I’m sorry, but I do not have any information on which project these equations were derived from. However, the equations do resemble polynomial regression models. If you could provide me with additional information, I could help you better.
or of a vector all have the factor of (1 – x1^2 -x2^2) or of the
square of this.
This is simply to adapt them to the theme or concept of the
localization, which, in this trial work, we chose to be simply
the domain of x1^2 + x2^2 <= +1 or simply a disc-like domain
bounded by the unit circle.
So integration was performed (nicely done by Mathematica) over
the domain of that disc of unit radius.
Based on the note you provided, it seems like the equation is related to integrating a polynomial over a disc-like domain bounded by the unit circle. The polynomials corresponding to the components of a tensor or vector all have the factor of (1 – x1^2 -x2^2) or of the square of this, which is used to adapt them to the localization theme or concept.
Without more information or context, it’s difficult to determine the specific equation that was incomplete. However, based on the information provided, a possible integral that matches the description is:
∫∫(1 – x1^2 – x2^2) * P(x1, x2) dA
where P(x1, x2) is a polynomial function and the integration is performed over the disc of unit radius centered at the origin, given by the inequality x1^2 + x2^2 <= 1. This integral can be evaluated using polar coordinates.
Again, without more context or information, it’s impossible to know if this is the exact equation that was incomplete.
I see. Based on the note you provided, it seems that the polynomials in question are adapted to the localization theme of the trial work, which is a disc-like domain bounded by the unit circle. The factor of (1 – x1^2 – x2^2) or the square of this is included in the polynomials to account for this domain.
It also appears that integration was performed over the domain of the unit disc using Mathematica. Without additional information or the actual equation, it is difficult to provide more specific insights or solutions. However, if you have any further questions or concerns, please let me know and I will do my best to help.
Based on the information you provided, it is difficult to determine exactly what the missing equation is. However, we can make some educated guesses based on the context.
The note mentions that the polynomials correspond to the components of a tensor or vector and all have the factor of (1 – x1^2 – x2^2) or the square of this. This suggests that the equation involves some kind of polynomial expansion involving the variables x1 and x2, perhaps in the context of a tensor or vector field.
The note also mentions that integration was performed over the domain of a disc of unit radius, which suggests that the equation involves some kind of integral or summation over a circular region.
Without more information, it is difficult to say exactly what the missing equation is, but these clues may be helpful in narrowing down the possibilities.
Here the polynomials corresponding to the components of a tensor
or of a vector all have the factor of (1 – x1^2 -x2^2) or of the
square of this.
This is simply to adapt them to the theme or concept of the
localization, which, in this trial work, we chose to be simply
the domain of x1^2 + x2^2 <= +1 or simply a disc-like domain
bounded by the unit circle.
So integration was performed (nicely done by Mathematica) over
the domain of that disc of unit radius.
