This technical report explains the derivation of W1(t), W2(t), W3(t), Theta_1_i, Theta_2_i, and Theta_3, i=1,..,4. The development is done with MAPLE ver. 10.0 and the files can be found on the web at http://www.ece.clemson.edu/crb/publictn/W1-W2.mw and http://www.ece.clemson.edu/crb/publictn/W3.mw. In this section the derivation of W1(t), W2(t), Theta_1_i, and Theta_2_i, i=1,..,4 is presented. with(LinearAlgebra): Rc is the constant camera extrinsic parameters. Rc:=matrix(3,3,[rc11,rc12,rc13,rc21,rc22,rc23,rc31,rc32,rc33]): Rr(t) is the end effector orientation of the robot manipulator. Rr:=matrix(3,3,[rr11,rr12,rr13,rr21,rr22,rr23,rr31,rr32,rr33]): A^bar is the constant camera intrinsic parameters. Abar:=matrix(2,3,[f*ku,f*ku*cotphi,u0,0,f*kv*cosecphi,v0]): Xr(t) is the end-effector position of the robot manipulator. Xr:=matrix(3,1,[xr1,xr2,xr3]): Pc is the constant distance between the end-effector of the robot manipulator and the camera. Pc:=matrix(3,1,[pc1,pc2,pc3]): Xpi, i=1,..,4 are the constant distances from the base frame of the robot manipulator to the feature points. Xp1:=matrix(3,1,[xp11,xp12,xp13]): Xp2:=matrix(3,1,[xp21,xp22,xp23]): Xp3:=matrix(3,1,[xp31,xp32,xp33]): Xp4:=matrix(3,1,[xp41,xp42,xp43]): Zi, i=1,..,4 are found based on Eqn#31 of Technical Report#CU-CRB-3-9-07-1. Z1:=evalm([0,0,1]&*(Rc&*transpose(Rr)&*(Xp1-Xr)+Pc)): Z2:=evalm([0,0,1]&*(Rc&*transpose(Rr)&*(Xp2-Xr)+Pc)): Z3:=evalm([0,0,1]&*(Rc&*transpose(Rr)&*(Xp3-Xr)+Pc)): Z4:=evalm([0,0,1]&*(Rc&*transpose(Rr)&*(Xp4-Xr)+Pc)): W2, introduced in Eqn#33 of Technical Report#CU-CRB-3-9-07-1, is found as follows: W2:=matrix(1,13,[-(rr11*xr1+rr21*xr2+rr31*xr3),-(rr12*xr1+rr22*xr2+rr32*xr3),-(rr13*xr1+rr23*xr2+rr33*xr3),rr11,rr12,rr13,rr21,rr22,rr23,rr31,rr32,rr33,1]);

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Theta_2i, i=1,..,4, intrduced in Eqn#33 of Technical Report#CU-CRB-3-9-07-1, are found as follows: Theta2_1:=matrix(13,1,[rc31,rc32,rc33,xp11*rc31,xp11*rc32,xp11*rc33,xp12*rc31,xp12*rc32,xp12*rc33,xp13*rc31,xp13*rc32,xp13*rc33,pc3]);

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

Theta2_2:=matrix(13,1,[rc31,rc32,rc33,xp21*rc31,xp21*rc32,xp21*rc33,xp22*rc31,xp22*rc32,xp22*rc33,xp23*rc31,xp23*rc32,xp23*rc33,pc3]);

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

Theta2_3:=matrix(13,1,[rc31,rc32,rc33,xp31*rc31,xp31*rc32,xp31*rc33,xp32*rc31,xp32*rc32,xp32*rc33,xp33*rc31,xp33*rc32,xp33*rc33,pc3]);

NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiUtSSNtaUdGJTY5USsmVGhldGE7Ml8zRigvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GKC8lJXNpemVHUSMxMkYoLyUlYm9sZEdRJmZhbHNlRigvJSdpdGFsaWNHUSV0cnVlRigvJSp1bmRlcmxpbmVHRjgvJSpzdWJzY3JpcHRHRjgvJSxzdXBlcnNjcmlwdEdGOC8lK2ZvcmVncm91bmRHUSpbMCwwLDI1NV1GKC8lK2JhY2tncm91bmRHUShbMCwwLDBdRigvJSdvcGFxdWVHRjgvJStleGVjdXRhYmxlR0Y4LyUpcmVhZG9ubHlHRjsvJSljb21wb3NlZEdGOC8lKmNvbnZlcnRlZEdGOC8lK2ltc2VsZWN0ZWRHRjgvJSxwbGFjZWhvbGRlckdGOC8lMGZvbnRfc3R5bGVfbmFtZUdRKjJEfk91dHB1dEYoLyUqbWF0aGNvbG9yR0ZELyUvbWF0aGJhY2tncm91bmRHRkcvJStmb250ZmFtaWx5R0YyLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGKC8lKW1hdGhzaXplR0Y1LUkjbW9HRiU2M1EjOj1GKC8lJWZvcm1HUSZpbmZpeEYoLyUmZmVuY2VHRjgvJSpzZXBhcmF0b3JHRjgvJSdsc3BhY2VHUS90aGlja21hdGhzcGFjZUYoLyUncnNwYWNlR0ZbcC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobWF4c2l6ZUdRKWluZmluaXR5RigvJShtaW5zaXplR1EiMUYoLyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJTBmb250X3N0eWxlX25hbWVHRlgvJSVzaXplR0Y1LyUrZm9yZWdyb3VuZEdGRC8lK2JhY2tncm91bmRHRkctRiQ2JS1GX282M1EiW0YoL0Zjb1EncHJlZml4RigvRmZvRjtGZ28vRmpvUS50aGlubWF0aHNwYWNlRigvRl1wRl9yL0ZfcEY7RmBwRmJwRmVwRmhwRmpwRlxxRl5xRmBxRmJxRmRxLUYkNiMtSSdtdGFibGVHRiU2Ly1JJG10ckdGJTYjLUkkbXRkR0YlNiMtRi02OVElcmMzMUYoRjBGM0Y2RjlGPEY+RkBGQkZFRkhGSkZMRk5GUEZSRlRGVkZZRmVuRmduRmluRlxvLUZocjYjLUZbczYjLUYtNjlRJXJjMzJGKEYwRjNGNkY5RjxGPkZARkJGRUZIRkpGTEZORlBGUkZURlZGWUZlbkZnbkZpbkZcby1GaHI2Iy1GW3M2Iy1GLTY5USVyYzMzRihGMEYzRjZGOUY8Rj5GQEZCRkVGSEZKRkxGTkZQRlJGVEZWRllGZW5GZ25GaW5GXG8tRmhyNiMtRltzNiMtRiQ2JS1GLTY5USV4cDMxRihGMEYzRjZGOUY8Rj5GQEZCRkVGSEZKRkxGTkZQRlJGVEZWRllGZW5GZ25GaW5GXG8tRl9vNjNRMSZJbnZpc2libGVUaW1lcztGKEZib0Zlb0Znby9Gam9RJDBlbUYoL0ZdcEZbdUZecEZgcEZicEZlcEZocEZqcEZccUZecUZgcUZicUZkcUZdcy1GaHI2Iy1GW3M2Iy1GJDYlRmR0Rmd0RmRzLUZocjYjLUZbczYjLUYkNiVGZHRGZ3RGW3QtRmhyNiMtRltzNiMtRiQ2JS1GLTY5USV4cDMyRihGMEYzRjZGOUY8Rj5GQEZCRkVGSEZKRkxGTkZQRlJGVEZWRllGZW5GZ25GaW5GXG9GZ3RGXXMtRmhyNiMtRltzNiMtRiQ2JUZfdkZndEZkcy1GaHI2Iy1GW3M2Iy1GJDYlRl92Rmd0Rlt0LUZocjYjLUZbczYjLUYkNiUtRi02OVEleHAzM0YoRjBGM0Y2RjlGPEY+RkBGQkZFRkhGSkZMRk5GUEZSRlRGVkZZRmVuRmduRmluRlxvRmd0Rl1zLUZocjYjLUZbczYjLUYkNiVGZHdGZ3RGZHMtRmhyNiMtRltzNiMtRiQ2JUZkd0ZndEZbdC1GaHI2Iy1GW3M2Iy1GLTY5USRwYzNGKEYwRjNGNkY5RjxGPkZARkJGRUZIRkpGTEZORlBGUkZURlZGWUZlbkZnbkZpbkZcby1GX282M1EiXUYoL0Zjb1EocG9zdGZpeEYoRl1yRmdvRl5yL0ZdcFEydmVyeXRoaW5tYXRoc3BhY2VGKEZhckZgcEZicEZlcEZocEZqcEZccUZecUZgcUZicUZkcTcjLV9GKUksbXByaW50c2xhc2hHRig2JDcjPkkpVGhldGEyXzNHRigtSSdtYXRyaXhHNiQlKnByb3RlY3RlZEdGKjYjNy83I0klcmMzMUdGKDcjSSVyYzMyR0YoNyNJJXJjMzNHRig3IyomSSV4cDMxR0YoIiIiRmB6Rmh6NyMqJkZnekZoekZiekZoejcjKiZGZ3pGaHpGZHpGaHo3IyomSSV4cDMyR0YoRmh6RmB6Rmh6NyMqJkZfW2xGaHpGYnpGaHo3IyomRl9bbEZoekZkekZoejcjKiZJJXhwMzNHRihGaHpGYHpGaHo3IyomRmZbbEZoekZiekZoejcjKiZGZltsRmh6RmR6Rmh6NyNJJHBjM0dGKDcjPUYoNiQ7Rmh6IiM4O0ZoekZoekVcW2wuNiRGYVxsRmh6RlxcbDYkIiIjRmh6RmJ6NiQiIihGaHpGXltsNiQiIzdGaHpGaltsNiQiIiRGaHpGZHo2JCIjNkZoekZoW2w2JCIiKUZoekZhW2w2JCIiJkZoekZqejYkIiM1Rmh6RmVbbDYkIiIlRmh6RmZ6NiQiIipGaHpGY1tsNiQiIidGaHpGXFtsNiRGaHpGaHpGYHo=

Theta2_4:=matrix(13,1,[rc31,rc32,rc33,xp41*rc31,xp41*rc32,xp41*rc33,xp42*rc31,xp42*rc32,xp42*rc33,xp43*rc31,xp43*rc32,xp43*rc33,pc3]);

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Checking the definitions of W2 and Theta_2i... check1:=simplify(Z1[1]-evalm(W2&*Theta2_1)[1,1]);

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check2:=simplify(Z2[1]-evalm(W2&*Theta2_2)[1,1]);

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

check3:=simplify(Z3[1]-evalm(W2&*Theta2_3)[1,1]);

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check4:=simplify(Z4[1]-evalm(W2&*Theta2_4)[1,1]);

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The numerator of each feature point are obtained based on Eqn#30 of Technical Report#CU-CRB-3-9-07-1. P1_num:=evalm(Abar&*(Rc&*transpose(Rr)&*(Xp1-Xr)+Pc)): P2_num:=evalm(Abar&*(Rc&*transpose(Rr)&*(Xp2-Xr)+Pc)): P3_num:=evalm(Abar&*(Rc&*transpose(Rr)&*(Xp3-Xr)+Pc)): P4_num:=evalm(Abar&*(Rc&*transpose(Rr)&*(Xp4-Xr)+Pc)): W1, intrduced in Eqn#32 of Technical Report#CU-CRB-3-9-07-1, is found as follows: W1:=matrix(2,65,[rr11,rr12,rr13,rr21,rr22,rr23,rr31,rr32,rr33,1,-(rr11*xr1+rr21*xr2+rr31*xr3),-(rr12*xr1+rr22*xr2+rr32*xr3),-(rr13*xr1+rr23*xr2+rr33*xr3),rr11,rr12,rr13,rr21,rr22,rr23,rr31,rr32,rr33,1,-(rr11*xr1+rr21*xr2+rr31*xr3),-(rr12*xr1+rr22*xr2+rr32*xr3),-(rr13*xr1+rr23*xr2+rr33*xr3),rr11,rr12,rr13,rr21,rr22,rr23,rr31,rr32,rr33,1,-(rr11*xr1+rr21*xr2+rr31*xr3),-(rr12*xr1+rr22*xr2+rr32*xr3),-(rr13*xr1+rr23*xr2+rr33*xr3),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,rr11,rr12,rr13,rr21,rr22,rr23,rr31,rr32,rr33,1,-(rr11*xr1+rr21*xr2+rr31*xr3),-(rr12*xr1+rr22*xr2+rr32*xr3),-(rr13*xr1+rr23*xr2+rr33*xr3),rr11,rr12,rr13,rr21,rr22,rr23,rr31,rr32,rr33,1,-(rr11*xr1+rr21*xr2+rr31*xr3),-(rr12*xr1+rr22*xr2+rr32*xr3),-(rr13*xr1+rr23*xr2+rr33*xr3)]);

NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiUtSSNtaUdGJTY5USNXMUYoLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRigvJSVzaXplR1EjMTJGKC8lJWJvbGRHUSZmYWxzZUYoLyUnaXRhbGljR1EldHJ1ZUYoLyUqdW5kZXJsaW5lR0Y4LyUqc3Vic2NyaXB0R0Y4LyUsc3VwZXJzY3JpcHRHRjgvJStmb3JlZ3JvdW5kR1EqWzAsMCwyNTVdRigvJStiYWNrZ3JvdW5kR1EoWzAsMCwwXUYoLyUnb3BhcXVlR0Y4LyUrZXhlY3V0YWJsZUdGOC8lKXJlYWRvbmx5R0Y7LyUpY29tcG9zZWRHRjgvJSpjb252ZXJ0ZWRHRjgvJStpbXNlbGVjdGVkR0Y4LyUscGxhY2Vob2xkZXJHRjgvJTBmb250X3N0eWxlX25hbWVHUSoyRH5PdXRwdXRGKC8lKm1hdGhjb2xvckdGRC8lL21hdGhiYWNrZ3JvdW5kR0ZHLyUrZm9udGZhbWlseUdGMi8lLG1hdGh2YXJpYW50R1EnaXRhbGljRigvJSltYXRoc2l6ZUdGNS1JI21vR0YlNjNRIzo9RigvJSVmb3JtR1EmaW5maXhGKC8lJmZlbmNlR0Y4LyUqc2VwYXJhdG9yR0Y4LyUnbHNwYWNlR1EvdGhpY2ttYXRoc3BhY2VGKC8lJ3JzcGFjZUdGW3AvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKG1heHNpemVHUSlpbmZpbml0eUYoLyUobWluc2l6ZUdRIjFGKC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUwZm9udF9zdHlsZV9uYW1lR0ZYLyUlc2l6ZUdGNS8lK2ZvcmVncm91bmRHRkQvJStiYWNrZ3JvdW5kR0ZHLUYkNiUtRl9vNjNRIltGKC9GY29RJ3ByZWZpeEYoL0Zmb0Y7RmdvL0Zqb1EudGhpbm1hdGhzcGFjZUYoL0ZdcEZfci9GX3BGO0ZgcEZicEZlcEZocEZqcEZccUZecUZgcUZicUZkcS1GJDYjLUknbXRhYmxlR0YlNiQtSSRtdHJHRiU2XW8tSSRtdGRHRiU2Iy1GLTY5USVycjExRihGMEYzRjZGOUY8Rj5GQEZCRkVGSEZKRkxGTkZQRlJGVEZWRllGZW5GZ25GaW5GXG8tRltzNiMtRi02OVElcnIxMkYoRjBGM0Y2RjlGPEY+RkBGQkZFRkhGSkZMRk5GUEZSRlRGVkZZRmVuRmduRmluRlxvLUZbczYjLUYtNjlRJXJyMTNGKEYwRjNGNkY5RjxGPkZARkJGRUZIRkpGTEZORlBGUkZURlZGWUZlbkZnbkZpbkZcby1GW3M2Iy1GLTY5USVycjIxRihGMEYzRjZGOUY8Rj5GQEZCRkVGSEZKRkxGTkZQRlJGVEZWRllGZW5GZ25GaW5GXG8tRltzNiMtRi02OVElcnIyMkYoRjBGM0Y2RjlGPEY+RkBGQkZFRkhGSkZMRk5GUEZSRlRGVkZZRmVuRmduRmluRlxvLUZbczYjLUYtNjlRJXJyMjNGKEYwRjNGNkY5RjxGPkZARkJGRUZIRkpGTEZORlBGUkZURlZGWUZlbkZnbkZpbkZcby1GW3M2Iy1GLTY5USVycjMxRihGMEYzRjZGOUY8Rj5GQEZCRkVGSEZKRkxGTkZQRlJGVEZWRllGZW5GZ25GaW5GXG8tRltzNiMtRi02OVElcnIzMkYoRjBGM0Y2RjlGPEY+RkBGQkZFRkhGSkZMRk5GUEZSRlRGVkZZRmVuRmduRmluRlxvLUZbczYjLUYtNjlRJXJyMzNGKEYwRjNGNkY5RjxGPkZARkJGRUZIRkpGTEZORlBGUkZURlZGWUZlbkZnbkZpbkZcby1GW3M2Iy1JI21uR0YlNjlGZ3BGMEYzRjYvRjpGOEY8Rj5GQEZCRkVGSEZKRkxGTkZQRlJGVEZWRllGZW5GZ24vRmpuUSdub3JtYWxGKEZcby1GW3M2Iy1GJDYoLUZfbzYzUSomdW1pbnVzMDtGKEZbckZlb0Znby9Gam9RJDBlbUYoL0ZdcEZodkZecEZgcEZicEZlcEZocEZqcEZccUZecUZgcUZicUZkcS1GJDYlRl1zLUZfbzYzUTEmSW52aXNpYmxlVGltZXM7RihGYm9GZW9GZ29GZ3ZGaXZGXnBGYHBGYnBGZXBGaHBGanBGXHFGXnFGYHFGYnFGZHEtRi02OVEkeHIxRihGMEYzRjZGOUY8Rj5GQEZCRkVGSEZKRkxGTkZQRlJGVEZWRllGZW5GZ25GaW5GXG8tRl9vNjNRKCZtaW51cztGKEZib0Zlb0Znby9Gam9RMG1lZGl1bW1hdGhzcGFjZUYoL0ZdcEZmd0ZecEZgcEZicEZlcEZocEZqcEZccUZecUZgcUZicUZkcS1GJDYlRlx0Rlx3LUYtNjlRJHhyMkYoRjBGM0Y2RjlGPEY+RkBGQkZFRkhGSkZMRk5GUEZSRlRGVkZZRmVuRmduRmluRlxvRmJ3LUYkNiVGW3VGXHctRi02OVEkeHIzRihGMEYzRjZGOUY8Rj5GQEZCRkVGSEZKRkxGTkZQRlJGVEZWRllGZW5GZ25GaW5GXG8tRltzNiMtRiQ2KEZkdi1GJDYlRmJzRlx3Rl93RmJ3LUYkNiVGYXRGXHdGandGYnctRiQ2JUZgdUZcd0ZfeC1GW3M2Iy1GJDYoRmR2LUYkNiVGZ3NGXHdGX3dGYnctRiQ2JUZmdEZcd0Zqd0Zidy1GJDYlRmV1Rlx3Rl94RmpyRmBzRmVzRmpzRl90RmR0Rml0Rl51RmN1Rmh1RmB2RmJ4Rlx5RmpyRmBzRmVzRmpzRl90RmR0Rml0Rl51RmN1Rmh1RmB2RmJ4Rlx5LUZbczYjLUZbdjY5USIwRihGMEYzRjZGXXZGPEY+RkBGQkZFRkhGSkZMRk5GUEZSRlRGVkZZRmVuRmduRl52RlxvRmZ5RmZ5RmZ5RmZ5RmZ5RmZ5RmZ5RmZ5RmZ5RmZ5RmZ5RmZ5RmZ5RmZ5RmZ5RmZ5RmZ5RmZ5RmZ5RmZ5RmZ5RmZ5RmZ5RmZ5RmZ5LUZocjZdb0ZmeUZmeUZmeUZmeUZmeUZmeUZmeUZmeUZmeUZmeUZmeUZmeUZmeUZmeUZmeUZmeUZmeUZmeUZmeUZmeUZmeUZmeUZmeUZmeUZmeUZmeUZmeUZmeUZmeUZmeUZmeUZmeUZmeUZmeUZmeUZmeUZmeUZmeUZmeUZqckZgc0Zlc0Zqc0ZfdEZkdEZpdEZedUZjdUZodUZgdkZieEZceUZqckZgc0Zlc0Zqc0ZfdEZkdEZpdEZedUZjdUZodUZgdkZieEZceS1GX282M1EiXUYoL0Zjb1EocG9zdGZpeEYoRl1yRmdvRl5yL0ZdcFEydmVyeXRoaW5tYXRoc3BhY2VGKEZhckZgcEZicEZlcEZocEZqcEZccUZecUZgcUZicUZkcTcjLV9GKUksbXByaW50c2xhc2hHRig2JDcjPkkjVzFHRigtSSdtYXRyaXhHNiQlKnByb3RlY3RlZEdGKjYjNyQ3XW9JJXJyMTFHRihJJXJyMTJHRihJJXJyMTNHRihJJXJyMjFHRihJJXJyMjJHRihJJXJyMjNHRihJJXJyMzFHRihJJXJyMzJHRihJJXJyMzNHRigiIiIsKComRmNbbEZcXGxJJHhyMUdGKEZcXGwhIiIqJkZmW2xGXFxsSSR4cjJHRihGXFxsRmBcbComRmlbbEZcXGxJJHhyM0dGKEZcXGxGYFxsLCgqJkZkW2xGXFxsRl9cbEZcXGxGYFxsKiZGZ1tsRlxcbEZiXGxGXFxsRmBcbComRmpbbEZcXGxGZFxsRlxcbEZgXGwsKComRmVbbEZcXGxGX1xsRlxcbEZgXGwqJkZoW2xGXFxsRmJcbEZcXGxGYFxsKiZGW1xsRlxcbEZkXGxGXFxsRmBcbEZjW2xGZFtsRmVbbEZmW2xGZ1tsRmhbbEZpW2xGaltsRltcbEZcXGxGXVxsRmVcbEZpXGxGY1tsRmRbbEZlW2xGZltsRmdbbEZoW2xGaVtsRmpbbEZbXGxGXFxsRl1cbEZlXGxGaVxsIiIhRl1dbEZdXWxGXV1sRl1dbEZdXWxGXV1sRl1dbEZdXWxGXV1sRl1dbEZdXWxGXV1sRl1dbEZdXWxGXV1sRl1dbEZdXWxGXV1sRl1dbEZdXWxGXV1sRl1dbEZdXWxGXV1sRl1dbDddb0ZdXWxGXV1sRl1dbEZdXWxGXV1sRl1dbEZdXWxGXV1sRl1dbEZdXWxGXV1sRl1dbEZdXWxGXV1sRl1dbEZdXWxGXV1sRl1dbEZdXWxGXV1sRl1dbEZdXWxGXV1sRl1dbEZdXWxGXV1sRl1dbEZdXWxGXV1sRl1dbEZdXWxGXV1sRl1dbEZdXWxGXV1sRl1dbEZdXWxGXV1sRl1dbEZjW2xGZFtsRmVbbEZmW2xGZ1tsRmhbbEZpW2xGaltsRltcbEZcXGxGXVxsRmVcbEZpXGxGY1tsRmRbbEZlW2xGZltsRmdbbEZoW2xGaVtsRmpbbEZbXGxGXFxsRl1cbEZlXGxGaVxsNyM9Rig2JDtGXFxsIiIjO0ZcXGwiI2xFXFtsXXM2JEZcXGwiI0dGZFtsNiRGXFxsIiNiRl1dbDYkRmNdbCIjTEZdXWw2JEZjXWwiI2dGaltsNiRGXFxsRlxebEZpW2w2JEZjXWwiIzZGXV1sNiRGY11sRlxcbEZdXWw2JEZcXGwiI0RGZVxsNiRGXFxsIiNlRl1dbDYkRmNdbCIjT0ZdXWw2JEZjXWwiI1pGaltsNiRGY11sIiNqRl1cbDYkRlxcbCIjSUZmW2w2JEZcXGwiI1lGXV1sNiRGXFxsIiIqRltcbDYkRmNdbCIjOUZdXWw2JEZcXGwiIz1GZ1tsNiRGXFxsIiNoRl1dbDYkRmNdbCIjUkZdXWw2JEZjXWwiI11GXVxsNiRGXFxsIiNWRl1dbDYkRmNdbCIjPEZdXWw2JEZjXWxGZV1sRmlcbDYkRlxcbCIjOkZkW2w2JEZcXGwiIidGaFtsNiRGXFxsIiNrRl1dbDYkRmNdbCIjRUZdXWw2JEZjXWwiI1VGZVtsNiRGY11sIiNgRmNbbDYkRlxcbCIjU0ZdXWw2JEZjXWwiIz9GXV1sNiRGY11sRmNdbEZdXWw2JEZcXGwiI0NGXVxsNiRGXFxsIiNmRl1dbDYkRmNdbCIjUEZdXWw2JEZjXWwiI1tGW1xsNiRGY11sRmdgbEZlXGw2JEZcXGwiI0hGZVtsNiRGXFxsIiNYRl1dbDYkRlxcbCIjNUZcXGw2JEZjXWwiIiRGXV1sNiRGY11sRmNgbEZdXWw2JEZcXGwiI2FGXV1sNiRGY11sIiNLRl1dbDYkRmNdbEZmYWxGaVtsNiRGXFxsIiNNRmpbbDYkRmNdbEZhYmxGXV1sNiRGXFxsRmRfbEZjW2w2JEZcXGwiIiZGZ1tsNiRGXFxsIiNcRl1dbDYkRmNdbCIjRkZdXWw2JEZjXWxGXmBsRmZbbDYkRmNdbEZmYmxGZFtsNiRGXFxsIiM4RmlcbDYkRlxcbEZqX2xGaVxsNiRGY11sRl9jbEZdXWw2JEZjXWwiI0BGXV1sNiRGXFxsIiM+RmhbbDYkRlxcbEZeXmxGXV1sNiRGY11sIiNRRl1dbDYkRmNdbEZhY2xGXFxsNiRGXFxsIiNXRl1dbDYkRmNdbCIjO0ZdXWw2JEZcXGxGYWFsRmlbbDYkRlxcbEZcX2xGXV1sNiRGY11sIiNURmRbbDYkRmNdbCIjX0ZpXGw2JEZcXGxGaWRsRl1dbDYkRmNdbEZdZGxGXV1sNiRGXFxsRmBgbEZmW2w2JEZcXGwiIilGaltsNiRGXFxsRlxgbEZdXWw2JEZjXWxGaF1sRl1dbDYkRmNdbEZjZGxGZ1tsNiRGY11sRmpdbEZlW2w2JEZjXWxGZ2NsRl1dbDYkRlxcbEZgZGxGZVxsNiRGY11sRmVgbEZdXWw2JEZjXWwiI0FGXV1sNiRGXFxsRmVdbEZdXWw2JEZcXGxGaWBsRmlcbDYkRlxcbEZdYWxGXV1sNiRGY11sIiIlRl1dbDYkRmNdbCIjSkZdXWw2JEZjXWxGZl5sRmhbbDYkRlxcbCIjTkZbXGw2JEZjXWxGYl9sRl1dbDYkRmNdbEZkXmxGXV1sNiRGXFxsRmNdbEZkW2w2JEZcXGwiI0JGXFxsNiRGXFxsIiNjRl1dbDYkRmNdbEZbY2xGXV1sNiRGY11sRmhfbEZbXGw2JEZcXGxGaGJsRmhbbDYkRlxcbEZqYWxGXV1sNiRGXFxsRmNibEZlW2w2JEZcXGxGYV5sRl1cbDYkRmNdbCIjN0ZdXWw2JEZcXGxGZWRsRmVbbDYkRlxcbCIiKEZpW2w2JEZcXGwiI15GXV1sNiRGY11sRl1ibEZdXWw2JEZjXWxGX2JsRmhbbDYkRmNdbEZqZmxGZltsNiRGXFxsRmhhbEZdXGw2JEZjXWxGZWdsRl1dbDYkRmNdbEZoZmxGXV1sNiRGXFxsRltkbEZqW2w2JEZcXGxGXmZsRmZbbDYkRlxcbCIjaUZdXWw2JEZjXWxGX2FsRmNbbDYkRmNdbEZnZ2xGZVxsNiRGXFxsRlthbEZdXWw2JEZjXWxGZl9sRl1dbDYkRlxcbEZpZWxGW1xsNiRGY11sRmBfbEZpW2w2JEZcXGwiI2RGXV1sNiRGY11sRmNmbEZdXWw2JEZjXWxGYWhsRlxcbDYkRlxcbEZgZmxGZ1tsNiRGXFxsRmpebEZdXWw2JEZcXGxGYmdsRmVcbDYkRlxcbEZjY2xGY1tsNiRGXFxsRltlbEZdXWw2JEZjXWxGXl9sRl1dbDYkRmNdbEZpaGxGZ1tsNiRGXFxsRmhebEZcXGw2JEZjXWxGYGVsRl1dbDYkRmNdbEZkYWxGXV1sNiRGXFxsRlxcbEZjW2w=

