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Copy pathMagneticBasis.txt
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10 lines (10 loc) · 7.08 KB
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{y, z, x}
{x*y, y*z, (-x^2 - y^2 + 2*z^2)/4, x*z, ((x - y)*(x + y))/2}
{x^2*y - y^3/3, 2*x*y*z, -(y*(x^2 + y^2 - 4*z^2))/4, -((x^2 + y^2)*z)/2 + z^3/3, -(x*(x^2 + y^2 - 4*z^2))/4, (x - y)*(x + y)*z, (x*(x^2 - 3*y^2))/3}
{x*(x - y)*y*(x + y), -(y*(-3*x^2 + y^2)*z), -(x*y*(x^2 + y^2 - 6*z^2))/2, (-3*y*(x^2 + y^2)*z)/4 + y*z^3, (3*(x^2 + y^2)^2 - 24*(x^2 + y^2)*z^2 + 8*z^4)/32, (-3*x*(x^2 + y^2)*z)/4 + x*z^3, -((x - y)*(x + y)*(x^2 + y^2 - 6*z^2))/4, x*(x^2 - 3*y^2)*z, (x^4 - 6*x^2*y^2 + y^4)/4}
{x^4*y - 2*x^2*y^3 + y^5/5, 4*x*(x - y)*y*(x + y)*z, (y*(-3*x^2 + y^2)*(x^2 + y^2 - 8*z^2))/4, -2*x*y*z*(x^2 + y^2 - 2*z^2), (y*((x^2 + y^2)^2 - 12*(x^2 + y^2)*z^2 + 8*z^4))/8, (3*(x^2 + y^2)^2*z)/8 - (x^2 + y^2)*z^3 + z^5/5, (x*((x^2 + y^2)^2 - 12*(x^2 + y^2)*z^2 + 8*z^4))/8, -((x - y)*(x + y)*z*(x^2 + y^2 - 2*z^2)), -(x*(x^2 - 3*y^2)*(x^2 + y^2 - 8*z^2))/4, (x^4 - 6*x^2*y^2 + y^4)*z, x^5/5 - 2*x^3*y^2 + x*y^4}
{x^5*y - (10*x^3*y^3)/3 + x*y^5, y*(5*x^4 - 10*x^2*y^2 + y^4)*z, -(x*(x - y)*y*(x + y)*(x^2 + y^2 - 10*z^2)), (5*y*(-3*x^2 + y^2)*z*(3*(x^2 + y^2) - 8*z^2))/12, (5*x*y*((x^2 + y^2)^2 - 16*(x^2 + y^2)*z^2 + 16*z^4))/16, (y*z*(5*(x^2 + y^2)^2 - 20*(x^2 + y^2)*z^2 + 8*z^4))/8, (-5*(x^2 + y^2)^3 + 90*(x^2 + y^2)^2*z^2 - 120*(x^2 + y^2)*z^4 + 16*z^6)/96, (x*z*(5*(x^2 + y^2)^2 - 20*(x^2 + y^2)*z^2 + 8*z^4))/8, (5*(x - y)*(x + y)*((x^2 + y^2)^2 - 16*(x^2 + y^2)*z^2 + 16*z^4))/32, (-5*x*(x^2 - 3*y^2)*z*(3*(x^2 + y^2) - 8*z^2))/12, -((x^4 - 6*x^2*y^2 + y^4)*(x^2 + y^2 - 10*z^2))/4, x*(x^4 - 10*x^2*y^2 + 5*y^4)*z, (x^6 - 15*x^4*y^2 + 15*x^2*y^4 - y^6)/6}
