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Using Maple to re-arrange equations

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Stephen Clark

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Jan 12, 2003, 3:29:20 PM1/12/03
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I have a set of four equations which define a relationship between four
betas plus a single theta and four alphas. I would like to re-arrange the
equations so that I can get an expression for the betas in terms of the
alphas. Here are the equations in Maple format.

> y1:=exp(beta1*Z1+beta4*Z4)=gamma*exp(alpha1*Z1);

> y2:=exp(beta2*Z2+beta4*Z4)=gamma*exp(alpha2*Z2);

>
y3:=(exp(beta1*Z1+beta4*Z4)+exp(beta2*Z2+beta4*Z4))**theta=sigma*(exp(alpha1
*Z1)+exp(alpha2*Z2)+exp(alpha4*Z4));

> y4:=(exp(beta3*Z3))**theta=gamma*exp(alpha3*Z3);

The gamma and sigma are just scaling parameters (ie constants). It is
possible to derive expressions for b1, b2, b3, b4 and theta? I know that I
have five unknowns and only four equations so maybe this is not possible?

Any advice welcome.


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Alec Mihailovs

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Jan 12, 2003, 3:46:29 PM1/12/03
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"Stephen Clark" <octo...@hotmail.com> wrote in message
news:104240336...@demeter.uk.clara.net...

> I have a set of four equations which define a relationship between four
> betas plus a single theta and four alphas. I would like to re-arrange the
> equations so that I can get an expression for the betas in terms of the
> alphas. Here are the equations in Maple format.
>
> > y1:=exp(beta1*Z1+beta4*Z4)=gamma*exp(alpha1*Z1);
>
> > y2:=exp(beta2*Z2+beta4*Z4)=gamma*exp(alpha2*Z2);
>
> >
>
y3:=(exp(beta1*Z1+beta4*Z4)+exp(beta2*Z2+beta4*Z4))**theta=sigma*(exp(alpha1
> *Z1)+exp(alpha2*Z2)+exp(alpha4*Z4));
>
> > y4:=(exp(beta3*Z3))**theta=gamma*exp(alpha3*Z3);
>
> The gamma and sigma are just scaling parameters (ie constants). It is
> possible to derive expressions for b1, b2, b3, b4 and theta? I know that I
> have five unknowns and only four equations so maybe this is not possible?
>
> Any advice welcome.

One might try

> solve({y1,y2,y3,y4},{beta1,beta2,beta3,beta4,theta});

Note that gamma is a constant in Maple, approximately 0.5772156649...

Alec Mihailovs
http://webpages.shepherd.edu/amihailo/

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