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For an overdetermined system (more ingredients than nutrients) there is theoretically no single solution. The recipe stretching confirm this. Stretching breaks the bound ingredients, but then bounds another ingredient. And this gives again an exact solution. When one stretches to much even bounding does not help and one needs a LS-fit to find a solution. Where lies these break points? If we can define these break points, we could define a range of possible recipes for  product. I suspect this can be solved mathematically.
 
For an overdetermined system (more ingredients than nutrients) there is theoretically no single solution. The recipe stretching confirm this. Stretching breaks the bound ingredients, but then bounds another ingredient. And this gives again an exact solution. When one stretches to much even bounding does not help and one needs a LS-fit to find a solution. Where lies these break points? If we can define these break points, we could define a range of possible recipes for  product. I suspect this can be solved mathematically.
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== Determined systems ==
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== Determined products ==
These are products where the number of ingredients equals the number of nutrients. For these products we can directly calculate the recipe. No fitting required.
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These are products where the number of ingredients equals the number of nutrients. For these products we can directly calculate the recipe. No fitting required.
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=== Rank ===
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This only works however when the ingredients are full rank, that is no ingredient can be defined as a sum of other ingredients. An added complexity is that one has to determine the non-negative rank to be sure of this.
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If the ingredients are NOT full rank, the product becomes underdetermined.
    
== Underdetermined systems ==
 
== Underdetermined systems ==
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