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| Line 1,603: |
Line 1,603: |
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| We’ll look in more detail later at how exactly to best find these generators, once you know which primes to make them out of. | | We’ll look in more detail later at how exactly to best find these generators, once you know which primes to make them out of. |
| {| class="wikitable"
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| |+
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| !operations
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| !progressive product (AKA wedge product, exterior product)
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| a ∧ b
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| !regressive product (AKA vee product)
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| a ∨ b
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| <nowiki>*</nowiki>(*a ∧ *b)
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| !right interior product
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| a ⨽ b
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| ∗(∗a ∧ b)
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| examples given where grade(a) ≥ grade(b)
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| !(left) interior product
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| a ⨼ b
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| <nowiki>*</nowiki>(a ∧ *b)
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| examples given where grade(a) < grade(b)
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| !symmetrical interior product
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|
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| a • b = if grade(a) ≥ grade(b), a ⨽ b; else a ⨼ b
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| |-
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| !resultant grade, assuming empty intersections
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| !grade(a) + grade(b)
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| !grade(a) + grade(b) - dimensionality
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| !grade(a) - grade(b)
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| !grade(b) - grade(a)
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| !if grade(a) ≥ grade(b), grade(a) - grade(b); else grade(b) - grade(a)
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| |-
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| !resultant variance
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| !same as a (and b)
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| !same as a (and b)
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| !same as a
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| !same as b
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| !if grade(a) ≥ grade(b), same as a; else same as b
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| |-
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| !multicovector with multicovector
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| ⟨] ⟨]
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| |⟨12 19 28 34] ∧ ⟨19 30 44 53] = ⟨⟨1 4 10 4 13 12]]
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| |⟨⟨⟨1 2 -3 -2 1 -4 -5 12 9 -19]]] ∨ ⟨⟨⟨⟨1 2 1 2 3]]]] = ⟨⟨-6 7 2 -15 25 20 -3 -15 -59 -49]]
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| |ND
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| |ND
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| |ND
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| |-
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| !multivector with multivector
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| [⟩ [⟩
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| |[4 -4 1 0⟩ ∧ [13 -10 0 1⟩ = [[12 -13 4 10 -4 1⟩⟩
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| |[[44 -30 19⟩⟩ ∨ [[28 -19 12⟩⟩ = [4 -4 1⟩
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| |ND
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| |ND
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| |ND
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| |-
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| !multicovector with multivector
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| ⟨] [⟩
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| |ND
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| |ND
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| |⟨⟨⟨1 2 -3 -2 1 -4 -5 12 9 -19]]] ⨽ [-3 2 -1 2 -1⟩ = ⟨⟨6 -7 -2 15 -25 -20 3 15 59 49]]
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| |⟨12 19 28] ⨼ [[44 -30 19⟩⟩ = [4 -4 1⟩
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| |(in terms of other two interior products)
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| |-
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| !multivector with multicovector
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| [⟩ ⟨]
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| |ND
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| |ND
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| |[[44 -30 19⟩⟩ ⨽ ⟨12 19 28] = [-4 4 -1⟩
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| |[-3 2 -1 2 -1⟩ ⨼ ⟨⟨⟨1 2 -3 -2 1 -4 -5 12 9 -19]]] = ⟨⟨-6 7 2 -15 25 20 -3 -15 -59 -49]]
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| |(in terms of other two interior products)
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| |}
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| == other topics (TBD) == | | == other topics (TBD) == |