Theta_1i, i=1,..,4, intrduced in Eqn#32 of Technical Report#CU-CRB-3-9-07-1, are found as follows: theta1_1:=matrix(65,1,[f*ku*xp11*rc11, f*ku*xp11*rc12, f*ku*xp11*rc13, f*ku*xp12*rc11, f*ku*xp12*rc12, f*ku*xp12*rc13, f*ku*xp13*rc11, f*ku*xp13*rc12, f*ku*xp13*rc13, f*ku*pc1, f*ku*rc11, f*ku*rc12, f*ku*rc13, f*ku*cotphi*xp11*rc21, f*ku*cotphi*xp11*rc22, f*ku*cotphi*xp11*rc23, f*ku*cotphi*xp12*rc21, f*ku*cotphi*xp12*rc22, f*ku*cotphi*xp12*rc23, f*ku*cotphi*xp13*rc21, f*ku*cotphi*xp13*rc22, f*ku*cotphi*xp13*rc23, f*ku*cotphi*pc2, f*ku*cotphi*rc21, f*ku*cotphi*rc22, f*ku*cotphi*rc23, u0*xp11*rc31, u0*xp11*rc32, u0*xp11*rc33, u0*xp12*rc31, u0*xp12*rc32, u0*xp12*rc33, u0*xp13*rc31, u0*xp13*rc32, u0*xp13*rc33, u0*pc3, u0*rc31, u0*rc32, u0*rc33, f*kv*cosecphi*xp11*rc21, f*kv*cosecphi*xp11*rc22, f*kv*cosecphi*xp11*rc23, f*kv*cosecphi*xp12*rc21, f*kv*cosecphi*xp12*rc22, f*kv*cosecphi*xp12*rc23, f*kv*cosecphi*xp13*rc21, f*kv*cosecphi*xp13*rc22, f*kv*cosecphi*xp13*rc23, f*kv*cosecphi*pc2, f*kv*cosecphi*rc21, f*kv*cosecphi*rc22, f*kv*cosecphi*rc23, v0*xp11*rc31, v0*xp11*rc32, v0*xp11*rc33, v0*xp12*rc31, v0*xp12*rc32, v0*xp12*rc33, v0*xp13*rc31, v0*xp13*rc32, v0*xp13*rc33, v0*pc3, v0*rc31, v0*rc32, v0*rc33]);