memo$92887479$ = {confirmed,that,list,agrees,as,to,cmn,dmn,emn,parts,
with,prior,older,work}
list456 = {{-7*c30 + 5*c50 – d21 + d41 – j40, -7*d30 + 5*d50 – e21 + e41 –
k40}, {-6*c21 + 4*c41 – 2*d12 – 4*d30 + 2*d32 – j31,
-6*d21 + 4*d41 – 2*e12 – 4*e30 + 2*e32 – k31},
{-5*c12 – 3*c30 + 3*c32 – 3*d03 – 5*d21 + 3*d23 – j22,
-5*d12 – 3*d30 + 3*d32 – 3*e03 – 5*e21 + 3*e23 – k22},
{-4*c03 – 2*c21 + 2*c23 – 6*d12 + 4*d14 – j13, -4*d03 – 2*d21 + 2*d23 –
6*e12 + 4*e14 – k13}, {-c12 + c14 – 7*d03 + 5*d05 – j04,
-d12 + d14 – 7*e03 + 5*e05 – k04}, {-8*c40 + 6*c60 – d31 + d51 – j50,
-8*d40 + 6*d60 – e31 + e51 – k50}, {-7*c31 + 5*c51 – 2*d22 – 4*d40 +
2*d42 – j41, -7*d31 + 5*d51 – 2*e22 – 4*e40 + 2*e42 – k41},
{-6*c22 – 4*c40 + 4*c42 – 3*d13 – 5*d31 + 3*d33 – j32,
-6*d22 – 4*d40 + 4*d42 – 3*e13 – 5*e31 + 3*e33 – k32},
{-5*c13 – 3*c31 + 3*c33 – 4*d04 – 6*d22 + 4*d24 – j23,
-5*d13 – 3*d31 + 3*d33 – 4*e04 – 6*e22 + 4*e24 – k23},
{-4*c04 – 2*c22 + 2*c24 – 7*d13 + 5*d15 – j14, -4*d04 – 2*d22 + 2*d24 –
7*e13 + 5*e15 – k14}, {-c13 + c15 – 8*d04 + 6*d06 – j05,
-d13 + d15 – 8*e04 + 6*e06 – k05}, {-9*c50 + 7*c70 – d41 + d61,
-9*d50 + 7*d70 – e41 + e61}, {-8*c41 + 6*c61 – 2*d32 – 4*d50 + 2*d52,
-8*d41 + 6*d61 – 2*e32 – 4*e50 + 2*e52},
{-7*c32 – 5*c50 + 5*c52 – 3*d23 – 5*d41 + 3*d43,
-7*d32 – 5*d50 + 5*d52 – 3*e23 – 5*e41 + 3*e43},
{-6*c23 – 4*c41 + 4*c43 – 4*d14 – 6*d32 + 4*d34,
-6*d23 – 4*d41 + 4*d43 – 4*e14 – 6*e32 + 4*e34},
{-5*c14 – 3*c32 + 3*c34 – 5*d05 – 7*d23 + 5*d25,
-5*d14 – 3*d32 + 3*d34 – 5*e05 – 7*e23 + 5*e25},
{-4*c05 – 2*c23 + 2*c25 – 8*d14 + 6*d16, -4*d05 – 2*d23 + 2*d25 –
8*e14 + 6*e16}, {-c14 + c16 – 9*d05 + 7*d07, -d14 + d16 – 9*e05 +
7*e07}}
memo$958273673118$ =
{checks,to,proper,count,of,90,and,7,and,8,degs,came,from,older}
list0to8 = {c10 + d01 – j00, d10 + e01 – k00, -4*c00 + 2*c20 + d11 – j10,
-4*d00 + 2*d20 + e11 – k10, c11 – 4*d00 + 2*d02 – j01,
