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@@ -25,22 +25,22 @@ This page explains the notation used in this mathematical formulation section of
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= \\&
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\text{COMMODITY_BALANCE}_{c h l n y}
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- The first line gives:
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- The equality (=) or inequality (< or >) relation is on a line by itself.
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This allows to distinguish the **left- and right-hand sides** of the expression.
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- The first line begins with the "for all …" symbol (:math:`\forall`) and gives:
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- The **dimensionality** of the equation or inequality, via a list of **indices** (in alphabetical order).
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In some cases, this is equivalent to the dimensionality of a single term on either side; for instance, in the example above, of COMMODITY_BALANCE.
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In some cases, this is equivalent to the dimensionality of a single term on either side.
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In the example above, this is COMMODITY_BALANCE.
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Where both sides are more complicated, the first line informs about the dimensionality.
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- Any **conditions or restrictions** on the set members to which the indices apply.
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Implicitly, indices without condition may take any value from their corresponding set.
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In the example above:
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- Index :math:`l` must be in the union of certain other sets.
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- The indices :math:`y` (for parameters/variables with a dimension named "year") must always align with indices :math:`y^A` (for parameters/variables with a dimension named "year_active").
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- Likewise, :math:`n`, :math:`n^D` (node_dest), and :math:`n_O` (node_origin) must all be aligned
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- The other indices are unconstrained, so implicitly :math:`c \in C` and :math:`h in H`.
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- The equality (=) or inequality (< or >) is on a line by itself.
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This allows to distinguish the **left- and right-hand sides** of the expression.
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- Likewise, :math:`n`, :math:`n^D` (node_dest), and :math:`n^O` (node_origin) must all be aligned
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- The other indices are unconstrained, so implicitly :math:`c \in C` and :math:`h \in H`.
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- References to items (exogenous **parameters** or endogenous **variables**) include:
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@@ -52,8 +52,8 @@ This page explains the notation used in this mathematical formulation section of
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These:
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- Always exactly restate the dimensionality of the item given elsewhere in this documentation.
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That is, it does not express aggregation or other operations.
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- *May* express an alignment or restriction of indices, if this is particular to one reference of the parameter/variable.
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That is, the indices do indicate aggregation or other operations.
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- *May* express an alignment or restriction of indices, *if and only if* this is particular to one reference of the parameter/variable.
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Otherwise, these are expressed in the first line, as described above.
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In the above example, 'duration_time_rel' has indices :math:`h^1, h^2`, but these are aligned differently in the two places it is used in the equation.
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- Facilitate understanding of alignment and broadcasting between elements of parameters/variables with different dimensionality.
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