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theta1_2:=matrix(65,1,[f*ku*xp21*rc11, f*ku*xp21*rc12, f*ku*xp21*rc13, f*ku*xp22*rc11, f*ku*xp22*rc12, f*ku*xp22*rc13, f*ku*xp23*rc11, f*ku*xp23*rc12, f*ku*xp23*rc13, f*ku*pc1, f*ku*rc11, f*ku*rc12, f*ku*rc13, f*ku*cotphi*xp21*rc21, f*ku*cotphi*xp21*rc22, f*ku*cotphi*xp21*rc23, f*ku*cotphi*xp22*rc21, f*ku*cotphi*xp22*rc22, f*ku*cotphi*xp22*rc23, f*ku*cotphi*xp23*rc21, f*ku*cotphi*xp23*rc22, f*ku*cotphi*xp23*rc23, f*ku*cotphi*pc2, f*ku*cotphi*rc21, f*ku*cotphi*rc22, f*ku*cotphi*rc23, u0*xp21*rc31, u0*xp21*rc32, u0*xp21*rc33, u0*xp22*rc31, u0*xp22*rc32, u0*xp22*rc33, u0*xp23*rc31, u0*xp23*rc32, u0*xp23*rc33, u0*pc3, u0*rc31, u0*rc32, u0*rc33, f*kv*cosecphi*xp21*rc21, f*kv*cosecphi*xp21*rc22, f*kv*cosecphi*xp21*rc23, f*kv*cosecphi*xp22*rc21, f*kv*cosecphi*xp22*rc22, f*kv*cosecphi*xp22*rc23, f*kv*cosecphi*xp23*rc21, f*kv*cosecphi*xp23*rc22, f*kv*cosecphi*xp23*rc23, f*kv*cosecphi*pc2, f*kv*cosecphi*rc21, f*kv*cosecphi*rc22, f*kv*cosecphi*rc23, v0*xp21*rc31, v0*xp21*rc32, v0*xp21*rc33, v0*xp22*rc31, v0*xp22*rc32, v0*xp22*rc33, v0*xp23*rc31, v0*xp23*rc32, v0*xp23*rc33, v0*pc3, v0*rc31, v0*rc32, v0*rc33]);

