Structures · Algebra
RootPairing.EmbeddedG2
A data-bearing typeclass which distinguishes a pair of roots whose pairing is -3. This is a
sufficient condition for the span of this pair of roots to be a 𝔤₂ root system.
- Shape
- One type argument · adds long, short, pairingIn_long_short
Extends2
Extended by0
Nothing extends this class yet.
Concrete types that are instances0
No instance on a concrete type; it is reached through other classes.
How is a type an instance?
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Assumed by52
- RootPairing.EmbeddedG2.short
- RootPairing.EmbeddedG2.long
- RootPairing.EmbeddedG2.shortRoot
- RootPairing.EmbeddedG2.longRoot
- RootPairing.EmbeddedG2.allRoots
- RootPairing.EmbeddedG2.shortAddLongRoot
- RootPairing.EmbeddedG2.twoShortAddLongRoot
- RootPairing.EmbeddedG2.threeShortAddLongRoot
- RootPairing.EmbeddedG2.threeShortAddTwoLongRoot
- RootPairing.EmbeddedG2.threeShortAddLong
- RootPairing.EmbeddedG2.threeShortAddTwoLong
- RootPairing.EmbeddedG2.shortAddLong
- RootPairing.EmbeddedG2.twoShortAddLong
- RootPairing.EmbeddedG2.long_eq_three_mul_short
- RootPairing.EmbeddedG2.pairing_long_short
- RootPairing.EmbeddedG2.pairing_short_long
- RootPairing.EmbeddedG2.twoShortAddLongRoot_eq
- RootPairing.EmbeddedG2.pairingIn_long_short
- RootPairing.EmbeddedG2.threeShortAddLongRoot_eq
- RootPairing.EmbeddedG2.threeShortAddTwoLongRoot_eq
- RootPairing.EmbeddedG2.indexEquivAllRoots
- RootPairing.EmbeddedG2.shortAddLongRoot_eq
- RootPairing.EmbeddedG2.isOrthogonal_short_and_long
- RootPairing.EmbeddedG2.pairingIn_short_long
- RootPairing.EmbeddedG2.allRoots_eq_map_allCoeffs
- RootPairing.EmbeddedG2.pairingIn_threeShortAddLong_left
- RootPairing.EmbeddedG2.span_eq_top
- RootPairing.EmbeddedG2.linearIndependent_short_long
- RootPairing.EmbeddedG2.basis
- RootPairing.EmbeddedG2.pairingIn_shortAddLong_right
- RootPairing.EmbeddedG2.shortAddLongRoot_shortRoot
- RootPairing.EmbeddedG2.threeShortAddTwoLongRoot_longRoot
- RootPairing.EmbeddedG2.twoShortAddLongRoot_shortRoot
- RootPairing.EmbeddedG2.threeShortAddLongRoot_longRoot
- RootPairing.EmbeddedG2.pairingIn_twoShortAddLong_right
- RootPairing.EmbeddedG2.pairingIn_twoShortAddLong_left
- RootPairing.EmbeddedG2.pairingIn_shortAddLong_left
- RootPairing.EmbeddedG2.setOfPred_index_eq_univ
- RootPairing.EmbeddedG2.pairingIn_threeShortAddTwoLong_left
- RootPairing.EmbeddedG2.mem_allRoots
- RootPairing.EmbeddedG2.mem_span_of_mem_allRoots
- RootPairing.EmbeddedG2.pairingIn_threeShortAddTwoLong_right
- RootPairing.EmbeddedG2.allRoots_nodup
- RootPairing.EmbeddedG2.pairingIn_threeShortAddLong_right
- RootPairing.EmbeddedG2.indexEquivAllRoots_symm_apply
- RootPairing.EmbeddedG2.toIsReduced
- RootPairing.EmbeddedG2.toIsValuedIn
- RootPairing.EmbeddedG2.indexEquivAllRoots_apply_coe
- RootPairing.EmbeddedG2.setOf_index_eq_univ
- RootPairing.EmbeddedG2.card_index_eq_twelve