monitsg.m

该程序用来解方程组的,非线性的和线性的,带有参数的方程组

syms  s u v p y0 z0 real;
s=x(1)
u=x(2)
v=x(3)
p=x(4)
y0=x(5)
z0=x(6)
r=1/6*(-728+18*p+6*(17088+240*p+141*p^2+6*p^3)^(1/2))^(1/3)-6*(11/9+1/6*p)/(-728+18*p+6*(17088+240*p+141*p^2+6*p^3)^(1/2))^(1/3)-1/3
r1=-1/12*(-728+18*p+6*(17088+240*p+141*p^2+6*p^3)^(1/2))^(1/3)+3*(11/9+1/6*p)/(-728+18*p+6*(17088+240*p+141*p^2+6*p^3)^(1/2))^(1/3)-1/3+1/2*i*3^(1/2)*(1/6*(-728+18*p+6*(17088+240*p+141*p^2+6*p^3)^(1/2))^(1/3)+6*(11/9+1/6*p)/(-728+18*p+6*(17088+240*p+141*p^2+6*p^3)^(1/2))^(1/3))
c1=s*(2*r-p)/(r^2+4)
b1=-s*(1+r)
a1=s
a2=-2*a1*(-r*c1+b1)/(8*r^3+8*r+4*r^2+8+p*r)
b2=2*(2*r+1)*a1*(-r*c1+b1)/(8*r^3+8*r+4*r^2+8+p*r)
c2=1/2*a1*(8*r*c1+8*c1+8*b1*r^2+4*b1*r+b1*p)/(8*r^3+8*r+4*r^2+8+p*r)
a3=2*(3*r*a1*c2+3*r*a2*c1-2*b1*a2-2*b2*a1)/(54*r^3+24*r+18*r^2+16+3*p*r)
b3=-2*(3*r+1)*(3*r*a1*c2+3*r*a2*c1-2*b1*a2-2*b2*a1)/(54*r^3+24*r+18*r^2+16+3*p*r)
c3=(12*r*a1*c2+12*r*a2*c1+8*a1*c2+8*a2*c1+18*r^2*b1*a2+18*r^2*b2*a1+6*r*b1*a2+6*r*b2*a1+p*b1*a2+p*b2*a1)/(54*r^3+24*r+18*r^2+16+3*p*r)
a4=-(-2*r*a1*c3-2*r*a2*c2-2*r*a3*c1+b1*a3+b2*a2+b3*a1)/(32*r^3+8*r+8*r^2+4+p*r)
b4=(4*r+1)*(-2*r*a1*c3-2*r*a2*c2-2*r*a3*c1+b1*a3+b2*a2+b3*a1)/(32*r^3+8*r+8*r^2+4+p*r)
c4=1/4*(16*r*a1*c3+16*r*a2*c2+16*r*a3*c1+8*a1*c3+8*a2*c2+8*a3*c1+32*r^2*b1*a3+32*r^2*b2*a2+32*r^2*b3*a1+8*r*b1*a3+8*r*b2*a2+8*r*b3*a1+p*b1*a3+p*b2*a2+p*b3*a1)/(32*r^3+8*r+8*r^2+4+p*r)
a5=2*(5*r*a1*c4+5*r*a2*c3+5*r*a3*c2+5*r*a4*c1-2*b1*a4-2*b2*a3-2*b3*a2-2*b4*a1)/(250*r^3+40*r+50*r^2+16+5*p*r)
b5=-2*(5*r+1)*(5*r*a1*c4+5*r*a2*c3+5*r*a3*c2+5*r*a4*c1-2*b1*a4-2*b2*a3-2*b3*a2-2*b4*a1)/(250*r^3+40*r+50*r^2+16+5*p*r)
c5= (20*r*a1*c4+20*r*a2*c3+20*r*a3*c2+20*r*a4*c1+8*a1*c4+8*a2*c3+8*a3*c2+8*a4*c1+50*r^2*b1*a4+50*r^2*b2*a3+50*r^2*b3*a2+50*r^2*b4*a1+10*r*b1*a4+10*r*b2*a3+10*r*b3*a2+10*r*b4*a1+p*b1*a4+p*b2*a3+p*b3*a2+p*b4*a1)/(250*r^3+40*r+50*r^2+16+5*p*r)
a6=-2*(-3*r*a1*c5-3*r*a2*c4-3*r*a3*c3-3*r*a4*c2-3*r*a5*c1+b1*a5+b2*a4+b3*a3+b4*a2+b5*a1)/(216*r^3+24*r+36*r^2+8+3*p*r)
b6=2*(6*r+1)*(-3*r*a1*c5-3*r*a2*c4-3*r*a3*c3-3*r*a4*c2-3*r*a5*c1+b1*a5+b2*a4+b3*a3+b4*a2+b5*a1)/(216*r^3+24*r+36*r^2+8+3*p*r)
