uiua 0.19.0-dev.4

A stack-based array programming language
Documentation 
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# Experimental!

# Multivector creation
⍤⤙≍ /+[e₁ 2e₂ 3e₃] 𝕍⌞[1 2 3]
⍤⤙≍ /+[e₁₂ 2e₃₁ 3e₂₃] 𝕍⌟[1 2 3]
⍤⤙≍ /+[e₀ e₁ 2e₂] 𝕍⌞[1 1 2]    # PGA!
⍤⤙≍ /+[e₀₁ 2e₂₀ e₁₂] 𝕍⌟[1 2 1] # PGA!

# Geometric product
⍤⤙≍ 𝕍⌞[11 2] × 𝕍[1 2] 𝕍[3 4]
⍤⤙≍ 𝕍 [11 2] × 𝕍[1 2] 𝕍₂[3 0 0 4]
⍤⤙≍ 𝕍 [11 2] × 𝕍[1 2] +3 4e₁₂
⍤⤙≍ 𝕍⌞ [¯5 10] × 𝕍⌞[1 2] 𝕍⌞[3 4]
⍤⤙≍ 𝕍⌞ [¯5 10] × 𝕍⌞[1 2] 𝕍₂[3 0 0 4]
⍤⤙≍ 𝕍⌞ [¯5 10] × 𝕍₂[1 0 0 2] 𝕍⌞[3 4]
⍤⤙≍ 𝕍⌞[0_1 0_2 ¯1_0] × 𝕍⌞ [0 1] 𝕍⌞ [1_0 2_0 0_1]
⍤⤙≍ 𝕍14 ˙× 𝕍 [1 2 3]
⍤⤙≍ 𝕍⌞[32 ¯3 6 ¯3] × 𝕍[4 5 6] 𝕍[1 2 3]
⍤⤙≍ 𝕍⌞[70 ¯4 ¯8 ¯12 ¯4 ¯8 ¯4 0] × 𝕍[5 6 7 8] 𝕍[1 2 3 4]
⍤⤙≍ 𝕍4 ˙× +0e₀𝕍[0 2]
⍤⤙≍ 𝕍0 ˙× 2e₀

# Inner product
⍤⤙≍ 𝕍1 ⨰ e₁ e₁
⍤⤙≍ 𝕍1 ⨰ e₂ e₂
⍤⤙≍ 𝕍0 ⨰ e₁ e₂
⍤⤙≍ e₂ ⨰ e₁₂ e₁
⍤⤙≍ ¯e₂ ⨰ e₁ e₁₂
⍤⤙≍ 𝕍0 ⨰ e₁ e₂₃
⍤⤙≍ 𝕍0 ⨰ e₁₂ e₂₃
⍤⤙≍ ¯e₃ ⨰ e₁₂₃ e₁₂
⍤⤙≍ ¯e₃ ⨰ e₁₂ e₁₂₃

# Contraction
⍤⤙≍ e₂ ⨰⌞ e₁₂ e₁
⍤⤙≍ 𝕍0 ⨰⌟ e₁₂ e₁

# Outer product
⍤⤙≍ 1 ⨱ 1 1
⍤⤙≍ 𝕍0 ⨱ e₁ e₁
⍤⤙≍ ¯6e₁₂ ⨱ 2e₁ 3e₂
⍤⤙≍ e₁₂ ⨱ e₂ e₁
⍤⤙≍ ¯e₁₂ ⨱ e₁ e₂
⍤⤙≍ e₃₁ ⨱ e₁ e₃
⍤⤙≍ ¯e₃₁ ⨱ e₃ e₁
⍤⤙≍ e₂₃ ⨱ e₃ e₂
⍤⤙≍ ¯e₂₃ ⨱ e₂ e₃
⍤⤙≍ e₁₂₃ ⨱ e₂₃ e₁
⍤⤙≍ e₁₂₃ ⨱ e₁ e₂₃
⍤⤙≍ e₁₂₃ ⨱ e₃₁ e₂
⍤⤙≍ e₁₂₃ ⨱ e₂ e₃₁
⍤⤙≍ e₁₂₃ ⨱ e₁₂ e₃
⍤⤙≍ e₁₂₃ ⨱ e₃ e₁₂

# Dual
⍤⤙≍ e₁ ¯₄ 𝕍₁1
⍤⤙≍ e₁₂ ¯₄ 𝕍₂1
⍤⤙≍ e₁₂₃ ¯₄ 𝕍₃1
⍤⤙≍ 𝕍[¯2 1] ¯₄ 𝕍 [1 2]
⍤⤙≍ -4e₃𝕍⌟[3 2 1] ¯₄ +4e₁₂ 𝕍 [1 2 3]

# Promotion
⍤⤙≍ 𝕍[1 2] + 𝕍[1] 𝕍[0 2]
⍤⤙≍ +0e₀𝕍[1 5] + +0e₀𝕍[0 2] 𝕍[1 3]
⍤⤙≍ e₁₂₃ ¯₄ 𝕍₃ 𝕍1
⍤⤙≍ e₂₃ ¯₄ 𝕍₃ 𝕍[1]
⍤⤙≍ e₃₁ ¯₄ 𝕍₃ 𝕍[0 1]