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theta1_3:=matrix(65,1,[f*ku*xp31*rc11, f*ku*xp31*rc12, f*ku*xp31*rc13, f*ku*xp32*rc11, f*ku*xp32*rc12, f*ku*xp32*rc13, f*ku*xp33*rc11, f*ku*xp33*rc12, f*ku*xp33*rc13, f*ku*pc1, f*ku*rc11, f*ku*rc12, f*ku*rc13, f*ku*cotphi*xp31*rc21, f*ku*cotphi*xp31*rc22, f*ku*cotphi*xp31*rc23, f*ku*cotphi*xp32*rc21, f*ku*cotphi*xp32*rc22, f*ku*cotphi*xp32*rc23, f*ku*cotphi*xp33*rc21, f*ku*cotphi*xp33*rc22, f*ku*cotphi*xp33*rc23, f*ku*cotphi*pc2, f*ku*cotphi*rc21, f*ku*cotphi*rc22, f*ku*cotphi*rc23, u0*xp31*rc31, u0*xp31*rc32, u0*xp31*rc33, u0*xp32*rc31, u0*xp32*rc32, u0*xp32*rc33, u0*xp33*rc31, u0*xp33*rc32, u0*xp33*rc33, u0*pc3, u0*rc31, u0*rc32, u0*rc33, f*kv*cosecphi*xp31*rc21, f*kv*cosecphi*xp31*rc22, f*kv*cosecphi*xp31*rc23, f*kv*cosecphi*xp32*rc21, f*kv*cosecphi*xp32*rc22, f*kv*cosecphi*xp32*rc23, f*kv*cosecphi*xp33*rc21, f*kv*cosecphi*xp33*rc22, f*kv*cosecphi*xp33*rc23, f*kv*cosecphi*pc2, f*kv*cosecphi*rc21, f*kv*cosecphi*rc22, f*kv*cosecphi*rc23, v0*xp31*rc31, v0*xp31*rc32, v0*xp31*rc33, v0*xp32*rc31, v0*xp32*rc32, v0*xp32*rc33, v0*xp33*rc31, v0*xp33*rc32, v0*xp33*rc33, v0*pc3, v0*rc31, v0*rc32, v0*rc33]);

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theta1_4:=matrix(65,1,[f*ku*xp41*rc11, f*ku*xp41*rc12, f*ku*xp41*rc13, f*ku*xp42*rc11, f*ku*xp42*rc12, f*ku*xp42*rc13, f*ku*xp43*rc11, f*ku*xp43*rc12, f*ku*xp43*rc13, f*ku*pc1, f*ku*rc11, f*ku*rc12, f*ku*rc13, f*ku*cotphi*xp41*rc21, f*ku*cotphi*xp41*rc22, f*ku*cotphi*xp41*rc23, f*ku*cotphi*xp42*rc21, f*ku*cotphi*xp42*rc22, f*ku*cotphi*xp42*rc23, f*ku*cotphi*xp43*rc21, f*ku*cotphi*xp43*rc22, f*ku*cotphi*xp43*rc23, f*ku*cotphi*pc2, f*ku*cotphi*rc21, f*ku*cotphi*rc22, f*ku*cotphi*rc23, u0*xp41*rc31, u0*xp41*rc32, u0*xp41*rc33, u0*xp42*rc31, u0*xp42*rc32, u0*xp42*rc33, u0*xp43*rc31, u0*xp43*rc32, u0*xp43*rc33, u0*pc3, u0*rc31, u0*rc32, u0*rc33, f*kv*cosecphi*xp41*rc21, f*kv*cosecphi*xp41*rc22, f*kv*cosecphi*xp41*rc23, f*kv*cosecphi*xp42*rc21, f*kv*cosecphi*xp42*rc22, f*kv*cosecphi*xp42*rc23, f*kv*cosecphi*xp43*rc21, f*kv*cosecphi*xp43*rc22, f*kv*cosecphi*xp43*rc23, f*kv*cosecphi*pc2, f*kv*cosecphi*rc21, f*kv*cosecphi*rc22, f*kv*cosecphi*rc23, v0*xp41*rc31, v0*xp41*rc32, v0*xp41*rc33, v0*xp42*rc31, v0*xp42*rc32, v0*xp42*rc33, v0*xp43*rc31, v0*xp43*rc32, v0*xp43*rc33, v0*pc3, v0*rc31, v0*rc32, v0*rc33]);

