read "MapleWeb/WDecomposition.mpl"; NzNJJ0NoYW5nZUc2IkktQ2hhbmdlQ29sdW1uR0YkSSpDaGFuZ2VSb3dHRiRJLkNvbXBhcmVNYXRyaXhHRiRJLkNvbXBhcmVDb2x1bW5HRiRJK0NvbXBhcmVSb3dHRiRJLlBlcm11dGVNYXRyaXhHRiRJM0pvaW5EaWFnb25hbE1hdHJpeEdGJEksRGVsZXRlQ29lZmZHRiRJKE1hdHJpeE5HRiRJKkFkZENvbHVtbkdGJEktRXhwYW5kTWF0cml4R0YkSTBNYXRyaXhOdWxsU3BhY2VHRiRJM1dEZWNvbXBvc2l0aW9uU3RlcEdGJEk1V0RlY29tcG9zaXRpb25NYXRyaXhHRiRJLlJlZ3VsYXJQZW5jaWxHRiRJNEludGVyc2VjdGlvblN1cmZhY2VHRiQ= A := Matrix(6, 7, {(1, 1) = 0, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (1, 6) = s, (1, 7) = s^2+1, (2, 1) = 0, (2, 2) = 0, (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (2, 6) = -s^2-1, (2, 7) = -s, (3, 1) = 0, (3, 2) = 0, (3, 3) = 0, (3, 4) = s, (3, 5) = s^2+1, (3, 6) = 0, (3, 7) = 0, (4, 1) = 1, (4, 2) = 0, (4, 3) = 0, (4, 4) = -1, (4, 5) = 0, (4, 6) = 0, (4, 7) = s, (5, 1) = 0, (5, 2) = 1, (5, 3) = 0, (5, 4) = 0, (5, 5) = -1, (5, 6) = s, (5, 7) = 0, (6, 1) = 0, (6, 2) = 0, (6, 3) = 1, (6, 4) = 0, (6, 5) = s, (6, 6) = 1, (6, 7) = 0}); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKnM/M3Ii B := Matrix(6, 7, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (1, 6) = 0, (1, 7) = 0, (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (2, 6) = 0, (2, 7) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1, (3, 4) = 0, (3, 5) = 0, (3, 6) = 0, (3, 7) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 0, (4, 5) = 0, (4, 6) = 0, (4, 7) = -1, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = 0, (5, 5) = 0, (5, 6) = 1, (5, 7) = 0, (6, 1) = 0, (6, 2) = 0, (6, 3) = 0, (6, 4) = 0, (6, 5) = -1, (6, 6) = 0, (6, 7) = 0}); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKitBM3Ii M, N := RegularPencil(A, B, s); NiQtSSdNYXRyaXhHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2Iy9JJCVpZEdGKCIqKyNRUz0tRiQ2Iy9GKyIqayNRUz0= A2 := Matrix(4, 7, {(1, 1) = t^4, (1, 2) = 0, (1, 3) = 0, (1, 4) = t^2+2*t+1, (1, 5) = 2*t^4, (1, 6) = 0, (1, 7) = t, (2, 1) = t^2+1, (2, 2) = -t, (2, 3) = 0, (2, 4) = 0, (2, 5) = 2*t^2+2, (2, 6) = -t, (2, 7) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1, (3, 4) = t-2, (3, 5) = 0, (3, 6) = 0, (3, 7) = t^2+1, (4, 1) = 0, (4, 2) = 2, (4, 3) = 0, (4, 4) = 0, (4, 5) = 0, (4, 6) = 2, (4, 7) = 0}); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKjcoUVM9 