:46 -0600 answered a question Solving a linear equation

Or did you intend sage: solve([g1,g2,g3,g4],[a,b,c,d]) instead of...

Yes!! Yesterday I sat an hour ...and now I have made a spelling error!

Thank you Thomas

2011-08-29 21:58:37 -0600 marked best answer Solving a linear equation

Your answer is just one of the ones for this.

sage: r1=-62/3675
sage: -10*r1-1/25
473/3675
sage: 25*r1+2/5
-16/735

Maxima returns a solve like this when there is a parameter. In this case, one parameter, r1, which can be any real number. Are you sure your matrix has non-zero determinant?

Or did you intend

sage: solve([g1,g2,g3,g4],[a,b,c,d])

instead of

sage: solve([g1,g2,g3,g3],[a,b,c,d])

Actually, I think this is the real issue - typos trip us all up :(

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2011-08-29 09:12:56 -0600 asked a question Solving a linear equation

Hello,

I have a problem with the solution of a linear equation given by sage.

sage: a,b,c,d=var('a,b,c,d')
sage: v(t)=a*t^3+b*t^2+c*t+d
sage: v1(t)=diff(v(t),t)
sage: g1=v(0)==0
sage: g2=v(5)==1
sage: g3=v1(5)==0
sage: g4=v(1.5)==0.2
sage: solve([g1,g2,g3,g3],[a,b,c,d])
[[a == r1, b == -10*r1 - 1/25, c == 25*r1 + 2/5, d == 0]]

The right solution is a=-62/3675, b=473/3675, c=-16/735, d=0!

What's wrong with my implementation in sage?

Thomas

By the way: How can I realize the typical pre-formatted "sage:... look" in my postings??

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2011-03-26 12:01:24 -0600 asked a question How-to: sum

Suppose I have defined a function

f(x)=x^2

and a list

x=[0,1,2,3,4]

Now I can calculate the product

x[2]*f(x[2])

But: If I use the command

k=var('k')
sum(x[k]*f(x[k]),k,0,4)

I will get the message:

TypeError: unable to convert x (=k) to an integer

How can I realize such a summation?

2011-03-26 11:45:09 -0600 commented answer How-to: (Linear ...) regression in Sage

Thank you for your answer

2011-03-26 11:44:35 -0600 marked best answer How-to: (Linear ...) regression in Sage

It turns out that this has even showed up on Stack Overflow.

Luckily, that page refers to the function I had completely forgotten about - find_fit.

sage: find_fit?

String Form:    <function find_fit at 0x10bee5cf8>
Namespace:      Interactive
File:           /Applications/MathApps/sage/local/lib/python2.6/site-packages/sage/numerical/optimize.py
Definition:     find_fit(data, model, initial_guess=None, parameters=None, variables=None, solution_dict=False)
Docstring:
       Finds numerical estimates for the parameters of the function model
       to give a best fit to data.

So this might work, and looks decent.

sage: R = [[1,2],[3.45,4],[6,5],[4,3]]
sage: var('a,b')
(a, b)
sage: model(x) = a*x+b
sage: find_fit(R,model)
[a == 0.56881365890949054, b == 1.445160655902004]
sage: points(R)+plot(model(a=find_fit(R,model)[0].rhs(),b=find_fit(R,model)[1].rhs()),(x,0,10),color='red')

If you are serious about your needs, though, you should probably use some of the tools in Scipy or R (numerous YouTube videos on this, though for reason I can't watch them right now.

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2011-03-15 08:42:53 -0600 asked a question How-to: (Linear ...) regression in Sage

Suppose I have the following set of points r = [(1,2),(3.45,4),(6,5),(4,3)]. How do I implement in Sage a (linear) regression with "bord tools"?