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refine_weight_percentage [topas wiki]

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—refine_weight_percentage [2022/11/03 15:08] (current) – external edit 127.0.0.1
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 +====== Set or refine weight percentages directly  ======
  
 +Macro to aid in the setting or refining of weight percentages for up to 9 phases. The scale factors are calculated from the given weight fractions. Weight fractions can be either fixed or refined.
 +
 +Contributors: Matthew Rowles, with [[refining_setting_weight_percents_directly|help from Alan]]
 +
 +The equations were calculated in Maple from the standard Hill/Howard quantification algorithm.
 +
 +The Maple syntax used was
 +<code>
 +> restart:
 +> f2 :=x2 *(s1*m1 + s3*m3 + s4*m4);
 +> f3 :=x3 *(s1*m1 + s2*m2 + s4*m4);
 +> f4 :=x4 *(s1*m1 + s2*m2 + s3*m3);
 +> solve({f2=s2, f3=s3, f4=s4},[s2, s3, s4]);
 +</code>
 +where
 +<code>
 +mn = cell_mass * cell_volume
 +xn = wn / (mn (100 - wn))
 +</code>
 +
 +===== To use the macro =====
 +
 +The first phase must have a scale factor: s1.
 +The remaining phases must have weight percentages: w2, w3, ... wp.
 +
 +Instead of giving a phase a scale factor, use this macro. You must tell the macro the number of the phase that it is in, as well as the total number of phases.
 +
 +The scale factor actually used is reported as the last value in the three-argument macro. If you don't want to know, then just use the two-argument macro.
 +
 +Potential usage
 +<code topas>
 +xdd
 +   prm s1 0.0035
 +   prm w1 = 100 - w2 - w3 - w4; : 0 ''this will just report the value
 +   prm !w2 20
 +   prm w3 30
 +   prm w4 30
 +   
 +   str
 +      wt_dets(1,4,0)
 +   str
 +      wt_dets(2,4,0)
 +   str
 +      wt_dets(3,4,0)
 +   str
 +      wt_dets(4,4,0)
 +</code>
 +
 +
 +<code topas>
 +macro wt_dets(n,p) { wt_dets(n,p,0) }
 +macro wt_dets(n,p,sc)
 +{
 +   prm m##n = Get(cell_mass) Get(cell_volume);
 +   prm x##n = w##n / (m##n (100 - w##n));
 +   
 +   
 +   #m_if p == 2; ''there are 2 phases in total
