| 1. | Vector addition and scalar multiplication are defined in the obvious manner.
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| 2. | Trace zero varieties feature a better scalar multiplication performance than elliptic curves.
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| 3. | The sum of two such elements and is and scalar multiplication is given by.
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| 4. | This set inherits the module structure via component-wise addition and scalar multiplication.
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| 5. | Because there is only one modular form of weight 8 up to scalar multiplication,
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| 6. | Addition and scalar multiplication is performed componentwise.
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| 7. | Scalar multiplication may be viewed as an action of the field on the vector space.
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| 8. | *By the definition of addition and scalar multiplication of linear functionals in the dual space,
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| 9. | Then scalar multiplication is defined as.
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| 10. | This set forms a supermodule over " R " under supermatrix addition and scalar multiplication.
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