{x^6*y - 5*x^4*y^3 + 3*x^2*y^5 - y^7/7, 2*y*(3*x^5 - 10*x^3*y^2 + 3*x*y^4)*z, -(y*(5*x^4 - 10*x^2*y^2 + y^4)*(x^2 + y^2 - 12*z^2))/4, -2*x*(x - y)*y*(x + y)*z*(3*(x^2 + y^2) - 10*z^2), -(y*(-3*x^2 + y^2)*(3*(x^2 + y^2)^2 - 60*(x^2 + y^2)*z^2 + 80*z^4))/16, (x*y*z*(15*(x^2 + y^2)^2 - 80*(x^2 + y^2)*z^2 + 48*z^4))/8, (y*(-5*(x^2 + y^2)^3 + 120*(x^2 + y^2)^2*z^2 - 240*(x^2 + y^2)*z^4 + 64*z^6))/64, (-5*(x^2 + y^2)^3*z)/16 + (15*(x^2 + y^2)^2*z^3)/8 - (3*(x^2 + y^2)*z^5)/2 + z^7/7, (x*(-5*(x^2 + y^2)^3 + 120*(x^2 + y^2)^2*z^2 - 240*(x^2 + y^2)*z^4 + 64*z^6))/64, (15*(x - y)*(x + y)*(x^2 + y^2)^2*z)/16 + 5*(-x^4 + y^4)*z^3 + 3*(x - y)*(x + y)*z^5, (x*(x^2 - 3*y^2)*(3*(x^2 + y^2)^2 - 60*(x^2 + y^2)*z^2 + 80*z^4))/16, -((x^4 - 6*x^2*y^2 + y^4)*z*(3*(x^2 + y^2) - 10*z^2))/2, -(x*(x^4 - 10*x^2*y^2 + 5*y^4)*(x^2 + y^2 - 12*z^2))/4, (x^6 - 15*x^4*y^2 + 15*x^2*y^4 - y^6)*z, x^7/7 - 3*x^5*y^2 + 5*x^3*y^4 - x*y^6}
{x*y*(x^6 - 7*x^4*y^2 + 7*x^2*y^4 - y^6), -(y*(-7*x^6 + 35*x^4*y^2 - 21*x^2*y^4 + y^6)*z), -(x*y*(3*x^4 - 10*x^2*y^2 + 3*y^4)*(x^2 + y^2 - 14*z^2))/2, (-7*y*(5*x^4 - 10*x^2*y^2 + y^4)*z*(x^2 + y^2 - 4*z^2))/4, (7*x*(x - y)*y*(x + y)*((x^2 + y^2)^2 - 24*(x^2 + y^2)*z^2 + 40*z^4))/8, (-7*y*(-3*x^2 + y^2)*z*(3*(x^2 + y^2)^2 - 20*(x^2 + y^2)*z^2 + 16*z^4))/16, (7*x*y*(-(x^2 + y^2)^3 + 30*(x^2 + y^2)^2*z^2 - 80*(x^2 + y^2)*z^4 + 32*z^6))/32, (y*z*(-35*(x^2 + y^2)^3 + 280*(x^2 + y^2)^2*z^2 - 336*(x^2 + y^2)*z^4 + 64*z^6))/64, (35*(x^2 + y^2)^4 - 1120*(x^2 + y^2)^3*z^2 + 3360*(x^2 + y^2)^2*z^4 - 1792*(x^2 + y^2)*z^6 + 128*z^8)/1024, (x*z*(-35*(x^2 + y^2)^3 + 280*(x^2 + y^2)^2*z^2 - 336*(x^2 + y^2)*z^4 + 64*z^6))/64, (7*(-((x - y)*(x + y)*(x^2 + y^2)^3) + 30*(x - y)*(x + y)*(x^2 + y^2)^2*z^2 + 80*(-x^4 + y^4)*z^4 + 32*(x - y)*(x + y)*z^6))/64, (7*x*(x^2 - 3*y^2)*z*(3*(x^2 + y^2)^2 - 20*(x^2 + y^2)*z^2 + 16*z^4))/16, (7*(x^4 - 6*x^2*y^2 + y^4)*((x^2 + y^2)^2 - 24*(x^2 + y^2)*z^2 + 40*z^4))/32, (-7*x*(x^4 - 10*x^2*y^2 + 5*y^4)*z*(x^2 + y^2 - 4*z^2))/4, -((x^6 - 15*x^4*y^2 + 15*x^2*y^4 - y^6)*(x^2 + y^2 - 14*z^2))/4, x*(x^6 - 21*x^4*y^2 + 35*x^2*y^4 - 7*y^6)*z, (x^8 - 28*x^6*y^2 + 70*x^4*y^4 - 28*x^2*y^6 + y^8)/8}
