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- #******************
- #* Dual of type A *
- #******************
- # Left complement
- DualA.left_complement(a12,a12)==a00
- DualA.left_complement(a12,a23)==a13
- DualA.left_complement(a12,a34)==a34
- DualA.left_complement(a12,a24)==a14
- DualA.left_complement(a12,a14)==a14
- DualA.left_complement(a23,a12)==a12
- DualA.left_complement(a23,a23)==a00
- DualA.left_complement(a23,a13)==a12
- DualA.left_complement(a23,a34)==a24
- DualA.left_complement(a23,a24)==a24
- DualA.left_complement(a23,a14)==a14
- DualA.left_complement(a13,a12)==a23
- DualA.left_complement(a13,a23)==a23
- DualA.left_complement(a13,a13)==a00
- DualA.left_complement(a13,a34)==a14
- DualA.left_complement(a13,a24)==a23*a14
- DualA.left_complement(a13,a14)==a14
- DualA.left_complement(a34,a12)==a12
- DualA.left_complement(a34,a23)==a23
- DualA.left_complement(a34,a13)==a13
- DualA.left_complement(a34,a34)==a00
- DualA.left_complement(a34,a24)==a23
- DualA.left_complement(a34,a14)==a13
- DualA.left_complement(a24,a12)==a12
- DualA.left_complement(a24,a23)==a34
- DualA.left_complement(a24,a13)==a34*a12
- DualA.left_complement(a24,a34)==a34
- DualA.left_complement(a24,a24)==a00
- DualA.left_complement(a24,a14)==a12
- DualA.left_complement(a14,a12)==a24
- DualA.left_complement(a14,a23)==a23
- DualA.left_complement(a14,a13)==a34
- DualA.left_complement(a14,a34)==a34
- DualA.left_complement(a14,a24)==a24
- DualA.left_complement(a14,a14)==a00
- # Right complement
- DualA.right_complement(a12,a12)==a00
- DualA.right_complement(a12,a23)==a23
- DualA.right_complement(a12,a13)==a23
- DualA.right_complement(a12,a34)==a34
- DualA.right_complement(a12,a24)==a24
- DualA.right_complement(a12,a14)==a24
- DualA.right_complement(a23,a12)==a13
- DualA.right_complement(a23,a23)==a00
- DualA.right_complement(a23,a13)==a13
- DualA.right_complement(a23,a34)==a34
- DualA.right_complement(a23,a24)==a34
- DualA.right_complement(a23,a14)==a14
- DualA.right_complement(a13,a12)==a12
- DualA.right_complement(a13,a23)==a12
- DualA.right_complement(a13,a13)==a00
- DualA.right_complement(a13,a34)==a34
- DualA.right_complement(a13,a24)==a34*a12
- DualA.right_complement(a13,a14)==a34
- DualA.right_complement(a34,a12)==a12
- DualA.right_complement(a34,a23)==a24
- DualA.right_complement(a34,a13)==a14
- DualA.right_complement(a34,a34)==a00
- DualA.right_complement(a34,a24)==a24
- DualA.right_complement(a34,a14)==a14
- DualA.right_complement(a24,a12)==a14
- DualA.right_complement(a24,a23)==a23
- DualA.right_complement(a24,a13)==a23*a14
- DualA.right_complement(a24,a34)==a23
- DualA.right_complement(a24,a24)==a00
- DualA.right_complement(a24,a14)==a14
- DualA.right_complement(a14,a12)==a12
- DualA.right_complement(a14,a23)==a23
- DualA.right_complement(a14,a13)==a13
- DualA.right_complement(a14,a34)==a13
- DualA.right_complement(a14,a24)==a12
- DualA.right_complement(a14,a14)==a00
- # Garside structure
- DualA.left_lcm_complement(a12,a23)==a13
- DualA.left_lcm_complement(a12,a12*a23)==a13
- DualA.left_lcm_complement(a12,a23*a12)==a23
- DualA.left_lcm(a12,a23)==a13*a12
- DualA.left_lcm(a12,a12*a23)==a13*a12
- DualA.left_lcm(a12,a23*a12)==a23*a12
- DualA.right_lcm_complement(a12,a23)==a23
- DualA.right_lcm_complement(a12,a12*a23)==a23
- DualA.right_lcm_complement(a12,a23*a12)==a23*a12
- DualA.right_lcm(a12,a23)==a12*a23
- DualA.right_lcm(a12,a12*a23)==a12*a23
- DualA.right_lcm(a12,a23*a12)==a12*a23*a12
- DualA.left_gcd(a12,a12*a23)==a12
- DualA.left_gcd(a12,a23*a12)==a00
- DualA.left_gcd(a12*a23,a12*a12*a23)==a12*a23
- DualA.right_gcd(a12,a12*a23)==a12
- DualA.right_gcd(a12,a23*a12)==a12
- DualA.right_gcd(a12*a23,a12*a12*a23)==a12*a23
- DualA.left_gcd_x(a12*a23*a34,a12*a23*a12)==(a12*a23,a34)
- DualA.left_gcd_x(a12*a23*a12,a12*a23*a34)==(a12*a23,a12)
- DualA.right_gcd_x(a12*a23*a34,a12*a23*a12)==(a12*a23,a14)
- DualA.right_gcd_x(a12*a23*a12,a12*a23*a34)==(a13*a12,a23)
- DualA.is_left_divisible(a12*a23,a12)
- DualA.is_left_divisible(a12*a23,a23)
- DualA.is_left_divisible(a12*a23,a13)
- DualA.is_left_divisible(a12*a23,a14)==false
- DualA.is_left_divisible(a12*a23,a12*a12)==false
- DualA.is_right_divisible(a12*a23,a12)
- DualA.is_right_divisible(a12*a23,a23)
- DualA.is_right_divisible(a12*a23,a13)
- DualA.is_right_divisible(a12*a23,a14)==false
- DualA.is_right_divisible(a12*a23,a12*a12)==false
- DualA.is_left_divisible_x(a12*a23,a12)==(true,a23)
- DualA.is_left_divisible_x(a12*a23,a23)==(true,a13)
- DualA.is_left_divisible_x(a12*a23,a13)==(true,a12)
- DualA.is_left_divisible_x(a12*a23,a14)==(false,a00)
- DualA.is_left_divisible_x(a12*a23,a12*a12)==(false,a00)
- DualA.is_right_divisible_x(a12*a23,a12)==(true,a13)
- DualA.is_right_divisible_x(a12*a23,a23)==(true,a12)
- DualA.is_right_divisible_x(a12*a23,a13)==(true,a23)
- DualA.is_right_divisible_x(a12*a23,a14)==(false,a00)
- DualA.is_right_divisible_x(a12*a23,a12*a12)==(false,a00)
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