 +    #m_if n == 1;
 +    ''do nothing, as s1 should already be defined elsewhere
 +    #m_elseif n == 2;
 +    prm s##n = x2*s1*m1;
 +    #m_endif
 +   
 +   #m_elseif p == 3; ''there are three phases in total
 +    #m_if n == 1;
 +    prm m_denom = (m2*m3*x2*x3-1);
 +    #m_elseif n == 2;
 +    prm s##n = -m1*s1*x2*(m3*x3+1)/m_denom;
 +    #m_elseif n == 3;
 +    prm s##n = -m1*s1*x3*(m2*x2+1)/m_denom;
 +    #m_endif
 +   
 +   #m_elseif p == 4;
 +    #m_if n == 1;
 +    prm m_denom = (2*m2*m3*m4*x2*x3*x4+m2*m3*x2*x3+m2*m4*x2*x4+m3*m4*x3*x4-1);
 +    #m_elseif n == 2;
 +    prm s##n = -m1*s1*x2*(m3*m4*x3*x4+m3*x3+m4*x4+1)/m_denom;
 +    #m_elseif n == 3;
 +    prm s##n = -m1*s1*x3*(m2*m4*x2*x4+m2*x2+m4*x4+1)/m_denom;
 +    #m_elseif n == 4;
 +    prm s##n = -m1*s1*x4*(m2*m3*x2*x3+m2*x2+m3*x3+1)/m_denom;
 +    #m_endif
 +   
 +   #m_elseif p == 5;
 +    #m_if n == 1;
 +    prm m_denom = (3*m2*m3*m4*m5*x2*x3*x4*x5+2*m2*m3*m4*x2*x3*x4+2*m2*m3*m5*x2*x3*x5+2*m2*m4*m5*x2*x4*x5+2*m3*m4*m5*x3*x4*x5+m2*m3*x2*x3+m2*m4*x2*x4+m2*m5*x2*x5+m3*m4*x3*x4+m3*m5*x3*x5+m4*m5*x4*x5-1);
 +    #m_elseif n == 2;
 +    prm s##n = -m1*s1*x2*(m3*m4*m5*x3*x4*x5+m3*m4*x3*x4+m3*m5*x3*x5+m4*m5*x4*x5+m3*x3+m4*x4+m5*x5+1)/m_denom;
 +    #m_elseif n == 3;
 +    prm s##n = -m1*s1*x3*(m2*m4*m5*x2*x4*x5+m2*m4*x2*x4+m2*m5*x2*x5+m4*m5*x4*x5+m2*x2+m4*x4+m5*x5+1)/m_denom;
 +    #m_elseif n == 4;
 +    prm s##n = -m1*s1*x4*(m2*m3*m5*x2*x3*x5+m2*m3*x2*x3+m2*m5*x2*x5+m3*m5*x3*x5+m2*x2+m3*x3+m5*x5+1)/m_denom;
 +    #m_elseif n == 5;
 +    prm s##n = -m1*s1*x5*(m2*m3*m4*x2*x3*x4+m2*m3*x2*x3+m2*m4*x2*x4+m3*m4*x3*x4+m2*x2+m3*x3+m4*x4+1)/m_denom;
 +    #m_endif
 +   
 +   #m_elseif p == 6;
 +    #m_if n == 1;
 +    prm m_denom = (4*m2*m3*m4*m5*m6*x2*x3*x4*x5*x6+3*m2*m3*m4*m5*x2*x3*x4*x5+3*m2*m3*m4*m6*x2*x3*x4*x6+3*m2*m3*m5*m6*x2*x3*x5*x6+3*m2*m4*m5*m6*x2*x4*x5*x6+3*m3*m4*m5*m6*x3*x4*x5*x6+2*m2*m3*m4*x2*x3*x4+2*m2*m3*m5*x2*x3*x5+2*m2*m3*m6*x2*x3*x6+2*m2*m4*m5*x2*x4*x5+2*m2*m4*m6*x2*x4*x6+2*m2*m5*m6*x2*x5*x6+2*m3*m4*m5*x3*x4*x5+2*m3*m4*m6*x3*x4*x6+2*m3*m5*m6*x3*x5*x6+2*m4*m5*m6*x4*x5*x6+m2*m3*x2*x3+m2*m4*x2*x4+m2*m5*x2*x5+m2*m6*x2*x6+m3*m4*x3*x4+m3*m5*x3*x5+m3*m6*x3*x6+m4*m5*x4*x5+m4*m6*x4*x6+m5*m6*x5*x6-1);