{x^8*y - (28*x^6*y^3)/3 + 14*x^4*y^5 - 4*x^2*y^7 + y^9/9, 8*x*y*(x^6 - 7*x^4*y^2 + 7*x^2*y^4 - y^6)*z, (y*(-7*x^6 + 35*x^4*y^2 - 21*x^2*y^4 + y^6)*(x^2 + y^2 - 16*z^2))/4, (-4*x*y*(3*x^4 - 10*x^2*y^2 + 3*y^4)*z*(3*(x^2 + y^2) - 14*z^2))/3, (y*(5*x^4 - 10*x^2*y^2 + y^4)*((x^2 + y^2)^2 - 28*(x^2 + y^2)*z^2 + 56*z^4))/4, 7*x*(x - y)*y*(x + y)*z*((x^2 + y^2)^2 - 8*(x^2 + y^2)*z^2 + 8*z^4), (7*y*(-3*x^2 + y^2)*((x^2 + y^2)^3 - 36*(x^2 + y^2)^2*z^2 + 120*(x^2 + y^2)*z^4 - 64*z^6))/48, (x*y*z*(-7*(x^2 + y^2)^3 + 70*(x^2 + y^2)^2*z^2 - 112*(x^2 + y^2)*z^4 + 32*z^6))/4, (7*y*(x^2 + y^2)^4)/128 - (35*y*(x^2 + y^2)^3*z^2)/16 + (35*y*(x^2 + y^2)^2*z^4)/4 - 7*y*(x^2 + y^2)*z^6 + y*z^8, (35*(x^2 + y^2)^4*z)/128 - (35*(x^2 + y^2)^3*z^3)/12 + (21*(x^2 + y^2)^2*z^5)/4 - 2*(x^2 + y^2)*z^7 + z^9/9, (7*x*(x^2 + y^2)^4)/128 - (35*x*(x^2 + y^2)^3*z^2)/16 + (35*x*(x^2 + y^2)^2*z^4)/4 - 7*x*(x^2 + y^2)*z^6 + x*z^8, (-7*(x - y)*(x + y)*(x^2 + y^2)^3*z)/8 + (35*(x - y)*(x + y)*(x^2 + y^2)^2*z^3)/4 + 14*(-x^4 + y^4)*z^5 + 4*(x - y)*(x + y)*z^7, (-7*x*(x^2 - 3*y^2)*((x^2 + y^2)^3 - 36*(x^2 + y^2)^2*z^2 + 120*(x^2 + y^2)*z^4 - 64*z^6))/48, (7*(x^4 - 6*x^2*y^2 + y^4)*z*((x^2 + y^2)^2 - 8*(x^2 + y^2)*z^2 + 8*z^4))/4, (x*(x^4 - 10*x^2*y^2 + 5*y^4)*((x^2 + y^2)^2 - 28*(x^2 + y^2)*z^2 + 56*z^4))/4, (-2*(x^6 - 15*x^4*y^2 + 15*x^2*y^4 - y^6)*z*(3*(x^2 + y^2) - 14*z^2))/3, -(x*(x^6 - 21*x^4*y^2 + 35*x^2*y^4 - 7*y^6)*(x^2 + y^2 - 16*z^2))/4, (x^8 - 28*x^6*y^2 + 70*x^4*y^4 - 28*x^2*y^6 + y^8)*z, x^9/9 - 4*x^7*y^2 + 14*x^5*y^4 - (28*x^3*y^6)/3 + x*y^8}