d11 – 4*e00 + 2*e02 – k01, -5*c10 + 3*c30 – d01 + d21 – j20,
-5*d10 + 3*d30 – e01 + e21 – k20, -4*c01 + 2*c21 – 4*d10 + 2*d12 – j11,
-4*d01 + 2*d21 – 4*e10 + 2*e12 – k11, -c10 + c12 – 5*d01 + 3*d03 – j02,
-d10 + d12 – 5*e01 + 3*e03 – k02, -6*c20 + 4*c40 – d11 + d31 – j30,
-6*d20 + 4*d40 – e11 + e31 – k30, -5*c11 + 3*c31 – 2*d02 – 4*d20 +
2*d22 – j21, -5*d11 + 3*d31 – 2*e02 – 4*e20 + 2*e22 – k21,
-4*c02 – 2*c20 + 2*c22 – 5*d11 + 3*d13 – j12, -4*d02 – 2*d20 + 2*d22 –
5*e11 + 3*e13 – k12, -c11 + c13 – 6*d02 + 4*d04 – j03,
-d11 + d13 – 6*e02 + 4*e04 – k03, -7*c30 + 5*c50 – d21 + d41 – j40,
-7*d30 + 5*d50 – e21 + e41 – k40, -6*c21 + 4*c41 – 2*d12 – 4*d30 +
2*d32 – j31, -6*d21 + 4*d41 – 2*e12 – 4*e30 + 2*e32 – k31,
-5*c12 – 3*c30 + 3*c32 – 3*d03 – 5*d21 + 3*d23 – j22,
-5*d12 – 3*d30 + 3*d32 – 3*e03 – 5*e21 + 3*e23 – k22,
-4*c03 – 2*c21 + 2*c23 – 6*d12 + 4*d14 – j13, -4*d03 – 2*d21 + 2*d23 –
6*e12 + 4*e14 – k13, -c12 + c14 – 7*d03 + 5*d05 – j04,
-d12 + d14 – 7*e03 + 5*e05 – k04, -8*c40 + 6*c60 – d31 + d51 – j50,
-8*d40 + 6*d60 – e31 + e51 – k50, -7*c31 + 5*c51 – 2*d22 – 4*d40 +
2*d42 – j41, -7*d31 + 5*d51 – 2*e22 – 4*e40 + 2*e42 – k41,
-6*c22 – 4*c40 + 4*c42 – 3*d13 – 5*d31 + 3*d33 – j32,
-6*d22 – 4*d40 + 4*d42 – 3*e13 – 5*e31 + 3*e33 – k32,
-5*c13 – 3*c31 + 3*c33 – 4*d04 – 6*d22 + 4*d24 – j23,
-5*d13 – 3*d31 + 3*d33 – 4*e04 – 6*e22 + 4*e24 – k23,
-4*c04 – 2*c22 + 2*c24 – 7*d13 + 5*d15 – j14, -4*d04 – 2*d22 + 2*d24 –
7*e13 + 5*e15 – k14, -c13 + c15 – 8*d04 + 6*d06 – j05,
-d13 + d15 – 8*e04 + 6*e06 – k05, -9*c50 + 7*c70 – d41 + d61,
-9*d50 + 7*d70 – e41 + e61, -8*c41 + 6*c61 – 2*d32 – 4*d50 + 2*d52,
-8*d41 + 6*d61 – 2*e32 – 4*e50 + 2*e52, -7*c32 – 5*c50 + 5*c52 – 3*d23 –
5*d41 + 3*d43, -7*d32 – 5*d50 + 5*d52 – 3*e23 – 5*e41 + 3*e43,
-6*c23 – 4*c41 + 4*c43 – 4*d14 – 6*d32 + 4*d34,
-6*d23 – 4*d41 + 4*d43 – 4*e14 – 6*e32 + 4*e34,
