# Question:How do I solve symbolic linear equations (which are homogenous of degree 1) for a ratio of variables?

## Question:How do I solve symbolic linear equations (which are homogenous of degree 1) for a ratio of variables?

Maple

Dear Maple community,

I am trying to solve a system of linear equations, each of which is homogenous of degree 1 (i.e., defined up to a scale/constant factor), and was wondering whether one can use Maple to solve for ratios of variables (defined relative to a numeraire). An example of my problem is attached (Example.mw). More specifically:

- Equation (1) defines the system,

- Equations (2) through (4) exemplify the system for J=3 and S=1 (creating the system of 3 equations in 3 unknowns: {dlog R[1,1], dlog R[2,1], dlog R[3,1]},

- Function A solves this system for the unknowns and the subsequent commands simplify dlog R[1,1] (and dlog R[2,1]) using the model's constraints (side relations). Not surprizingly, I get the error message "Error, (in simplify/siderels:-Recurse) indeterminate expression of the form 0/0", which results from the fact that the system is homogenous of degree 1 (and, hence, each dlog R is defined only up to a scale),

- However, in principle, it should be possible to choose one of the dlog R's, say, dlog R[1,1] as a numeraire and express the other two "unknowns" (dlog R[2,1], and dlog R[3,1]), relative to it, in order to ultimately solve this system for dlog R[2,1]/dlog R[1,1] and dlog R[3,1]/dlog R[1,1] as functions of exogenous variables only.

I'd appreciate any advice how I can use Maple to tackle this problem. Thank you very much in advance!

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