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## Demonstration of XDistributedPolynomial

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Q ==> Fraction Integer
Type: Void
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V ==> OrderedVariableList(['y11,'y12,'y21,'y22])
Type: Void
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v := enumerate()\$V
 (1)
Type: List(OrderedVariableList([y11,y12,y21,y22]))
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X ==> XDistributedPolynomial(V, Q)
Type: Void
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z11: X := v.1
 (2)
Type: XDistributedPolynomial(OrderedVariableList([y11,y12,y21,y22]),Fraction(Integer))
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z12: X := v.2
 (3)
Type: XDistributedPolynomial(OrderedVariableList([y11,y12,y21,y22]),Fraction(Integer))
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z21: X := v.3
 (4)
Type: XDistributedPolynomial(OrderedVariableList([y11,y12,y21,y22]),Fraction(Integer))
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z22: X := v.4
 (5)
Type: XDistributedPolynomial(OrderedVariableList([y11,y12,y21,y22]),Fraction(Integer))
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q: Matrix X := matrix [[z11, z12],[z21,z22]]
 (6)
Type: Matrix(XDistributedPolynomial(OrderedVariableList([y11,y12,y21,y22]),Fraction(Integer)))
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K := kroneckerProduct(q, q)
 (7)
Type: Matrix(XDistributedPolynomial(OrderedVariableList([y11,y12,y21,y22]),Fraction(Integer)))
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MM: Matrix(Q) :=matrix([[1,0,0,1], [0,1,1,0], [0,1,-1,0], [1,0,0,-1]])
 (8)
Type: Matrix(Fraction(Integer))
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T := MM*K*inverse(MM)
 (9)
Type: Matrix(XDistributedPolynomial(OrderedVariableList([y11,y12,y21,y22]),Fraction(Integer)))
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r1 := (z11*z11+z21*z21-1)
 (10)
Type: XDistributedPolynomial(OrderedVariableList([y11,y12,y21,y22]),Fraction(Integer))
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r2 := (z11*z11+z12*z12-1)
 (11)
Type: XDistributedPolynomial(OrderedVariableList([y11,y12,y21,y22]),Fraction(Integer))
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r3 := (z12*z12+z22*z22-1)
 (12)
Type: XDistributedPolynomial(OrderedVariableList([y11,y12,y21,y22]),Fraction(Integer))
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r4 := (z21*z21+z22*z22-1)
 (13)
Type: XDistributedPolynomial(OrderedVariableList([y11,y12,y21,y22]),Fraction(Integer))
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r5 := (z11*z12+z21*z22)
 (14)
Type: XDistributedPolynomial(OrderedVariableList([y11,y12,y21,y22]),Fraction(Integer))
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r6 := (z11*z21+z12*z22)
 (15)
Type: XDistributedPolynomial(OrderedVariableList([y11,y12,y21,y22]),Fraction(Integer))
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r7 := (z12*z11+z22*z21)
 (16)
Type: XDistributedPolynomial(OrderedVariableList([y11,y12,y21,y22]),Fraction(Integer))
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r8 := (z21*z11+z22*z12);
Type: XDistributedPolynomial(OrderedVariableList([y11,y12,y21,y22]),Fraction(Integer))
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sigma ==> 1111;
Type: Void
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r9 := z11*z22+z12*z21-sigma
 (17)
Type: XDistributedPolynomial(OrderedVariableList([y11,y12,y21,y22]),Fraction(Integer))
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ra := (z11*z22-z22*z11)
 (18)
Type: XDistributedPolynomial(OrderedVariableList([y11,y12,y21,y22]),Fraction(Integer))
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rb := (z12*z21-z21*z12)
 (19)
Type: XDistributedPolynomial(OrderedVariableList([y11,y12,y21,y22]),Fraction(Integer))
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rc := (z11*z12+z12*z11)
 (20)
Type: XDistributedPolynomial(OrderedVariableList([y11,y12,y21,y22]),Fraction(Integer))
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rd := (z21*z22+z22*z21)
 (21)
Type: XDistributedPolynomial(OrderedVariableList([y11,y12,y21,y22]),Fraction(Integer))
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re := (z11*z21+z21*z11)
 (22)
Type: XDistributedPolynomial(OrderedVariableList([y11,y12,y21,y22]),Fraction(Integer))
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rf := (z22*z12+z12*z22)
 (23)
Type: XDistributedPolynomial(OrderedVariableList([y11,y12,y21,y22]),Fraction(Integer))
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t11 := 2*T(1,1) - r3 - r1
 (24)
Type: XDistributedPolynomial(OrderedVariableList([y11,y12,y21,y22]),Fraction(Integer))
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t12 := 2*T(1,2) - r7 - r5
 (25)
Type: XDistributedPolynomial(OrderedVariableList([y11,y12,y21,y22]),Fraction(Integer))
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t21 := 2*T(2,1) - r8 - r6
 (26)
Type: XDistributedPolynomial(OrderedVariableList([y11,y12,y21,y22]),Fraction(Integer))
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t22 := 2*T(2,2) + ra + rb - 2*r9
 (27)
Type: XDistributedPolynomial(OrderedVariableList([y11,y12,y21,y22]),Fraction(Integer))

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