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book: Start collecting tips and tricks
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- [Concepts](concepts.md)
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- [User Documentation](user.md)
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- [Gadgets](user/gadgets.md)
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- [Tips and tricks](user/tips-and-tricks.md)
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- [Design](design.md)
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# Tips and tricks
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This section contains various ideas and snippets that you might find useful while writing
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halo2 circuits.
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## Small range constraints
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A common constraint used in R1CS circuits is the boolean constraint: $b * (1 - b) = 0$.
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This constraint can only be satisfied by $b = 0$ or $b = 1$.
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In halo2 circuits, you can similarly constrain a cell to have one of a small set of
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values. For example, to constrain $a$ to the range $[0..5]$, you would create a gate of
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the form:
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$$a * (1 - a) * (2 - a) * (3 - a) * (4 - a) = 0$$
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while to constraint $c$ to be either 7 or 13, you would use:
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$$(7 - c) * (13 - c) = 0$$
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> The underlying principle here is that we create a polynomial constraint with roots at
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> each value in the set of possible values we want to allow. In R1CS circuits, the maximum
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> supported polynomial degree is 2 (due to all constraints being of the form $a * b = c$).
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> In halo2 circuits, you can use arbitrary-degree polynomials - with the proviso that
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> higher-degree constraints are more expensive to use.
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