| Symbol | Meaning | Code | Doran | Hollmeier | Chisolm |
|---|---|---|---|---|---|
| greek αβγδ | scalar | alpha |
greek | latin/greek | greek |
| eₙ | basis vector | e_$dim / e[$dim] = [0,0,1] |
σ₁, σ₂, σ₃ | e₁, e₂, e₃ | e₁, e₂, e₃ |
| γₙ | STA basis vector | gamma_$dim / gamma[n] |
γ₀,γ₁, γ₂, γ₃ | γ₀,γ₁, γ₂, γ₃ | |
| latin abcd | vector | a / av[n] |
latin | latin | latin |
| B,C,Θ | bivector | bivB ? |
Latin/Greek | Latin/Greek | A₂, B₂ |
| A,B,M | multivector | mvA |
Latin/Greek | Latin | Latin |
| I | pseudoscalar (top grade) | `` | I (I² = -1) | I = e₁₂₃ | I (I² = ±1) |
| Aᵣ | blade (ndim) | blade_$ndim |
Aᵣ | Latin | BOLD Latin |
| R | rotor (even versor) | rotor_$ndim |
R | R | R |
| Symbol | Meaning | Code | Doran | Hollmeier | Chisolm |
|---|---|---|---|---|---|
| ⟨A⟩ᵣ₋ₛ | grade from to | .grade(r, s) |
⟨M⟩ᵣ | ⟨M⟩ₖ | ⟨A⟩ᵣ |
| ⟨A⟩ | scalar / grade 0 | .grade(r=0) |
⟨M⟩ | ⟨M⟩₀ / ⟨M⟩ | ⟨A⟩ |
A† / Ã |
reverse | .reverse() |
M̃ (~) | M̃ (~) | A† (dagger) |
| A‡ | clifford conjugate | .cliffordconj() |
M̃ = (M̃)* | A‡ ≅ A⃰† | |
| A* | odd grades *-1 | .involute() |
M̃ = (M̃) ⃰ | ||
| A⁻¹ | inverse | .inverse() |
M⁻¹ = M̃ / |M|² | M⁻¹ = M̃ / |M|² | A⁻¹ = Ã / |A|² |
| A⊥ | dual | .dual() |
MI⁻¹ or M̃I | ∗H (Hodge) or Iv | A⊥ = A⌋I⁻¹ |
| |M|² | magn. squared | .normsqr() |
|M|² = ⟨MM̃⟩ | |M|² | |A|² = A*A |
| Symbol | Meaning | Code | Doran | Hollmeier | Chisolm |
|---|---|---|---|---|---|
| ab AB | geometric product | A.mul(B) |
AB | AB | AB |
| a · b | inner / dot | A.dot(B) |
A · B = ⟨AB⟩ᵣ₋ₛ | A · B = ⟨AB⟩ₖ₋ₗ | u · v |
| A ⌋ B | contract left | B.contract(A) |
A ⌋ B | A · B | A ⌋ B = ⟨AB⟩ₛ₋ᵣ |
| A ⌊ B | contract right | A.contract(B) |
A ⌊ B | A · B | A ⌊ B = ⟨AB⟩ᵣ₋ₛ |
| a ∧ b | outer / wedge | A.wedge(B) |
A ∧ B = ⟨AB⟩ᵣ₊ₛ | A ∧ B = ⟨AB⟩ₖ₊ₗ | A ∧ B = ⟨AB⟩ᵣ₊ₛ |
| A × B | commute | commute(A, B) |
A × B = ½(AB - BA) | [A,B] = AB-BA | A × B = ½(AB - BA) |
| A ∗ B | scalar product | A.scalarprod(B) |
A ∗ B = ⟨AB⟩ | ⟨AB⟩ | A ∗ B = ⟨A † B⟩ |