-5*c14 – 3*c32 + 3*c34 – 5*d05 – 7*d23 + 5*d25,
-5*d14 – 3*d32 + 3*d34 – 5*e05 – 7*e23 + 5*e25,
-4*c05 – 2*c23 + 2*c25 – 8*d14 + 6*d16, -4*d05 – 2*d23 + 2*d25 – 8*e14 +
6*e16, -c14 + c16 – 9*d05 + 7*d07, -d14 + d16 – 9*e05 + 7*e07,
-10*c60 – d51, -10*d60 – e51, -9*c51 – 2*d42 – 4*d60,
-9*d51 – 2*e42 – 4*e60, -8*c42 – 6*c60 – 3*d33 – 5*d51,
-8*d42 – 6*d60 – 3*e33 – 5*e51, -7*c33 – 5*c51 – 4*d24 – 6*d42,
-7*d33 – 5*d51 – 4*e24 – 6*e42, -6*c24 – 4*c42 – 5*d15 – 7*d33,
-6*d24 – 4*d42 – 5*e15 – 7*e33, -5*c15 – 3*c33 – 6*d06 – 8*d24,
-5*d15 – 3*d33 – 6*e06 – 8*e24, -4*c06 – 2*c24 – 9*d15,
-4*d06 – 2*d24 – 9*e15, -c15 – 10*d06, -d15 – 10*e06, -11*c70 – d61,
-11*d70 – e61, -10*c61 – 2*d52 – 4*d70, -10*d61 – 2*e52 – 4*e70,
-9*c52 – 7*c70 – 3*d43 – 5*d61, -9*d52 – 7*d70 – 3*e43 – 5*e61,
-8*c43 – 6*c61 – 4*d34 – 6*d52, -8*d43 – 6*d61 – 4*e34 – 6*e52,
-7*c34 – 5*c52 – 5*d25 – 7*d43, -7*d34 – 5*d52 – 5*e25 – 7*e43,
-6*c25 – 4*c43 – 6*d16 – 8*d34, -6*d25 – 4*d43 – 6*e16 – 8*e34,
-5*c16 – 3*c34 – 7*d07 – 9*d25, -5*d16 – 3*d34 – 7*e07 – 9*e25,
-4*c07 – 2*c25 – 10*d16, -4*d07 – 2*d25 – 10*e16, -c16 – 11*d07,
-d16 – 11*e07}
eqK1 = c10 + d01 – j00 – 4*c00*x1 + 2*c20*x1 + d11*x1 – j10*x1 – 5*c10*x1^2 +
3*c30*x1^2 – d01*x1^2 + d21*x1^2 – j20*x1^2 – 6*c20*x1^3 + 4*c40*x1^3 –
d11*x1^3 + d31*x1^3 – j30*x1^3 – 7*c30*x1^4 + 5*c50*x1^4 – d21*x1^4 +
d41*x1^4 – j40*x1^4 – 8*c40*x1^5 + 6*c60*x1^5 – d31*x1^5 + d51*x1^5 –
j50*x1^5 – 9*c50*x1^6 + 7*c70*x1^6 – d41*x1^6 + d61*x1^6 – 10*c60*x1^7 –
d51*x1^7 – 11*c70*x1^8 – d61*x1^8 + c11*x2 – 4*d00*x2 + 2*d02*x2 –
j01*x2 – 4*c01*x1*x2 + 2*c21*x1*x2 – 4*d10*x1*x2 + 2*d12*x1*x2 –
j11*x1*x2 – 5*c11*x1^2*x2 + 3*c31*x1^2*x2 – 2*d02*x1^2*x2 –
4*d20*x1^2*x2 + 2*d22*x1^2*x2 – j21*x1^2*x2 – 6*c21*x1^3*x2 +
4*c41*x1^3*x2 – 2*d12*x1^3*x2 – 4*d30*x1^3*x2 + 2*d32*x1^3*x2 –
j31*x1^3*x2 – 7*c31*x1^4*x2 + 5*c51*x1^4*x2 – 2*d22*x1^4*x2 –
4*d40*x1^4*x2 + 2*d42*x1^4*x2 – j41*x1^4*x2 – 8*c41*x1^5*x2 +