{x^9*y - 12*x^7*y^3 + (126*x^5*y^5)/5 - 12*x^3*y^7 + x*y^9, y*(9*x^8 - 84*x^6*y^2 + 126*x^4*y^4 - 36*x^2*y^6 + y^8)*z, -2*x*y*(x^6 - 7*x^4*y^2 + 7*x^2*y^4 - y^6)*(x^2 + y^2 - 18*z^2), (3*y*(-7*x^6 + 35*x^4*y^2 - 21*x^2*y^4 + y^6)*z*(3*(x^2 + y^2) - 16*z^2))/4, (3*x*y*(3*x^4 - 10*x^2*y^2 + 3*y^4)*(3*(x^2 + y^2)^2 - 96*(x^2 + y^2)*z^2 + 224*z^4))/16, (3*y*(5*x^4 - 10*x^2*y^2 + y^4)*z*(15*(x^2 + y^2)^2 - 140*(x^2 + y^2)*z^2 + 168*z^4))/20, (3*x*y*(-((x - y)*(x + y)*(x^2 + y^2)^3) + 42*(x - y)*(x + y)*(x^2 + y^2)^2*z^2 + 168*(-x^4 + y^4)*z^4 + 112*(x - y)*(x + y)*z^6))/4, (3*y*(-3*x^2 + y^2)*z*(7*(x^2 + y^2)^3 - 84*(x^2 + y^2)^2*z^2 + 168*(x^2 + y^2)*z^4 - 64*z^6))/16, (3*x*y*(7*(x^2 + y^2)^4 - 336*(x^2 + y^2)^3*z^2 + 1680*(x^2 + y^2)^2*z^4 - 1792*(x^2 + y^2)*z^6 + 384*z^8))/128, (63*y*(x^2 + y^2)^4*z)/128 - (105*y*(x^2 + y^2)^3*z^3)/16 + (63*y*(x^2 + y^2)^2*z^5)/4 - 9*y*(x^2 + y^2)*z^7 + y*z^9, (-63*(x^2 + y^2)^5 + 3150*(x^2 + y^2)^4*z^2 - 16800*(x^2 + y^2)^3*z^4 + 20160*(x^2 + y^2)^2*z^6 - 5760*(x^2 + y^2)*z^8 + 256*z^10)/2560, (63*x*(x^2 + y^2)^4*z)/128 - (105*x*(x^2 + y^2)^3*z^3)/16 + (63*x*(x^2 + y^2)^2*z^5)/4 - 9*x*(x^2 + y^2)*z^7 + x*z^9, (3*(7*(x - y)*(x + y)*(x^2 + y^2)^4 - 336*(x - y)*(x + y)*(x^2 + y^2)^3*z^2 + 1680*(x - y)*(x + y)*(x^2 + y^2)^2*z^4 - 1792*(x^4 - y^4)*z^6 + 384*(x - y)*(x + y)*z^8))/256, (3*x*(x^2 - 3*y^2)*z*(-7*(x^2 + y^2)^3 + 84*(x^2 + y^2)^2*z^2 - 168*(x^2 + y^2)*z^4 + 64*z^6))/16, (-3*(x^4 - 6*x^2*y^2 + y^4)*((x^2 + y^2)^3 - 42*(x^2 + y^2)^2*z^2 + 168*(x^2 + y^2)*z^4 - 112*z^6))/16, (3*x*(x^4 - 10*x^2*y^2 + 5*y^4)*z*(15*(x^2 + y^2)^2 - 140*(x^2 + y^2)*z^2 + 168*z^4))/20, (3*(x^6 - 15*x^4*y^2 + 15*x^2*y^4 - y^6)*(3*(x^2 + y^2)^2 - 96*(x^2 + y^2)*z^2 + 224*z^4))/32, (-3*x*(x^6 - 21*x^4*y^2 + 35*x^2*y^4 - 7*y^6)*z*(3*(x^2 + y^2) - 16*z^2))/4, -((x^8 - 28*x^6*y^2 + 70*x^4*y^4 - 28*x^2*y^6 + y^8)*(x^2 + y^2 - 18*z^2))/4, x*(x^8 - 36*x^6*y^2 + 126*x^4*y^4 - 84*x^2*y^6 + 9*y^8)*z, (x^10 - 45*x^8*y^2 + 210*x^6*y^4 - 210*x^4*y^6 + 45*x^2*y^8 - y^10)/10}