# Reverse
⍤⤙≍ 𝕍₃⍜(↘4)¯⟜(¯⌟𝕍₃)⇡₁8
⍤⤙≍ 𝕍₄⍜(↙10↘5)¯⟜(¯⌟𝕍₄)⇡₁16

# Scalar decomposition
⍤⤙≍ ↯3_2 0 °𝕍 [1 2 3]
⍤⤙≍ ≡¤[1 2 3] °𝕍⌞ [1 2 3]
⍤⤙≍ ≡¤[0 0 0] °𝕍⌟ [1 2 3]
⍤⤙≍ [1_0 2_0 3_0] °𝕍₁ [1 2 3]
⍤⤙≍ ⊞×[1 2 3] [1 0 0 0] °𝕍₂ [1 2 3]
⍤⤙≍ [1_0 2_0 3_0] °𝕍₂⌞ [1 2 3]
⍤⤙≍ ↯3_2 0 °𝕍₂⌟ [1 2 3]

# Complex decomposition
A ← ≡/˜ℂ °△3_2
⍤⤙≍ ↯3_2 0 °𝕍 A
⍤⤙≍ °△3_2 °𝕍⌞ A
⍤⤙≍ ↯3_2 0 °𝕍⌟ A
⍤⤙≍ [0_0 2_0 4_0] °𝕍₁ A
⍤⤙≍ [0_0_0_1 2_0_0_3 4_0_0_5] °𝕍₂ A
⍤⤙≍ [[0 0 0 0 1 0 0 0] [2 0 0 0 3 0 0 0] [4 0 0 0 5 0 0 0]] °𝕍₃ A
⍤⤙≍ ≡¤[0 2 4] °𝕍₁⌞ A
⍤⤙≍ ≡¤[0 0 0] °𝕍₁⌟ A
⍤⤙≍ °△3_2 °𝕍₂⌞ A
⍤⤙≍ ↯3_2 0 °𝕍₂⌟ A
⍤⤙≍ [0_1_0_0 2_3_0_0 4_5_0_0] °𝕍₃⌞ A
⍤⤙≍ ↯3_4 0 °𝕍₃⌟ A

# Multivector decomposition
⍤⤙≍ [1 2 3] °𝕍 𝕍[1 2 3]
⍤⤙≍ [] °𝕍 𝕍1
⍤⤙≍ [1] °𝕍⌞ 𝕍1
⍤⤙≍ [0] °𝕍⌟ 𝕍1
⍤⤙≍ [1] °𝕍₀ 𝕍1
⍤⤙≍ [1 0] °𝕍₁ 𝕍1
⍤⤙≍ [1 0 0 0] °𝕍₂ 𝕍1
⍤⤙≍ [1 0] °𝕍₂⌞ 𝕍1
⍤⤙≍ [0 0] °𝕍₂⌟ 𝕍1

⍤⤙≍ [1] °𝕍 𝕍[1]
⍤⤙≍ [1 2] °𝕍 𝕍[1 2]
⍤⤙≍ [1 2 3] °𝕍 𝕍[1 2 3]
⍤⤙≍ [1 2 3 4] °𝕍 𝕍[1 2 3 4]
⍤⤙≍ [0 0 0] °𝕍 𝕍⌞[1 2 3 4]
⍤⤙≍ [1 2 3 4] °𝕍⌞ 𝕍⌞[1 2 3 4]
⍤⤙≍ [0 0 0 0] °𝕍⌟ 𝕍⌞[1 2 3 4]
⍤⤙≍ [1 0 0 2] °𝕍₂ 𝕍⌞[1 2 3 4]
⍤⤙≍ [1 0 0 0 2 3 4 0] °𝕍₃ 𝕍⌞[1 2 3 4]
⍤⤙≍ [1 0 0 2] °𝕍₂ 𝕍⌞[1 2 3 4]
⍤⤙≍ [1 0 0 0 0 2 3 0 4 0 0 0 0 0 0 0] °𝕍₄ 𝕍⌞[1 2 3 4]
⍤⤙≍ [1 2 3 0 4 0 0 0] °𝕍₄⌞ 𝕍⌞[1 2 3 4]
⍤⤙≍ [0 0 0 0 0 0 0 0] °𝕍₄⌟ 𝕍⌞[1 2 3 4]
⍤⤙≍ ↯3[1 2 3 0 4 0 0 0] °𝕍₄⌞ ↯3 𝕍⌞[1 2 3 4]

# Resize
⍤⤙≍ 𝕍₃[1 2 3 0 4 0 0 0] 𝕍₃ 𝕍₂[1 2 3 4]
⍤⤙≍ 𝕍₄[1 2 3 0 0 4 0 0 0 0 0 0 0 0 0 0] 𝕍₄ 𝕍₂[1 2 3 4]
⍤⤙≍ 𝕍₂ [1 2 3 5] 𝕍₂ 𝕍₃[1 2 3 4 5 6 7 8]
⍤⤙≍ 𝕍₂ [1 2 3 6] 𝕍₂ 𝕍₄[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16]
# Flipping of e₃₁
⍤⤙≍ 𝕍₄⌞[0 3 0 0 0 0] + 𝕍₄⌞[0 4 0 0 0 0] 𝕍⌟[0 1 0]
⍤⤙≍ 𝕍⌟[0 ¯3 0] 𝕍₃ 𝕍₄⌞[0 3 0 0 0 0]

# Flavor promotion
⍤⤙≍ [1 2] °𝕍 +e₀ 𝕍[2]
⍤⤙≍ [1 2 3] °𝕍 +e₀ 𝕍[2 3]
⍤⤙≍ [1 2 3 4] °𝕍 +e₀ 𝕍[2 3 4]

# Grade decomposition
⍤⤙≍ [1_5_9 [𝕍2_3 𝕍6_7 𝕍10_11] ×e₁₂[4 8 12]] °/+ 𝕍₂ +1°△3_4
⍤⤙≍ [1_3_0 0_0_0 0_4i_i] °/+ [1 3r4i i]