6*c61*x1^5*x2 – 2*d32*x1^5*x2 – 4*d50*x1^5*x2 + 2*d52*x1^5*x2 –
9*c51*x1^6*x2 – 2*d42*x1^6*x2 – 4*d60*x1^6*x2 – 10*c61*x1^7*x2 –
2*d52*x1^7*x2 – 4*d70*x1^7*x2 – c10*x2^2 + c12*x2^2 – 5*d01*x2^2 +
3*d03*x2^2 – j02*x2^2 – 4*c02*x1*x2^2 – 2*c20*x1*x2^2 + 2*c22*x1*x2^2 –
5*d11*x1*x2^2 + 3*d13*x1*x2^2 – j12*x1*x2^2 – 5*c12*x1^2*x2^2 –
3*c30*x1^2*x2^2 + 3*c32*x1^2*x2^2 – 3*d03*x1^2*x2^2 – 5*d21*x1^2*x2^2 +
3*d23*x1^2*x2^2 – j22*x1^2*x2^2 – 6*c22*x1^3*x2^2 – 4*c40*x1^3*x2^2 +
4*c42*x1^3*x2^2 – 3*d13*x1^3*x2^2 – 5*d31*x1^3*x2^2 + 3*d33*x1^3*x2^2 –
j32*x1^3*x2^2 – 7*c32*x1^4*x2^2 – 5*c50*x1^4*x2^2 + 5*c52*x1^4*x2^2 –
3*d23*x1^4*x2^2 – 5*d41*x1^4*x2^2 + 3*d43*x1^4*x2^2 – 8*c42*x1^5*x2^2 –
6*c60*x1^5*x2^2 – 3*d33*x1^5*x2^2 – 5*d51*x1^5*x2^2 – 9*c52*x1^6*x2^2 –
7*c70*x1^6*x2^2 – 3*d43*x1^6*x2^2 – 5*d61*x1^6*x2^2 – c11*x2^3 +
c13*x2^3 – 6*d02*x2^3 + 4*d04*x2^3 – j03*x2^3 – 4*c03*x1*x2^3 –
2*c21*x1*x2^3 + 2*c23*x1*x2^3 – 6*d12*x1*x2^3 + 4*d14*x1*x2^3 –
j13*x1*x2^3 – 5*c13*x1^2*x2^3 – 3*c31*x1^2*x2^3 + 3*c33*x1^2*x2^3 –
4*d04*x1^2*x2^3 – 6*d22*x1^2*x2^3 + 4*d24*x1^2*x2^3 – j23*x1^2*x2^3 –
6*c23*x1^3*x2^3 – 4*c41*x1^3*x2^3 + 4*c43*x1^3*x2^3 – 4*d14*x1^3*x2^3 –
6*d32*x1^3*x2^3 + 4*d34*x1^3*x2^3 – 7*c33*x1^4*x2^3 – 5*c51*x1^4*x2^3 –
4*d24*x1^4*x2^3 – 6*d42*x1^4*x2^3 – 8*c43*x1^5*x2^3 – 6*c61*x1^5*x2^3 –
4*d34*x1^5*x2^3 – 6*d52*x1^5*x2^3 – c12*x2^4 + c14*x2^4 – 7*d03*x2^4 +
5*d05*x2^4 – j04*x2^4 – 4*c04*x1*x2^4 – 2*c22*x1*x2^4 + 2*c24*x1*x2^4 –
7*d13*x1*x2^4 + 5*d15*x1*x2^4 – j14*x1*x2^4 – 5*c14*x1^2*x2^4 –
3*c32*x1^2*x2^4 + 3*c34*x1^2*x2^4 – 5*d05*x1^2*x2^4 – 7*d23*x1^2*x2^4 +
5*d25*x1^2*x2^4 – 6*c24*x1^3*x2^4 – 4*c42*x1^3*x2^4 – 5*d15*x1^3*x2^4 –
7*d33*x1^3*x2^4 – 7*c34*x1^4*x2^4 – 5*c52*x1^4*x2^4 – 5*d25*x1^4*x2^4 –
7*d43*x1^4*x2^4 – c13*x2^5 + c15*x2^5 – 8*d04*x2^5 + 6*d06*x2^5 –
j05*x2^5 – 4*c05*x1*x2^5 – 2*c23*x1*x2^5 + 2*c25*x1*x2^5 –
