MOS substitution: Difference between revisions
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Here the scale is thought as traversing a series of rows one step of the row at a time, and | Here the scale is thought as traversing a series of rows one step of the row at a time, and | ||
* <math>\{\mathbf{a} + i\mathbf{v}\}_{i=a}^{n-1}</math> is a tail of the first row | * <math>\{\mathbf{a} + i\mathbf{v}\}_{i=a}^{n-1}</math> is a (nonempty) tail of the first row | ||
* <math>\{\mathbf{a} + i\mathbf{v} + j\mathbf{w}\}_{(i,j) \in [n]_0 \times [m-2]_1}</math> is a (possibly empty) parallelogram where rows are traversed fully | * <math>\{\mathbf{a} + i\mathbf{v} + j\mathbf{w}\}_{(i,j) \in [n]_0 \times [m-2]_1}</math> is a (possibly empty) parallelogram where rows are traversed fully | ||
* <math>\{\mathbf{a} + i\mathbf{v} + (m-1)\mathbf{w}\}_{i=0}^{b}</math> is a prefix of the last row | * <math>\{\mathbf{a} + i\mathbf{v} + (m-1)\mathbf{w}\}_{i=0}^{b}</math> is a (nonempty) prefix of the last row | ||
* '''v''' and '''w''' are the generator and offset | |||
In the above case, {{nowrap| ''n'' {{=}} ''q'' | '''v''' {{=}} subst(''p''<sub>''T''</sub>, '''X''', ''p''<sub>''F''</sub>) | and '''w''' {{=}} subst((''p''<sub>''T''</sub>)<sup>''q''</sup>, '''X''', ''G''<sup>''r''</sup>) (the aggregate generator)}}. | In the above case, {{nowrap| ''n'' {{=}} ''q'' | '''v''' {{=}} subst(''p''<sub>''T''</sub>, '''X''', ''p''<sub>''F''</sub>) | and '''w''' {{=}} subst((''p''<sub>''T''</sub>)<sup>''q''</sup>, '''X''', ''G''<sup>''r''</sup>) (the aggregate generator)}}. | ||