 +    #m_elseif n == 2;
 +    prm s##n = -m1*s1*x2*(m3*m4*m5*m6*x3*x4*x5*x6+m3*m4*m5*x3*x4*x5+m3*m4*m6*x3*x4*x6+m3*m5*m6*x3*x5*x6+m4*m5*m6*x4*x5*x6+m3*m4*x3*x4+m3*m5*x3*x5+m3*m6*x3*x6+m4*m5*x4*x5+m4*m6*x4*x6+m5*m6*x5*x6+m3*x3+m4*x4+m5*x5+m6*x6+1)/m_denom;
 +    #m_elseif n == 3;
 +    prm s##n = -s1*m1*x3*(m2*m4*m6*x2*x4*x6+m2*m4*x2*x4+m2*m6*x2*x6+m4*m6*x4*x6+m2*x2+m4*x4+m6*x6+1)*(m5*x5+1)/m_denom;
 +    #m_elseif n == 4;
 +    prm s##n = -m1*s1*x4*(m2*m3*m5*m6*x2*x3*x5*x6+m2*m3*m5*x2*x3*x5+m2*m3*m6*x2*x3*x6+m2*m5*m6*x2*x5*x6+m3*m5*m6*x3*x5*x6+m2*m3*x2*x3+m2*m5*x2*x5+m2*m6*x2*x6+m3*m5*x3*x5+m3*m6*x3*x6+m5*m6*x5*x6+m2*x2+m3*x3+m5*x5+m6*x6+1)/m_denom;
 +    #m_elseif n == 5;
 +    prm s##n = -m1*s1*x5*(m2*m3*m4*m6*x2*x3*x4*x6+m2*m3*m4*x2*x3*x4+m2*m3*m6*x2*x3*x6+m2*m4*m6*x2*x4*x6+m3*m4*m6*x3*x4*x6+m2*m3*x2*x3+m2*m4*x2*x4+m2*m6*x2*x6+m3*m4*x3*x4+m3*m6*x3*x6+m4*m6*x4*x6+m2*x2+m3*x3+m4*x4+m6*x6+1)/m_denom;
 +    #m_elseif n == 6;
 +    prm s##n = -m1*s1*x6*(m2*m3*m4*m5*x2*x3*x4*x5+m2*m3*m4*x2*x3*x4+m2*m3*m5*x2*x3*x5+m2*m4*m5*x2*x4*x5+m3*m4*m5*x3*x4*x5+m2*m3*x2*x3+m2*m4*x2*x4+m2*m5*x2*x5+m3*m4*x3*x4+m3*m5*x3*x5+m4*m5*x4*x5+m2*x2+m3*x3+m4*x4+m5*x5+1)/m_denom;
 +    #m_endif
 +   
 +   #m_elseif p == 7;
 +    #m_if n == 1;
 +    prm m_denom = (5*m2*m3*m4*m5*m6*m7*x2*x3*x4*x5*x6*x7+4*m2*m3*m4*m5*m6*x2*x3*x4*x5*x6+4*m2*m3*m4*m5*m7*x2*x3*x4*x5*x7+4*m2*m3*m4*m6*m7*x2*x3*x4*x6*x7+4*m2*m3*m5*m6*m7*x2*x3*x5*x6*x7+4*m2*m4*m5*m6*m7*x2*x4*x5*x6*x7+4*m3*m4*m5*m6*m7*x3*x4*x5*x6*x7+3*m2*m3*m4*m5*x2*x3*x4*x5+3*m2*m3*m4*m6*x2*x3*x4*x6+3*m2*m3*m4*m7*x2*x3*x4*x7+3*m2*m3*m5*m6*x2*x3*x5*x6+3*m2*m3*m5*m7*x2*x3*x5*x7+3*m2*m3*m6*m7*x2*x3*x6*x7+3*m2*m4*m5*m6*x2*x4*x5*x6+3*m2*m4*m5*m7*x2*x4*x5*x7+3*m2*m4*m6*m7*x2*x4*x6*x7+3*m2*m5*m6*m7*x2*x5*x6*x7+3*m3*m4*m5*m6*x3*x4*x5*x6+3*m3*m4*m5*m7*x3*x4*x5*x7+3*m3*m4*m6*m7*x3*x4*x6*x7+3*m3*m5*m6*m7*x3*x5*x6*x7+3*m4*m5*m6*m7*x4*x5*x6*x7+2*m2*m3*m4*x2*x3*x4+2*m2*m3*m5*x2*x3*x5+2*m2*m3*m6*x2*x3*x6+2*m2*m3*m7*x2*x3*x7