8*d14*x1*x2^5 + 6*d16*x1*x2^5 – 5*c15*x1^2*x2^5 – 3*c33*x1^2*x2^5 –
6*d06*x1^2*x2^5 – 8*d24*x1^2*x2^5 – 6*c25*x1^3*x2^5 – 4*c43*x1^3*x2^5 –
6*d16*x1^3*x2^5 – 8*d34*x1^3*x2^5 – c14*x2^6 + c16*x2^6 – 9*d05*x2^6 +
7*d07*x2^6 – 4*c06*x1*x2^6 – 2*c24*x1*x2^6 – 9*d15*x1*x2^6 –
5*c16*x1^2*x2^6 – 3*c34*x1^2*x2^6 – 7*d07*x1^2*x2^6 – 9*d25*x1^2*x2^6 –
c15*x2^7 – 10*d06*x2^7 – 4*c07*x1*x2^7 – 2*c25*x1*x2^7 –
10*d16*x1*x2^7 – c16*x2^8 – 11*d07*x2^8
eqK2 = d10 + e01 – k00 – 4*d00*x1 + 2*d20*x1 + e11*x1 – k10*x1 – 5*d10*x1^2 +
3*d30*x1^2 – e01*x1^2 + e21*x1^2 – k20*x1^2 – 6*d20*x1^3 + 4*d40*x1^3 –
e11*x1^3 + e31*x1^3 – k30*x1^3 – 7*d30*x1^4 + 5*d50*x1^4 – e21*x1^4 +
e41*x1^4 – k40*x1^4 – 8*d40*x1^5 + 6*d60*x1^5 – e31*x1^5 + e51*x1^5 –
k50*x1^5 – 9*d50*x1^6 + 7*d70*x1^6 – e41*x1^6 + e61*x1^6 – 10*d60*x1^7 –
e51*x1^7 – 11*d70*x1^8 – e61*x1^8 + d11*x2 – 4*e00*x2 + 2*e02*x2 –
k01*x2 – 4*d01*x1*x2 + 2*d21*x1*x2 – 4*e10*x1*x2 + 2*e12*x1*x2 –
k11*x1*x2 – 5*d11*x1^2*x2 + 3*d31*x1^2*x2 – 2*e02*x1^2*x2 –
4*e20*x1^2*x2 + 2*e22*x1^2*x2 – k21*x1^2*x2 – 6*d21*x1^3*x2 +
4*d41*x1^3*x2 – 2*e12*x1^3*x2 – 4*e30*x1^3*x2 + 2*e32*x1^3*x2 –
k31*x1^3*x2 – 7*d31*x1^4*x2 + 5*d51*x1^4*x2 – 2*e22*x1^4*x2 –
4*e40*x1^4*x2 + 2*e42*x1^4*x2 – k41*x1^4*x2 – 8*d41*x1^5*x2 +
6*d61*x1^5*x2 – 2*e32*x1^5*x2 – 4*e50*x1^5*x2 + 2*e52*x1^5*x2 –
9*d51*x1^6*x2 – 2*e42*x1^6*x2 – 4*e60*x1^6*x2 – 10*d61*x1^7*x2 –
2*e52*x1^7*x2 – 4*e70*x1^7*x2 – d10*x2^2 + d12*x2^2 – 5*e01*x2^2 +
3*e03*x2^2 – k02*x2^2 – 4*d02*x1*x2^2 – 2*d20*x1*x2^2 + 2*d22*x1*x2^2 –
5*e11*x1*x2^2 + 3*e13*x1*x2^2 – k12*x1*x2^2 – 5*d12*x1^2*x2^2 –
3*d30*x1^2*x2^2 + 3*d32*x1^2*x2^2 – 3*e03*x1^2*x2^2 – 5*e21*x1^2*x2^2 +
3*e23*x1^2*x2^2 – k22*x1^2*x2^2 – 6*d22*x1^3*x2^2 – 4*d40*x1^3*x2^2 +
4*d42*x1^3*x2^2 – 3*e13*x1^3*x2^2 – 5*e31*x1^3*x2^2 + 3*e33*x1^3*x2^2 –
k32*x1^3*x2^2 – 7*d32*x1^4*x2^2 – 5*d50*x1^4*x2^2 + 5*d52*x1^4*x2^2 –