6$-I%mrowG6#/I+modulenameG6"I,TypesettingGI(_syslibGF(6%-I#miGF%69Q+&theta;1_4F(/%'familyGQ0Times~New~RomanF(/%%sizeGQ#12F(/%%boldGQ&falseF(/%'italicGQ%trueF(/%*underlineGF8/%*subscriptGF8/%,superscriptGF8/%+foregroundGQ*[0,0,255]F(/%+backgroundGQ([0,0,0]F(/%'opaqueGF8/%+executableGF8/%)readonlyGF;/%)composedGF8/%*convertedGF8/%+imselectedGF8/%,placeholderGF8/%0font_style_nameGQ*2D~OutputF(/%*mathcolorGFD/%/mathbackgroundGFG/%+fontfamilyGF2/%,mathvariantGQ'italicF(/%)mathsizeGF5-I#moGF%63Q#:=F(/%%formGQ&infixF(/%&fenceGF8/%*separatorGF8/%'lspaceGQ/thickmathspaceF(/%'rspaceGF[p/%)stretchyGF8/%*symmetricGF8/%(maxsizeGQ)infinityF(/%(minsizeGQ"1F(/%(largeopGF8/%.movablelimitsGF8/%'accentGF8/%0font_style_nameGFX/%%sizeGF5/%+foregroundGFD/%+backgroundGFG-F$6%-F_o63Q"[F(/FcoQ'prefixF(/FfoF;Fgo/FjoQ.thinmathspaceF(/F]pF_r/F_pF;F`pFbpFepFhpFjpF\qF^qF`qFbqFdq-F$6#-I'mtableGF%6]o-I$mtrGF%6#-I$mtdGF%6#-F$6)-F-69Q"fF(F0F3F6F9F<F>F@FBFEFHFJFLFNFPFRFTFVFYFenFgnFinF\o-F_o63Q1&InvisibleTimes;F(FboFeoFgo/FjoQ$0emF(/F]pFfsF^pF`pFbpFepFhpFjpF\qF^qF`qFbqFdq-F-69Q#kuF(F0F3F6F9F<F>F@FBFEFHFJFLFNFPFRFTFVFYFenFgnFinF\oFbs-F-69Q%xp41F(F0F3F6F9F<F>F@FBFEFHFJFLFNFPFRFTFVFYFenFgnFinF\oFbs-F-69Q%rc11F(F0F3F6F9F<F>F@FBFEFHFJFLFNFPFRFTFVFYFenFgnFinF\o-Fhr6#-F[s6#-F$6)F_sFbsFhsFbsF[tFbs-F-69Q%rc12F(F0F3F6F9F<F>F@FBFEFHFJFLFNFPFRFTFVFYFenFgnFinF\o-Fhr6#-F[s6#-F$6)F_sFbsFhsFbsF[tFbs-F-69Q%rc13F(F0F3F6F9F<F>F@FBFEFHFJFLFNFPFRFTFVFYFenFgnFinF\o-Fhr6#-F[s6#-F$6)F_sFbsFhsFbs-F-69Q%xp42F(F0F3F6F9F<F>F@FBFEFHFJFLFNFPFRFTFVFYFenFgnFinF\oFbsF^t-Fhr6#-F[s6#-F$6)F_sFbsFhsFbsFiuFbsFgt-Fhr6#-F[s6#-F$6)F_sFbsFhsFbsFiuFbsF`u-Fhr6#-F[s6#-F$6)F_sFbsFhsFbs-F-69Q%xp43F(F0F3F6F9F<F>F@FBFEFHFJFLFNFPFRFTFVFYFenFgnFinF\oFbsF^t-Fhr6#-F[s6#-F$6)F_sFbsFhsFbsF^wFbsFgt-Fhr6#-F[s6#-F$6)F_sFbsFhsFbsF^wFbsF`u-Fhr6#-F[s6#-F$6'F_sFbsFhsFbs-F-69Q$pc1F(F0F3F6F9F<F>F@FBFEFHFJFLFNFPFRFTFVFYFenFgnFinF\o-Fhr6#-F[s6#-F$6'F_sFbsFhsFbsF^t-Fhr6#-F[s6#-F$6'F_sFbsFhsFbsFgt-Fhr6#-F[s6#-F$6'F_sFbsFhsFbsF`u-Fhr6#-F[s6#-F$6+F_sFbsFhsFbs-F-69Q'cotphiF(F0F3F6F9F<F>F@FBFEFHFJFLFNFPFRFTFVFYFenFgnFinF\oFbsF[tFbs-F-69Q%rc21F(F0F3F6F9F<F>F@FBFEFHFJFLFNFPFRFTFVFYFenFgnFinF\o-Fhr6#-F[s6#-F$6+F_sFbsFhsFbsF^zFbsF[tFbs-F-69Q%rc22F(F0F3F6F9F<F>F@FBFEFHFJFLFNFPFRFTFVFYFenFgnFinF\o-Fhr6#-F[s6#-F$6+F_sFbsFhsFbsF^zFbsF[tFbs-F-69Q%rc23F(F0F3F6F9F<F>F@FBFEFHFJFLFNFPFRFTFVFYFenFgnFinF\o-Fhr6#-F[s6#-F$6+F_sFbsFhsFbsF^zFbsFiuFbsFaz-Fhr6#-F[s6#-F$6+F_sFbsFhsFbsF^zFbsFiuFbsFjz-Fhr6#-F[s6#-F$6+F_sFbsFhsFbsF^zFbsFiuFbsFc[l-Fhr6#-F[s6#-F$6+F_sFbsFhsFbsF^zFbsF^wFbsFaz-Fhr6#-F[s6#-F$6+F_sFbsFhsFbsF^zFbsF^wFbsFjz-Fhr6#-F[s6#-F$6+F_sFbsFhsFbsF^zFbsF^wFbsFc[l-Fhr6#-F[s6#-F$6)F_sFbsFhsFbsF^zFbs-F-69Q$pc2F(F0F3F6F9F<F>F@FBFEFHFJFLFNFPFRFTFVFYFenFgnFinF\o-Fhr6#-F[s6#-F$6)F_sFbsFhsFbsF^zFbsFaz-Fhr6#-F[s6#-F$6)F_sFbsFhsFbsF^zFbsFjz-Fhr6#-F[s6#-F$6)F_sFbsFhsFbsF^zFbsFc[l-Fhr6#-F[s6#-F$6'-F-69Q#u0F(F0F3F6F9F<F>F@FBFEFHFJFLFNFPFRFTFVFYFenFgnFinF\oFbsF[tFbs-F-69Q%rc31F(F0F3F6F9F<F>F@FBFEFHFJFLFNFPFRFTFVFYFenFgnFinF\o-Fhr6#-F[s6#-F$6'F[`lFbsF[tFbs-F-69Q%rc32F(F0F3F6F9F<F>F@FBFEFHFJFLFNFPFRFTFVFYFenFgnFinF\o-Fhr6#-F[s6#-F$6'F[`lFbsF[tFbs-F-69Q%rc33F(F0F3F6F9F<F>F@FBFEFHFJFLFNFPFRFTFVFYFenFgnFinF\o-Fhr6#-F[s6#-F$6'F[`lFbsFiuFbsF^`l-Fhr6#-F[s6#-F$6'F[`lFbsFiuFbsFg`l-Fhr6#-F[s6#-F$6'F[`lFbsFiuFbsF`al-Fhr6#-F[s6#-F$6'F[`lFbsF^wFbsF^`l-Fhr6#-F[s6#-F$6'F[`lFbsF^wFbsFg`l-Fhr6#-F[s6#-F$6'F[`lFbsF^wFbsF`al-Fhr6#-F[s6#-F$6%F[`lFbs-F-69Q$pc3F(F0F3F6F9F<F>F@FBFEFHFJFLFNFPFRFTFVFYFenFgnFinF\o-Fhr6#-F[s6#-F$6%F[`lFbsF^`l-Fhr6#-F[s6#-F$6%F[`lFbsFg`l-Fhr6#-F[s6#-F$6%F[`lFbsF`al-Fhr6#-F[s6#-F$6+F_sFbs-F-69Q#kvF(F0F3F6F9F<F>F@FBFEFHFJFLFNFPFRFTFVFYFenFgnFinF\oFbs-F-69Q)cosecphiF(F0F3F6F9F<F>F@FBFEFHFJFLFNFPFRFTFVFYFenFgnFinF\oFbsF[tFbsFaz-Fhr6#-F[s6#-F$6+F_sFbsFhelFbsF[flFbsF[tFbsFjz-Fhr6#-F[s6#-F$6+F_sFbsFhelFbsF[flFbsF[tFbsFc[l-Fhr6#-F[s6#-F$6+F_sFbsFhelFbsF[flFbsFiuFbsFaz-Fhr6#-F[s6#-F$6+F_sFbsFhelFbsF[flFbsFiuFbsFjz-Fhr6#-F[s6#-F$6+F_sFbsFhelFbsF[flFbsFiuFbsFc[l-Fhr6#-F[s6#-F$6+F_sFbsFhelFbsF[flFbsF^wFbsFaz-Fhr6#-F[s6#-F$6+F_sFbsFhelFbsF[flFbsF^wFbsFjz-Fhr6#-F[s6#-F$6+F_sFbsFhelFbsF[flFbsF^wFbsFc[l-Fhr6#-F[s6#-F$6)F_sFbsFhelFbsF[flFbsF`^l-Fhr6#-F[s6#-F$6)F_sFbsFhelFbsF[flFbsFaz-Fhr6#-F[s6#-F$6)F_sFbsFhelFbsF[flFbsFjz-Fhr6#-F[s6#-F$6)F_sFbsFhelFbsF[flFbsFc[l-Fhr6#-F[s6#-F$6'-F-69Q#v0F(F0F3F6F9F<F>F@FBFEFHFJFLFNFPFRFTFVFYFenFgnFinF\oFbsF[tFbsF^`l-Fhr6#-F[s6#-F$6'F\[mFbsF[tFbsFg`l-Fhr6#-F[s6#-F$6'F\[mFbsF[tFbsF`al-Fhr6#-F[s6#-F$6'F\[mFbsFiuFbsF^`l-Fhr6#-F[s6#-F$6'F\[mFbsFiuFbsFg`l-Fhr6#-F[s6#-F$6'F\[mFbsFiuFbsF`al-Fhr6#-F[s6#-F$6'F\[mFbsF^wFbsF^`l-Fhr6#-F[s6#-F$6'F\[mFbsF^wFbsFg`l-Fhr6#-F[s6#-F$6'F\[mFbsF^wFbsF`al-Fhr6#-F[s6#-F$6%F\[mFbsF]dl-Fhr6#-F[s6#-F$6%F\[mFbsF^`l-Fhr6#-F[s6#-F$6%F\[mFbsFg`l-Fhr6#-F[s6#-F$6%F\[mFbsF`al-F_o63Q"]F(/FcoQ(postfixF(F]rFgoF^r/F]pQ2verythinmathspaceF(FarF`pFbpFepFhpFjpF\qF^qF`qFbqFdq7#-_F)I,mprintslashGF(6$7#>I)theta1_4GF(-I'matrixG6$%*protectedGF*6#7]o7#**I"fGF("""I#kuGF(F_amI%xp41GF(F_amI%rc11GF(F_am7#**F^amF_amF`amF_amFaamF_amI%rc12GF(F_am7#**F^amF_amF`amF_amFaamF_amI%rc13GF(F_am7#**F^amF_amF`amF_amI%xp42GF(F_amF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Checking the definitions of W1 and Theta_1i... check5:=simplify(P1_num[1,1]-evalm(W1&*theta1_1)[1,1]);

