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I have coded the following:
jst coded biliniear transformation, Expected result should have highest degree=8,But in solution highest degree=20, Can any one help me what is the mistake i have done?

Code:
var('s,z') g1=12108.8236080100s^4 + 3016.35528790190s^3 + 10600.0709715245s^2 + 1937.60970085071s + 409.016662847740/s + 472.343751699259/s^2 + 28.3730874809756/s^3 + 24.0436698653890/s^4 + 3397.06167138687
g2=g1.subs(s=((z-1)/(z+1)))
g2.full_simplify()
solution:
(31993.69841156735z^20 - 158174.2276629893z^19 + 216392.4500464178z^18 + 280148.4057432631z^17 - 1211263.434674058z^16 + 1037191.771384268z^15 + 1264180.797481716z^14 - 3364714.4688927z^13 + 1723475.12974153z^12 + 2648901.578200325z^11 - 4385755.889381289z^10 + 1244061.427447394z^9 + 2634639.643830222z^8 - 2874359.710320266z^7 + 417712.5402619956z^6 + 1209501.453649961z^5 - 917808.742510938z^4 + 93647.83955663575z^3 + 205222.817859467z^2 - 116204.0691059264z + 21210.98893340469)/(z^20 - 10.0z^18 + 45.0z^16 - 120.0z^14 + 210.0z^12 - 252.0z^10 + 210.0z^8 - 120.0z^6 + 45.0z^4 - 10.0*z^2 + 1.0)

I have coded the following:
jst coded biliniear transformation, Expected result should have highest degree=8,But in solution highest degree=20, Can any one help me what is the mistake i have done?

Code:
var('s,z') var('s,z')
g1=12108.8236080100s^4 + 3016.35528790190s^3 + 10600.0709715245s^2 + 1937.60970085071s + 409.016662847740/s + 472.343751699259/s^2 + 28.3730874809756/s^3 + 24.0436698653890/s^4 + 3397.06167138687
g2=g1.subs(s=((z-1)/(z+1)))
g2.full_simplify()
solution:
(31993.69841156735z^20 - 158174.2276629893z^19 + 216392.4500464178z^18 + 280148.4057432631z^17 - 1211263.434674058z^16 + 1037191.771384268z^15 + 1264180.797481716z^14 - 3364714.4688927z^13 + 1723475.12974153z^12 + 2648901.578200325z^11 - 4385755.889381289z^10 + 1244061.427447394z^9 + 2634639.643830222z^8 - 2874359.710320266z^7 + 417712.5402619956z^6 + 1209501.453649961z^5 - 917808.742510938z^4 + 93647.83955663575z^3 + 205222.817859467z^2 - 116204.0691059264z + 21210.98893340469)/(z^20 - 10.0z^18 + 45.0z^16 - 120.0z^14 + 210.0z^12 - 252.0z^10 + 210.0z^8 - 120.0z^6 + 45.0z^4 - 10.0*z^2 + 1.0)

I have coded the following:
jst coded biliniear transformation, Expected result should have highest degree=8,But in solution highest degree=20, Can any one help me what is the mistake i have done?

Code:

var('s,z') 
  g1=12108.8236080100s^4 g1=12108.8236080100*s^4 + 3016.35528790190s^3 3016.35528790190*s^3 + 10600.0709715245s^2 10600.0709715245*s^2 + 1937.60970085071s 1937.60970085071*s + 409.016662847740/s + 472.343751699259/s^2 + 28.3730874809756/s^3 + 24.0436698653890/s^4 + 3397.06167138687 
 
g2=g1.subs(s=((z-1)/(z+1))) 
  g2.full_simplify() 
g2.full_simplify()

(31993.69841156735*z^20 - 158174.2276629893z^19 158174.2276629893*z^19 + 216392.4500464178z^18 216392.4500464178*z^18 + 280148.4057432631z^17 280148.4057432631*z^17 - 1211263.434674058z^16 1211263.434674058*z^16 + 1037191.771384268z^15 1037191.771384268*z^15 + 1264180.797481716z^14 1264180.797481716*z^14 - 3364714.4688927z^13 3364714.4688927*z^13 + 1723475.12974153z^12 1723475.12974153*z^12 + 2648901.578200325z^11 2648901.578200325*z^11 - 4385755.889381289z^10 4385755.889381289*z^10 + 1244061.427447394z^9 1244061.427447394*z^9 + 2634639.643830222z^8 2634639.643830222*z^8 - 2874359.710320266z^7 2874359.710320266*z^7 + 417712.5402619956z^6 417712.5402619956*z^6 + 1209501.453649961z^5 1209501.453649961*z^5 - 917808.742510938z^4 917808.742510938*z^4 + 93647.83955663575z^3 93647.83955663575*z^3 + 205222.817859467z^2 205222.817859467*z^2 - 116204.0691059264z 116204.0691059264*z + 21210.98893340469)/(z^20 - 10.0z^18 10.0*z^18 + 45.0z^16 45.0*z^16 - 120.0z^14 120.0*z^14 + 210.0z^12 210.0*z^12 - 252.0z^10 252.0*z^10 + 210.0z^8 210.0*z^8 - 120.0z^6 120.0*z^6 + 45.0z^4 45.0*z^4 - 10.0*z^2 + 1.0)
1.0)

I have coded applied full_simplify to an expression obtained by substituting a quotient of two polynomials in a polynomial expression, as illustrated below.

The highest degree in the following:
result was expected to be 8, but I get an output where the highest degree is 20.

var('s,z')  
g1=12108.8236080100*s^4 var('s,z')
g1 = 12108.8236080100*s^4 + 3016.35528790190*s^3 + 10600.0709715245*s^2 + 1937.60970085071*s + 409.016662847740/s + 472.343751699259/s^2 + 28.3730874809756/s^3 + 24.0436698653890/s^4 + 3397.06167138687  
g2=g1.subs(s=((z-1)/(z+1)))  
g2 = g1.subs(s=(z-1)/(z+1))
g2.full_simplify()

(31993.69841156735*z^20 - 158174.2276629893*z^19 + 216392.4500464178*z^18 + 280148.4057432631*z^17 - 1211263.434674058*z^16 + 1037191.771384268*z^15 + 1264180.797481716*z^14 - 3364714.4688927*z^13 + 1723475.12974153*z^12 + 2648901.578200325*z^11 - 4385755.889381289*z^10 + 1244061.427447394*z^9 + 2634639.643830222*z^8 - 2874359.710320266*z^7 + 417712.5402619956*z^6 + 1209501.453649961*z^5 - 917808.742510938*z^4 + 93647.83955663575*z^3 + 205222.817859467*z^2 - 116204.0691059264*z + 21210.98893340469)/(z^20 - 10.0*z^18 + 45.0*z^16 - 120.0*z^14 + 210.0*z^12 - 252.0*z^10 + 210.0*z^8 - 120.0*z^6 + 45.0*z^4 - 10.0*z^2 + 1.0)