3*e23*x1^4*x2^2 – 5*e41*x1^4*x2^2 + 3*e43*x1^4*x2^2 – 8*d42*x1^5*x2^2 –
6*d60*x1^5*x2^2 – 3*e33*x1^5*x2^2 – 5*e51*x1^5*x2^2 – 9*d52*x1^6*x2^2 –
7*d70*x1^6*x2^2 – 3*e43*x1^6*x2^2 – 5*e61*x1^6*x2^2 – d11*x2^3 +
d13*x2^3 – 6*e02*x2^3 + 4*e04*x2^3 – k03*x2^3 – 4*d03*x1*x2^3 –
2*d21*x1*x2^3 + 2*d23*x1*x2^3 – 6*e12*x1*x2^3 + 4*e14*x1*x2^3 –
k13*x1*x2^3 – 5*d13*x1^2*x2^3 – 3*d31*x1^2*x2^3 + 3*d33*x1^2*x2^3 –
4*e04*x1^2*x2^3 – 6*e22*x1^2*x2^3 + 4*e24*x1^2*x2^3 – k23*x1^2*x2^3 –
6*d23*x1^3*x2^3 – 4*d41*x1^3*x2^3 + 4*d43*x1^3*x2^3 – 4*e14*x1^3*x2^3 –
6*e32*x1^3*x2^3 + 4*e34*x1^3*x2^3 – 7*d33*x1^4*x2^3 – 5*d51*x1^4*x2^3 –
4*e24*x1^4*x2^3 – 6*e42*x1^4*x2^3 – 8*d43*x1^5*x2^3 – 6*d61*x1^5*x2^3 –
4*e34*x1^5*x2^3 – 6*e52*x1^5*x2^3 – d12*x2^4 + d14*x2^4 – 7*e03*x2^4 +
5*e05*x2^4 – k04*x2^4 – 4*d04*x1*x2^4 – 2*d22*x1*x2^4 + 2*d24*x1*x2^4 –
7*e13*x1*x2^4 + 5*e15*x1*x2^4 – k14*x1*x2^4 – 5*d14*x1^2*x2^4 –
3*d32*x1^2*x2^4 + 3*d34*x1^2*x2^4 – 5*e05*x1^2*x2^4 – 7*e23*x1^2*x2^4 +
5*e25*x1^2*x2^4 – 6*d24*x1^3*x2^4 – 4*d42*x1^3*x2^4 – 5*e15*x1^3*x2^4 –
7*e33*x1^3*x2^4 – 7*d34*x1^4*x2^4 – 5*d52*x1^4*x2^4 – 5*e25*x1^4*x2^4 –
7*e43*x1^4*x2^4 – d13*x2^5 + d15*x2^5 – 8*e04*x2^5 + 6*e06*x2^5 –
k05*x2^5 – 4*d05*x1*x2^5 – 2*d23*x1*x2^5 + 2*d25*x1*x2^5 –
8*e14*x1*x2^5 + 6*e16*x1*x2^5 – 5*d15*x1^2*x2^5 – 3*d33*x1^2*x2^5 –
6*e06*x1^2*x2^5 – 8*e24*x1^2*x2^5 – 6*d25*x1^3*x2^5 – 4*d43*x1^3*x2^5 –
6*e16*x1^3*x2^5 – 8*e34*x1^3*x2^5 – d14*x2^6 + d16*x2^6 – 9*e05*x2^6 +
7*e07*x2^6 – 4*d06*x1*x2^6 – 2*d24*x1*x2^6 – 9*e15*x1*x2^6 –
5*d16*x1^2*x2^6 – 3*d34*x1^2*x2^6 – 7*e07*x1^2*x2^6 – 9*e25*x1^2*x2^6 –
d15*x2^7 – 10*e06*x2^7 – 4*d07*x1*x2^7 – 2*d25*x1*x2^7 –
10*e16*x1*x2^7 – d16*x2^8 – 11*e07*x2^8
E1 = 1 – x1^2 – x2^2
E2 = (1 – x1^2 – x2^2)^2
I11 = (1 – x1^2 – x2^2)^2*(c00 + c10*x1 + c20*x1^2 + c30*x1^3 + c40*x1^4 +
c50*x1^5 + c60*x1^6 + c70*x1^7 + c01*x2 + c11*x1*x2 + c21*x1^2*x2 +