B2 := Matrix(4, 7, {(1, 1) = t^3, (1, 2) = 0, (1, 3) = 0, (1, 4) = t^2+2*t+1, (1, 5) = 2*t^3, (1, 6) = 0, (1, 7) = t, (2, 1) = t^2+1, (2, 2) = -t, (2, 3) = 0, (2, 4) = 0, (2, 5) = 2*t^2+2, (2, 6) = -t, (2, 7) = 0, (3, 1) = t, (3, 2) = 0, (3, 3) = 1, (3, 4) = t-2, (3, 5) = 0, (3, 6) = 0, (3, 7) = t^2+1, (4, 1) = 0, (4, 2) = 2, (4, 3) = 0, (4, 4) = 0, (4, 5) = 0, (4, 6) = 2, (4, 7) = 0}); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKncoUVM9 A3, B3 := RegularPencil(A2, B2, t); NiQtSSdNYXRyaXhHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2Iy9JJCVpZEdGKCIqO3loIz4tRiQ2Iy9GKyIqISl5aCM+ M := Matrix(6, 7, {(1, 1) = s^3, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (1, 6) = s, (1, 7) = s^2+1, (2, 1) = 0, (2, 2) = 0, (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (2, 6) = -s^2-1, (2, 7) = -s, (3, 1) = 0, (3, 2) = 0, (3, 3) = 0, (3, 4) = s, (3, 5) = s^2+1, (3, 6) = 0, (3, 7) = 0, (4, 1) = 1, (4, 2) = 0, (4, 3) = 0, (4, 4) = -1, (4, 5) = 0, (4, 6) = 0, (4, 7) = s, (5, 1) = 0, (5, 2) = 1, (5, 3) = 0, (5, 4) = 0, (5, 5) = -1, (5, 6) = s, (5, 7) = 0, (6, 1) = 0, (6, 2) = 0, (6, 3) = 1, (6, 4) = 0, (6, 5) = s, (6, 6) = 1, (6, 7) = 0}); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKkckPUU+ WDecompositionMatrix(M, s); NiQtSSdNYXRyaXhHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2Iy9JJCVpZEdGKCIqOyZ6XD0tRiQ2Iy9GKyIqJSkqUmM9 ExpandMatrix(Multiply(M,WDecompositionMatrix(M, s)[2])); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKltXem8i Determinant(WDecompositionMatrix(M,s)[2]); IiIi N := Matrix(4, 3, {(1, 1) = 2*t^2+3*t+1, (1, 2) = t+1, (1, 3) = 2*t^2+2*t, (2, 1) = 1, (2, 2) = 5*t^2, (2, 3) = -5*t^2+1, (3, 1) = 2*t+1, (3, 2) = 3, (3, 3) = 2*t-2, (4, 1) = t, (4, 2) = t, (4, 3) = 0}); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKmdseSI9 WDecompositionMatrix(N, t); NiQtSSdNYXRyaXhHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2Iy9JJCVpZEdGKCIqb2Z6Ij0tRiQ2Iy9GKyIqd2V1Iz0= Determinant(WDecompositionMatrix(N,s)[2]); ISIi