c6=1/2*(8*a1*c5+8*a2*c4+72*r^2*b1*a5+72*r^2*b2*a4+72*r^2*b3*a3+72*r^2*b4*a2+72*r^2*b5*a1+8*a3*c3+8*a5*c1+12*r*b1*a5+12*r*b2*a4+12*r*b3*a3+12*r*b4*a2+12*r*b5*a1+p*b1*a5+p*b2*a4+p*b3*a3+p*b4*a2+p*b5*a1+8*a4*c2+24*r*a2*c4+24*r*a3*c3+24*r*a4*c2+24*r*a5*c1+24*r*a1*c5)/(216*r^3+24*r+36*r^2+8+3*p*r)
a7=2*(7*r*a1*c6+7*r*a2*c5+7*r*a3*c4+7*r*a4*c3+7*r*a5*c2+7*r*a6*c1-2*b1*a6-2*b2*a5-2*b3*a4-2*b4*a3-2*b5*a2-2*b6*a1)/(686*r^3+56*r+98*r^2+16+7*p*r)
b7=-2*(7*r+1)*(7*r*a1*c6+7*r*a2*c5+7*r*a3*c4+7*r*a4*c3+7*r*a5*c2+7*r*a6*c1-2*b1*a6-2*b2*a5-2*b3*a4-2*b4*a3-2*b5*a2-2*b6*a1)/(686*r^3+56*r+98*r^2+16+7*p*r)
c7=(8*a1*c6+8*a2*c5+98*r^2*b1*a6+98*r^2*b2*a5+98*r^2*b3*a4+98*r^2*b4*a3+98*r^2*b5*a2+98*r^2*b6*a1+14*r*b1*a6+14*r*b2*a5+14*r*b3*a4+14*r*b4*a3+14*r*b5*a2+14*r*b6*a1+p*b1*a6+p*b2*a5+p*b3*a4+p*b4*a3+p*b5*a2+8*a3*c4+8*a5*c2+28*r*a2*c5+28*r*a3*c4+28*r*a4*c3+28*r*a5*c2+28*r*a6*c1+8*a4*c3+p*b6*a1+8*a6*c1+28*r*a1*c6)/(686*r^3+56*r+98*r^2+16+7*p*r)
c11=(u+v*i)*(2*r1-p)/(r1^2+4)
b11=-(u+v*i)*(1+r1)
a11=u+v*i
a22=2*a11*(r1*c11-b11)/(8*r1^3+8*r1+4*r1^2+8+p*r1)
b22=-2*(2*r1+1)*a11*(r1*c11-b11)/(8*r1^3+8*r1+4*r1^2+8+p*r1)
c22= 1/2*a11*(8*r1*c11+8*c11+8*b11*r1^2+4*b11*r1+b11*p)/(8*r1^3+8*r1+4*r1^2+8+p*r1)
a33=-2*(-3*r1*a11*c22-3*r1*a22*c11+2*b11*a22+2*b22*a11)/(54*r1^3+24*r1+18*r1^2+16+3*p*r1)
b33=2*(3*r1+1)*(-3*r1*a11*c22-3*r1*a22*c11+2*b11*a22+2*b22*a11)/(54*r1^3+24*r1+18*r1^2+16+3*p*r1)
c33=(12*r1*a11*c22+12*r1*a22*c11+8*a11*c22+8*a22*c11+18*r1^2*b11*a22+18*r1^2*b22*a11+6*r1*b11*a22+6*r1*b22*a11+p*b11*a22+p*b22*a11)/(54*r1^3+24*r1+18*r1^2+16+3*p*r1)
a44=-(-2*r1*a11*c33-2*r1*a22*c22-2*r1*a33*c11+b11*a33+b22*a22+b33*a11)/(32*r1^3+8*r1+8*r1^2+4+p*r1)
b44=(4*r1+1)*(-2*r1*a11*c33-2*r1*a22*c22-2*r1*a33*c11+b11*a33+b22*a22+b33*a11)/(32*r1^3+8*r1+8*r1^2+4+p*r1)
c44=1/4*(16*r1*a11*c33+16*r1*a22*c22+16*r1*a33*c11+8*a11*c33+8*a22*c22+8*a33*c11+32*r1^2*b11*a33+32*r1^2*b22*a22+32*r1^2*b33*a11+8*r1*b11*a33+8*r1*b22*a22+8*r1*b33*a11+p*b11*a33+p*b22*a22+p*b33*a11)/(32*r1^3+8*r1+8*r1^2+4+p*r1)
a55=-2*(-5*r1*a11*c44-5*r1*a22*c33-5*r1*a33*c22-5*r1*a44*c11+2*b11*a44+2*b22*a33+2*b33*a22+2*b44*a11)/(250*r1^3+40*r1+50*r1^2+16+5*p*r1)