c31*x1^3*x2 + c41*x1^4*x2 + c51*x1^5*x2 + c61*x1^6*x2 + c02*x2^2 +
c12*x1*x2^2 + c22*x1^2*x2^2 + c32*x1^3*x2^2 + c42*x1^4*x2^2 +
c52*x1^5*x2^2 + c03*x2^3 + c13*x1*x2^3 + c23*x1^2*x2^3 +
c33*x1^3*x2^3 + c43*x1^4*x2^3 + c04*x2^4 + c14*x1*x2^4 +
c24*x1^2*x2^4 + c34*x1^3*x2^4 + c05*x2^5 + c15*x1*x2^5 +
c25*x1^2*x2^5 + c06*x2^6 + c16*x1*x2^6 + c07*x2^7)
I12 = (1 – x1^2 – x2^2)^2*(d00 + d10*x1 + d20*x1^2 + d30*x1^3 + d40*x1^4 +
d50*x1^5 + d60*x1^6 + d70*x1^7 + d01*x2 + d11*x1*x2 + d21*x1^2*x2 +
d31*x1^3*x2 + d41*x1^4*x2 + d51*x1^5*x2 + d61*x1^6*x2 + d02*x2^2 +
d12*x1*x2^2 + d22*x1^2*x2^2 + d32*x1^3*x2^2 + d42*x1^4*x2^2 +
d52*x1^5*x2^2 + d03*x2^3 + d13*x1*x2^3 + d23*x1^2*x2^3 +
d33*x1^3*x2^3 + d43*x1^4*x2^3 + d04*x2^4 + d14*x1*x2^4 +
d24*x1^2*x2^4 + d34*x1^3*x2^4 + d05*x2^5 + d15*x1*x2^5 +
d25*x1^2*x2^5 + d06*x2^6 + d16*x1*x2^6 + d07*x2^7)
I21 = (1 – x1^2 – x2^2)^2*(d00 + d10*x1 + d20*x1^2 + d30*x1^3 + d40*x1^4 +
d50*x1^5 + d60*x1^6 + d70*x1^7 + d01*x2 + d11*x1*x2 + d21*x1^2*x2 +
d31*x1^3*x2 + d41*x1^4*x2 + d51*x1^5*x2 + d61*x1^6*x2 + d02*x2^2 +
d12*x1*x2^2 + d22*x1^2*x2^2 + d32*x1^3*x2^2 + d42*x1^4*x2^2 +
d52*x1^5*x2^2 + d03*x2^3 + d13*x1*x2^3 + d23*x1^2*x2^3 +
d33*x1^3*x2^3 + d43*x1^4*x2^3 + d04*x2^4 + d14*x1*x2^4 +
d24*x1^2*x2^4 + d34*x1^3*x2^4 + d05*x2^5 + d15*x1*x2^5 +
d25*x1^2*x2^5 + d06*x2^6 + d16*x1*x2^6 + d07*x2^7)
I22 = (1 – x1^2 – x2^2)^2*(e00 + e10*x1 + e20*x1^2 + e30*x1^3 + e40*x1^4 +
e50*x1^5 + e60*x1^6 + e70*x1^7 + e01*x2 + e11*x1*x2 + e21*x1^2*x2 +
e31*x1^3*x2 + e41*x1^4*x2 + e51*x1^5*x2 + e61*x1^6*x2 + e02*x2^2 +
e12*x1*x2^2 + e22*x1^2*x2^2 + e32*x1^3*x2^2 + e42*x1^4*x2^2 +
e52*x1^5*x2^2 + e03*x2^3 + e13*x1*x2^3 + e23*x1^2*x2^3 +
e33*x1^3*x2^3 + e43*x1^4*x2^3 + e04*x2^4 + e14*x1*x2^4 +
e24*x1^2*x2^4 + e34*x1^3*x2^4 + e05*x2^5 + e15*x1*x2^5 +
e25*x1^2*x2^5 + e06*x2^6 + e16*x1*x2^6 + e07*x2^7)
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