TTdSMApJNlJUQUJMRV9TQVZFLzE3MTA4MjA3MlgsJSlhbnl0aGluZ0c2IkYlW2dsISIlISEhI0siJyIoIiIhRiZGJiIiIkYmRiZGJkYmRiZGJkYnRiZGJkYmRiZGJkYmRidGJkYmJSJzRyEiIkYmRiZGJkYmLCYqJEYoIiIjRidGJ0YnRiZGKUYoRigsJkYrRilGKUYnRiZGJkYoRidGKiwkRihGKUYmRihGJkYmRiU=TTdSMApJNlJUQUJMRV9TQVZFLzE3MTA4MjIwMFgsJSlhbnl0aGluZ0c2IkYlW2dsISIlISEhI0siJyIoIiIiIiIhRidGJ0YnRidGJ0YmRidGJ0YnRidGJ0YnRiZGJ0YnRidGJ0YnRidGJ0YnRidGJ0YnRidGJ0YnISIiRidGJ0YnRidGJkYnRidGJ0YnRihGJ0YnRiU=TTdSMApJNlJUQUJMRV9TQVZFLzE4NDAzODIwMFgsJSlhbnl0aGluZ0c2IkYlW2dsISIlISEhIzEiJSIlLCQlInNHISIiIiIiIiIhLCYqJEYnIiIjRilGKUYpRiYsJEYsRihGJ0YpRipGKkYpRipGKUYqRihGKkYlTTdSMApJNlJUQUJMRV9TQVZFLzE4NDAzODI2NFgsJSlhbnl0aGluZ0c2IkYlW2dsISIlISEhIzEiJSIlIiIiIiIhRidGJ0YnRidGJkYnRidGJkYnRidGJyEiIkYnRihGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzE4NDAzODcxMlgsJSlhbnl0aGluZ0c2IkYlW2dsISIlISEhIz0iJSIoKiQlInRHIiIlLCYqJEYnIiIjIiIiRixGLCIiIUYtRi0sJEYnISIiRi1GK0YtRi1GLEYtLChGKkYsRidGK0YsRixGLSwmRidGLCEiI0YsRi0sJEYmRissJkYqRitGK0YsRi1GLUYtRi5GLUYrRidGLUYpRi1GJQ==TTdSMApJNlJUQUJMRV9TQVZFLzE4NDAzODc3NlgsJSlhbnl0aGluZ0c2IkYlW2dsISIlISEhIz0iJSIoKiQlInRHIiIkLCYqJEYnIiIjIiIiRixGLEYnIiIhRi0sJEYnISIiRi1GK0YtRi1GLEYtLChGKkYsRidGK0YsRixGLSwmRidGLCEiI0YsRi0sJEYmRissJkYqRitGK0YsRi1GLUYtRi5GLUYrRidGLUYpRi1GJQ==TTdSMApJNlJUQUJMRV9TQVZFLzE5MjYxNzgxNlgsJSlhbnl0aGluZ0c2IkYlW2dsISIlISEhIyoiJCIkIiIhIiIiRiYiIiMsJCUidEchIiMsJEYqIiIlLCRGKiEiIkYmRihGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzE5MjYxNzg4MFgsJSlhbnl0aGluZ0c2IkYlW2dsISIlISEhIyoiJCIkIiIhIiIiRiYiIiMsKCokJSJ0RyIiJSEiI0YrRi0qJEYrIiIkRigsJEYrRiwsJEYrISIiRiZGKEYlTTdSMApJNlJUQUJMRV9TQVZFLzE5MjYxODMyOFgsJSlhbnl0aGluZ0c2IkYlW2dsISIlISEhI0siJyIoKiQlInNHIiIkIiIhRikiIiJGKUYpRilGKUYpRilGKkYpRilGKUYpRilGKUYqRilGKUYnISIiRilGKUYpRiksJiokRiciIiNGKkYqRipGKUYrRidGJywmRi1GK0YrRipGKUYpRidGKkYsLCRGJ0YrRilGJ0YpRilGJQ==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TTdSMApJNlJUQUJMRV9TQVZFLzE2ODc5NDQ0OFgsJSlhbnl0aGluZ0c2IkYlW2dsISIlISEhI0siJyIoIiIhRiZGJkYmIiIiRiZGJkYmRidGJiEiIkYmRiZGKEYmRidGJkYnRidGJkYnRiZGKEYmRiZGKEYmIiIjRiZGJ0YmRiZGJkYmRiZGJ0YmRiZGJkYmRiZGJkYlTTdSMApJNlJUQUJMRV9TQVZFLzE4MTc4NjU2MFgsJSlhbnl0aGluZ0c2IkYlW2dsISIlISEhIy0iJSIkLCgqJCUidEciIiNGKUYoIiIkIiIiRitGKywmRihGKUYrRitGKCwmRihGK0YrRissJEYnIiImRipGKCwmRidGKUYoRiksJkYnISImRitGKywmRihGKSEiI0YrIiIhRiU=TTdSMApJNlJUQUJMRV9TQVZFLzE4MTc5NTk2OFgsJSlhbnl0aGluZ0c2IkYlW2dsISIlISEhIy0iJSIkLCYqJCUidEciIiNGKUYoRiksJkYnISImIiIiRiwsJkYoRikhIiNGLCIiISwmRihGLEYsRiwsJEYnIiImIiIkRihGL0YvRi9GL0YlTTdSMApJNlJUQUJMRV9TQVZFLzE4Mjc0NTg3NlgsJSlhbnl0aGluZ0c2IkYlW2dsISIlISEhIyoiJCIkIiIhRiYiIiJGJkYnRiZGJyEiIkYoRiU=