Simplify, Solve Equation and use solution

asked 2011-01-28 10:07:13 +0100

manifold
95 ●3 ●7 ●14

updated 2011-01-28 10:18:02 +0100

DSM

5242 ●21 ●68 ●112

Hi, I'm new to sage, and have the following question: I have the following code:

x,y=var('x y')

f(x,y)= sin(x)*cos(y)+sin(y)*cos(x)
f.full_simplify
show(f(x,y))



s1=solve([f(x,y)==1],x,y)
show(s1)

Sage obiously doesn't simplify the function f... (simple trigonometric expression). And it doesn't solve it.

1) How can I simplify the function?

2) How can I use the result? For example: I have as an result: solution=[x == -1] How can I replace this x in an other function (example: sin(x)). In mathematica I would do: sin(x) /. solution or manually: sin(x) /. x->(-1)

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answered 2011-01-28 10:33:45 +0100

kcrisman
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A few comments.

If you use the f(x,y) syntax, you don't have to declare the variables ahead of time.
Using results is not too bad, because you can ask for them as a dictionary. There are other examples in the doc, I think, but for example:

sage: B = (x^2-1).solve(x)

sage: G = x^3+3*x

sage: [G.subs(b) for b in B]

[-4, 4]

sage: B = (x^2-1).solve(x,solution_dict=True)

sage: [G.subs(b) for b in B]

[-4, 4]
The actual first question is hard to find, and maybe should be part of our full simplification...:

sage: f(x,y)=sin(x)cos(y)+sin(y)cos(x)

sage: f.trig_reduce()

(x, y) |--> sin(x + y)

Note to Evgeny: I cannot get code formatted text after a bullet point. What gives? I asked this on the askbot website too.

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Beat me by three minutes. :^)

DSM ( 2011-01-28 10:37:57 +0100 )edit

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answered 2011-01-28 10:59:18 +0100

manifold
95 ●3 ●7 ●14

updated 2011-01-28 11:07:17 +0100

Thanks it works!

Here for everyone the code to show it:

# Solve an equation an use the solution 
mysol=solve([2+x^2==-1],x)
show(mysol)


G = x^3-i
show(G)

newG=G.subs(mysol[0])
show(newG)

[G.subs(j) for j in mysol]

But the trig reduce doesn't work with this code:

f(x,y)= sin(x)*cos(y)+sin(y)*cos(x)
f.trig_reduce()
show(f)



s1=solve([f(x,y)==1],x,y)
show(s1)

I still get (x, y) |--> sin(x)cos(y) + sin(y)cos(x)

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f.trig_reduce() returns a *copy* of f which has been trig_reduced. It doesn't affect f. Try f=f.trig_reduce().

DSM ( 2011-01-28 11:17:09 +0100 )edit

thanks! it works.

manifold ( 2011-01-28 11:27:49 +0100 )edit

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