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Question: Simplifications and substitutions

Question:Simplifications and substitutions

Ronan 1441 Maple 2026
substitution
3 hours ago
1

I am trying to follow a series of substitutions used in a paper. I have given some examples of the substitutions. But I am having difficulty getting them to work. I know if all else fails I can manually recreate an expression with the substitution variables and then check backwards using eval(f,vals).
Would appreciate any insight on substitution techniques here.
 

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restart
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sidrels := [a*c - b^2 = Delta, a + c - 2*b = d, a - b = c__bar, a - c = b__bar, c - b = a__bar];

[a*c-b^2 = Delta, a+c-2*b = d, a-b = c__bar, a-c = b__bar, c-b = a__bar]

 (1)
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vals:='rhs=lhs'~(sidrels)

[Delta = a*c-b^2, d = a+c-2*b, c__bar = a-b, b__bar = a-c, a__bar = c-b]

 (2)
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t1:=a + c - 2*b;
simplify(t1,sidrels); #this should be d

a+c-2*b

  

d

 (3)
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t2:=Vector[column](3, [-a + b, c - b, 0]);
simplify(t2,sidrels) ; # This should be <-c__bar,a__bar,0> or <c__bar,-a__bar,0,>r

Vector(3, {(1) = -a+b, (2) = c-b, (3) = 0})

  

Vector[column](%id = 36893490321805397396)

 (4)
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t3:=normal(1 - b^2/(a*c));

(a*c-b^2)/(a*c)

 (5)
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simplify((5),sidrels); # This should be Delta/(a*c)

Delta/(b^2+Delta)

 (6)
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simplify(numer((5)),sidrels,'mindeg')/(denom((5)) ); # This works
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Delta/(a*c)

 (7)
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t4:=[(-b^2 + b*c)/(a*c - b^2), (a*b - b^2)/(a*c - b^2)]

[(-b^2+b*c)/(a*c-b^2), (a*b-b^2)/(a*c-b^2)]

 (8)
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simplify(t4,sidrels,'mindeg');# this should be [(b*a__bar)/Delta, (b*b__bar)/Delta]

[-b*(-c+b)/Delta, b*(a-b)/Delta]

 (9)
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t5:=simplify(Vector[column](3, [3*b*c__bar - Delta, -3*a__bar*b + Delta, b*(-c__bar + a__bar)]))

Vector(3, {(1) = 3*b*c__bar-Delta, (2) = -3*a__bar*b+Delta, (3) = b*(-c__bar+a__bar)})

 (10)
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t5[3]:=simplify(t5[3],sidrels)  ;#This should be b*b__bar
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-a__bar^2+(2*b+d)*a__bar-Delta

 (11)
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t5

Vector(3, {(1) = 3*b*c__bar-Delta, (2) = -3*a__bar*b+Delta, (3) = -a__bar^2+(2*b+d)*a__bar-Delta})

 (12)
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subs(sidrels[-2],b*(-c__bar + a__bar))

b*(-c__bar+a__bar)

 (13)
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algsubs(sidrels[-2],b*(-c__bar + a__bar))

b*(-c__bar+a__bar)

 (14)
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