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

check6:=simplify(P1_num[2,1]-evalm(W1&*theta1_1)[2,1]);

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

check7:=simplify(P2_num[1,1]-evalm(W1&*theta1_2)[1,1]);

NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiUtSSNtaUdGJTY5USdjaGVjazdGKC8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYoLyUlc2l6ZUdRIzEyRigvJSVib2xkR1EmZmFsc2VGKC8lJ2l0YWxpY0dRJXRydWVGKC8lKnVuZGVybGluZUdGOC8lKnN1YnNjcmlwdEdGOC8lLHN1cGVyc2NyaXB0R0Y4LyUrZm9yZWdyb3VuZEdRKlswLDAsMjU1XUYoLyUrYmFja2dyb3VuZEdRKFswLDAsMF1GKC8lJ29wYXF1ZUdGOC8lK2V4ZWN1dGFibGVHRjgvJSlyZWFkb25seUdGOy8lKWNvbXBvc2VkR0Y4LyUqY29udmVydGVkR0Y4LyUraW1zZWxlY3RlZEdGOC8lLHBsYWNlaG9sZGVyR0Y4LyUwZm9udF9zdHlsZV9uYW1lR1EqMkR+T3V0cHV0RigvJSptYXRoY29sb3JHRkQvJS9tYXRoYmFja2dyb3VuZEdGRy8lK2ZvbnRmYW1pbHlHRjIvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YoLyUpbWF0aHNpemVHRjUtSSNtb0dGJTYzUSM6PUYoLyUlZm9ybUdRJmluZml4RigvJSZmZW5jZUdGOC8lKnNlcGFyYXRvckdGOC8lJ2xzcGFjZUdRL3RoaWNrbWF0aHNwYWNlRigvJSdyc3BhY2VHRltwLyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShtYXhzaXplR1EpaW5maW5pdHlGKC8lKG1pbnNpemVHUSIxRigvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lMGZvbnRfc3R5bGVfbmFtZUdGWC8lJXNpemVHRjUvJStmb3JlZ3JvdW5kR0ZELyUrYmFja2dyb3VuZEdGRy1JI21uR0YlNjlRIjBGKEYwRjNGNi9GOkY4RjxGPkZARkJGRUZIRkpGTEZORlBGUkZURlZGWUZlbkZnbi9Gam5RJ25vcm1hbEYoRlxvNyMtX0YpSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdjaGVjazdHRigiIiE3I0Zlcg==

check8:=simplify(P2_num[2,1]-evalm(W1&*theta1_2)[2,1]);

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

check9:=simplify(P3_num[1,1]-evalm(W1&*theta1_3)[1,1]);

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

check10:=simplify(P3_num[2,1]-evalm(W1&*theta1_3)[2,1]);

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

check11:=simplify(P4_num[1,1]-evalm(W1&*theta1_4)[1,1]);

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

check12:=simplify(P4_num[2,1]-evalm(W1&*theta1_4)[2,1]);

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