2009/4/3 Brian <[email protected]>:
>
> Indeed, thanks William. I'm not understanding the problem though, as
> range works with "ordinary" variables:
>
> x=5
> [t for t in range(1,x)]
Here x "is" (or rather -- points to) the constant integer 5. It's not
a symbolic variable.
If you do
x = var('x')
then x is a symbolic variable.
>
> Anyway, I changed the units function to not use a list comprehension,
> and instead use this formula:
> http://i.investopedia.com/inv/tutorials/site/advancedbond/yield9.GIF
>
> The new units function:
> def units(C, n, F, r):
> return C * ((1 - (1 / (1 + r) ^ n)) / r) + F * (1 / (1 + r) ^ n)
>
> And here we have arrived, successful, with the 3d plot expression:
>
> plot3d(price(70,var('n'),1000,var('r')), (n,1,5), (r,0,5))
>
> Hooray sage! Very cool.
>
> On Apr 3, 8:53 pm, William Stein <[email protected]> wrote:
>> On Fri, Apr 3, 2009 at 7:45 PM, Brian <[email protected]> wrote:
>>
>> > Thank you Timothy. Here is the correct (I believe) code for that
>> > equation.
>>
>> > def units(C, n, F, r):
>> > return sum([C / (1 + r) ^ t for t in range(1, n+1)]) + F / (1 + r)
>> > ^ n
>>
>> > def price(C, n, F, r):
>> > return 100 * (units(C, n, F, r) / F)
>>
>> > Here, units expresses the equation I linked to, and price gives the
>> > scaled price, 100 being par.
>>
>> > For example, evaluating the expression below demonstrates the example
>> > calculation from this site:
>> >http://www.moneychimp.com/articles/finworks/fmbondytm.htm
>>
>> > units(70,4,1000,.0853)
>>
>> > That evaluates to ~950 as in the example, therefore giving a price of
>> > ~95:
>>
>> > price(70,4,1000,.0853)
>>
>> > And sure enough, plotting the price yield curve gives sensible
>> > results:
>> > plot(price(70,4,1000,var('y')),0,.2)
>>
>> > Now I would like to make a 3d plot where n and r are free. The
>> > trouble is, when I try it, I get the following error. Would someone
>> > point out my error?
>>
>> > plot(price(70,var('n'),1000,var('y')))
>>
>> > TypeError: range() integer start argument expected, got
>> > sage.rings.integer.Integer.
>>
>> The problem is that you're giving the symbolic variable "n" as input
>> to the range command (in your units function), but the range command
>> takes a pair of integers as input.
>>
>> William
> >
>
--
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org
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