b55=2*(5*r1+1)*(-5*r1*a11*c44-5*r1*a22*c33-5*r1*a33*c22-5*r1*a44*c11+2*b11*a44+2*b22*a33+2*b33*a22+2*b44*a11)/(250*r1^3+40*r1+50*r1^2+16+5*p*r1)
c55=(20*r1*a11*c44+20*r1*a22*c33+20*r1*a33*c22+20*r1*a44*c11+8*a11*c44+8*a22*c33+8*a33*c22+8*a44*c11+50*r1^2*b11*a44+50*r1^2*b22*a33+50*r1^2*b33*a22+50*r1^2*b44*a11+10*r1*b11*a44+10*r1*b22*a33+10*r1*b33*a22+10*r1*b44*a11+p*b11*a44+p*b22*a33+p*b33*a22+p*b44*a11)/(250*r1^3+40*r1+50*r1^2+16+5*p*r1)
a66=2*(3*r1*a11*c55+3*r1*a22*c44+3*r1*a33*c33+3*r1*a44*c22+3*r1*a55*c11-b11*a55-b22*a44-b33*a33-b44*a22-b55*a11)/(216*r1^3+24*r1+36*r1^2+8+3*p*r1)
b66=-2*(6*r1+1)*(3*r1*a11*c55+3*r1*a22*c44+3*r1*a33*c33+3*r1*a44*c22+3*r1*a55*c11-b11*a55-b22*a44-b33*a33-b44*a22-b55*a11)/(216*r1^3+24*r1+36*r1^2+8+3*p*r1)
c66=1/2*(8*a11*c55+8*a22*c44+72*r1^2*b11*a55+72*r1^2*b22*a44+72*r1^2*b33*a33+72*r1^2*b44*a22+72*r1^2*b55*a11+12*r1*b11*a55+12*r1*b22*a44+12*r1*b33*a33+12*r1*b44*a22+12*r1*b55*a11+p*b11*a55+p*b22*a44+p*b33*a33+p*b44*a22+p*b55*a11+8*a33*c33+8*a44*c22+8*a55*c11+24*r1*a11*c55+24*r1*a22*c44+24*r1*a33*c33+24*r1*a44*c22+24*r1*a55*c11)/(216*r1^3+24*r1+36*r1^2+8+3*p*r1)
a77=  2*(7*r1*a11*c66+7*r1*a22*c55+7*r1*a33*c44+7*r1*a44*c33+7*r1*a55*c22+7*r1*a66*c11-2*b11*a66-2*b22*a55-2*b33*a44-2*b44*a33-2*b55*c22-2*b66*a11)/(686*r1^3+56*r1+98*r1^2+16+7*p*r1)
b77=-2*(7*r1+1)*(7*r1*a11*c66+7*r1*a22*c55+7*r1*a33*c44+7*r1*a44*c33+7*r1*a55*c22+7*r1*a66*c11-2*b11*a66-2*b22*a55-2*b33*a44-2*b44*a33-2*b55*c22-2*b66*a11)/(686*r1^3+56*r1+98*r1^2+16+7*p*r1)
c77= (8*a44*c33+8*a55*c22+98*r1^2*b11*a66+98*r1^2*b22*a55+98*r1^2*b33*a44+98*r1^2*b44*a33+98*r1^2*b55*c22+98*r1^2*b66*a11+14*r1*b11*a66+14*r1*b22*a55+14*r1*b33*a44+14*r1*b44*a33+14*r1*b55*c22+14*r1*b66*a11+p*b11*a66+p*b22*a55+p*b33*a44+p*b44*a33+p*b55*c22+p*b66*a11+8*a66*c11+28*r1*a11*c66+28*r1*a22*c55+28*r1*a33*c44+28*r1*a44*c33+28*r1*a55*c22+28*r1*a66*c11+8*a11*c66+8*a22*c55+8*a33*c44)/(686*r1^3+56*r1+98*r1^2+16+7*p*r1)
s1=a1+a2+a3+a4+a5+a6+a7
s2=real(a11+a22+a33+a44+a55+a66+a77)
q1=b1+b2+b3+b4+b5+b6+b7
q2=real(b11+b22+b33+b44+b55+b66+b77)
r11=c1+c2+c3+c4+c5+c6+c7
r22=real(c11+c22+c33+c44+c55+c66+c77)
m(1)=-2+s1-(s2-2)
m(2)=2+q1-(q2+2)
m(3)=-p/2+r11-(r22-p/2)
m(4)=-2+s1+y0
m(5)=2+q1-y0
m(6)=-p/2+r11-z0