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I am absolute novice in Maple, sorry... Please, help. When solving simple system of equations like the one described in manual: solve({x+2*y = 3, y+1/x = 1}, [x, y]), everything works nice. But when trying to solve my system of 12 equations, error Error, (in solve) invalid arguments is thrown. What is wrong?

My system:

solve( {
y0 = a0+b0*x0+c0*x0^2+d0*x0^3,
y1 = a0+b0*x1+c0*x1^2+d0*x1^3,
y1 = a1+b1*x1+c1*x1^2+d1*x1^3,
y2 = a1+b1*x2+c1*x2^2+d1*x2^3,
y2 = a2+b2*x2+c2*x2^2+d2*x2^3,
y3 = a2+b2*x3+c3*x3^2+d2*x3^2, 

2/((x2-x1)/(y2-y1)+(x1-x0)/(y1-y0)) = b0+2*c0*x1+3*d0*x1^2,
2/((x3-x2)/(y3-y2)+(x2-x1)/(y2-y1)) = b1+2*c1*x1+3*d1*x1^2,
2/((x2-x1)/(y2-y1)+(x1-x0)/(y1-y0)) = b1+2*c1*x2+3*d1*x2^2,
2/((x3-x2)/(y3-y2)+(x2-x1)/(y2-y1)) = b2+2*c2*x2+3*d2*x2^2,

diff(2/((x2-x1)/(y2-y1)+(x1-x0)/(y1-y0)), x1) = 0,
diff(2/((x3-x2)/(y3-y2)+(x2-x1)/(y2-y1)), x2) = 0
}, [a0,b0,c0,d0,a1,b1,c1,d1,a2,b2,c2,d2])
crashmstr
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Josef Kokes
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  • What version (major and minor number) are you using? Check with command kernelopts(version) – acer Feb 02 '15 at 01:55

2 Answers2

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Are the x_i's set to fixed numbers? Or should your a/b/c/d's be fixed to fix numbers?

Right now, this command solves for [a0,b0,c0,d0,a1,b1,c1,d1,a2,b2,c2,d2] in terms of [x1,x2,x3].

By the way, y3 has a c3 variable in it, is this a typo?

In Maple 12, I get that maple cannot find a solution, or there are no solutions:

> solve( {
> y0 = a0+b0*x0+c0*x0^2+d0*x0^3,
> y1 = a0+b0*x1+c0*x1^2+d0*x1^3,
> y1 = a1+b1*x1+c1*x1^2+d1*x1^3,
> y2 = a1+b1*x2+c1*x2^2+d1*x2^3,
> y2 = a2+b2*x2+c2*x2^2+d2*x2^3,
> y3 = a2+b2*x3+c3*x3^2+d2*x3^2, 
> 
> 2/((x2-x1)/(y2-y1)+(x1-x0)/(y1-y0)) = b0+2*c0*x1+3*d0*x1^2,
> 2/((x3-x2)/(y3-y2)+(x2-x1)/(y2-y1)) = b1+2*c1*x1+3*d1*x1^2,
> 2/((x2-x1)/(y2-y1)+(x1-x0)/(y1-y0)) = b1+2*c1*x2+3*d1*x2^2,
> 2/((x3-x2)/(y3-y2)+(x2-x1)/(y2-y1)) = b2+2*c2*x2+3*d2*x2^2,
> 
> diff(2/((x2-x1)/(y2-y1)+(x1-x0)/(y1-y0)), x1) = 0,
> diff(2/((x3-x2)/(y3-y2)+(x2-x1)/(y2-y1)), x2) = 0
> }, [a0,b0,c0,d0,a1,b1,c1,d1,a2,b2,c2,d2,c3]);
                                      []

Have you tried setting some numbers for the a/b/c/d's and solve for the x's like so:

a0:= some number
...
d2:=some number;
y0 := a0+b0*x0+c0*x0^2+d0*x0^3;
y1 := a0+b0*x1+c0*x1^2+d0*x1^3;
y1 := a1+b1*x1+c1*x1^2+d1*x1^3;
y2 := a1+b1*x2+c1*x2^2+d1*x2^3;
y2 := a2+b2*x2+c2*x2^2+d2*x2^3;
y3 := a2+b2*x3+c2*x3^2+d2*x3^2; 
solve( {
2/((x2-x1)/(y2-y1)+(x1-x0)/(y1-y0)) = b0+2*c0*x1+3*d0*x1^2,
2/((x3-x2)/(y3-y2)+(x2-x1)/(y2-y1)) = b1+2*c1*x1+3*d1*x1^2,
2/((x2-x1)/(y2-y1)+(x1-x0)/(y1-y0)) = b1+2*c1*x2+3*d1*x2^2,
2/((x3-x2)/(y3-y2)+(x2-x1)/(y2-y1)) = b2+2*c2*x2+3*d2*x2^2,
diff(2/((x2-x1)/(y2-y1)+(x1-x0)/(y1-y0)), x1) = 0,
diff(2/((x3-x2)/(y3-y2)+(x2-x1)/(y2-y1)), x2) = 0
}, [x1,x2,x3]);
BeDutra
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DeButra: Thanks for your kind assistance! 1) yes, c3 is a typo - should be c2 2) I need a symbolic, not numeric solution. I need express a0,a1, ... d2 in terms of [x1,x2,x3]. 3) You had a bright idea to try setting some numbers. I am trying to do so and I send a feedback. Thanks again.

Josef Kokes
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