On Thu, Mar 26, 2009 at 8:00 AM, Drini <pdsanc...@gmail.com> wrote:
>
>
>
> Jason Grout wrote:
>
>>
>> Here it is using linear algebra:
>>
>> sage: var('a,b,c,d,x,y')
>> (a, b, c, d, x, y)
>> sage: A=matrix(2,[a,b,c,d]); A
>> [a b]
>> [c d]
>> sage: result=vector([3,5]); result
>> (3, 5)
>> sage: soln=A.solve_right(result) # you could also do soln=A\result
>> sage: soln
>> (3/a - b*(5 - 3*c/a)/(a*(d - b*c/a)), (5 - 3*c/a)/(d - b*c/a))
>>
>>
>> Now, checking our answers:
>>
>>
>> sage: (a*x+b*y).subs(x=soln[0],y=soln[1]).simplify_full()
>> 3
>> sage: (c*x+d*y).subs(x=soln[0],y=soln[1]).simplify_full()
>> 5
>>
>>
>> Or just checking it with matrix multiplication:
>>
>> sage: A*soln
>> (a*(3/a - b*(5 - 3*c/a)/(a*(d - b*c/a))) + b*(5 - 3*c/a)/(d - b*c/a),
>> c*(3/a - b*(5 - 3*c/a)/(a*(d - b*c/a))) + (5 - 3*c/a)*d/(d - b*c/a))
>>
>> Let's simplify each entry by applying the "simplify_full" function to
>> each entry:
>>
>> sage: (A*soln).apply_map(lambda x: x.simplify_full())
>> (3, 5)
>>
>>
>> This example probably ought to go into some documentation somewhere...
>>
>> Jason
>
> Well :) it was almost too nice to be true:
>
> n=var('n')
> T=vector([3,n])
> A=matrix([[6,2],[7,1]])
> A.solve_right(T)
>
> Traceback (most recent call last):
> File "<stdin>", line 1, in <module>
> File "/home/drini/.sage/sage_notebook/worksheets/admin/6/code/
> 34.py", line 6, in <module>
> (......)
> TypeError: unable to convert n to a rational
>
> Likewise with A\T
>
> it's kinda strange that such elemental system of equations can't be
> done symbollically by matrix way:
> 6x + 2y = 3
> 7x + y = n
>
> of course, changing n for some number works.
Do this:
sage: n=var('n')
sage: T=vector([3,n])
sage: A=matrix(SR,[[6,2],[7,1]])
sage: A.solve_right(T)
((n - 7/2)/4 + 1/2, -3*(n - 7/2)/4)
Robert Dodier -- yes, it's using Maxima.
-- William
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