+2*m2*m4*m5*x2*x4*x5+2*m2*m4*m6*x2*x4*x6+2*m2*m4*m7*x2*x4*x7+2*m2*m5*m6*x2*x5*x6+2*m2*m5*m7*x2*x5*x7+2*m2*m6*m7*x2*x6*x7+2*m3*m4*m5*x3*x4*x5+2*m3*m4*m6*x3*x4*x6+2*m3*m4*m7*x3*x4*x7+2*m3*m5*m6*x3*x5*x6+2*m3*m5*m7*x3*x5*x7+2*m3*m6*m7*x3*x6*x7+2*m4*m5*m6*x4*x5*x6+2*m4*m5*m7*x4*x5*x7+2*m4*m6*m7*x4*x6*x7+2*m5*m6*m7*x5*x6*x7+m2*m3*x2*x3+m2*m4*x2*x4+m2*m5*x2*x5+m2*m6*x2*x6+m2*m7*x2*x7+m3*m4*x3*x4+m3*m5*x3*x5+m3*m6*x3*x6+m3*m7*x3*x7+m4*m5*x4*x5+m4*m6*x4*x6+m4*m7*x4*x7+m5*m6*x5*x6+m5*m7*x5*x7+m6*m7*x6*x7-1);
 +    #m_elseif n == 2;
 +    prm s##n = -(m3*m4*m5*m6*m7*x3*x4*x5*x6*x7+m3*m4*m5*m6*x3*x4*x5*x6+m3*m4*m5*m7*x3*x4*x5*x7+m3*m4*m6*m7*x3*x4*x6*x7+m3*m5*m6*m7*x3*x5*x6*x7+m4*m5*m6*m7*x4*x5*x6*x7+m3*m4*m5*x3*x4*x5+m3*m4*m6*x3*x4*x6+m3*m4*m7*x3*x4*x7+m3*m5*m6*x3*x5*x6+m3*m5*m7*x3*x5*x7+m3*m6*m7*x3*x6*x7+m4*m5*m6*x4*x5*x6+m4*m5*m7*x4*x5*x7+m4*m6*m7*x4*x6*x7+m5*m6*m7*x5*x6*x7+m3*m4*x3*x4+m3*m5*x3*x5+m3*m6*x3*x6+m3*m7*x3*x7+m4*m5*x4*x5+m4*m6*x4*x6+m4*m7*x4*x7+m5*m6*x5*x6+m5*m7*x5*x7+m6*m7*x6*x7+m3*x3+m4*x4+m5*x5+m6*x6+m7*x7+1)*m1*s1*x2/m_denom;
 +    #m_elseif n == 3;
 +    prm s##n = -(m2*m4*m5*m6*m7*x2*x4*x5*x6*x7+m2*m4*m5*m6*x2*x4*x5*x6+m2*m4*m5*m7*x2*x4*x5*x7+m2*m4*m6*m7*x2*x4*x6*x7+m2*m5*m6*m7*x2*x5*x6*x7+m4*m5*m6*m7*x4*x5*x6*x7+m2*m4*m5*x2*x4*x5+m2*m4*m6*x2*x4*x6+m2*m4*m7*x2*x4*x7+m2*m5*m6*x2*x5*x6+m2*m5*m7*x2*x5*x7+m2*m6*m7*x2*x6*x7+m4*m5*m6*x4*x5*x6+m4*m5*m7*x4*x5*x7+m4*m6*m7*x4*x6*x7+m5*m6*m7*x5*x6*x7+m2*m4*x2*x4+m2*m5*x2*x5+m2*m6*x2*x6+m2*m7*x2*x7+m4*m5*x4*x5+m4*m6*x4*x6+m4*m7*x4*x7+m5*m6*x5*x6+m5*m7*x5*x7+m6*m7*x6*x7+m2*x2+m4*x4+m5*x5+m6*x6+m7*x7+1)*m1*s1*x3/m_denom;
 +    #m_elseif n == 4;
 +    prm s##n = -m1*s1*x4*(m5*x5+1)*(m6*x6+1)*(m2*m3*m7*x2*x3*x7+m2*m3*x2*x3+m2*m7*x2*x7+m3*m7*x3*x7+m2*x2+m3*x3+m7*x7+1)/m_denom;
 +    #m_elseif n == 5;
 +    prm s##n = -(m2*m3*m4*m7*x2*x3*x4*x7+m2*m3*m4*x2*x3*x4+m2*m3*m7*x2*x3*x7+m2*m4*m7*x2*x4*x7+m3*m4*m7*x3*x4*x7+m2*m3*x2*x3+m2*m4*x2*x4+m2*m7*x2*x7+m3*m4*x3*x4+m3*m7*x3*x7+m4*m7*x4*x7+m2*x2+m3*x3+m4*x4+m7*x7+1)*s1*m1*x5*(m6*x6+1)/m_denom;
 +    #m_elseif n == 6;
 +    prm s##n = -m1*s1*x6*(m2*m3*m4*m5*m7*x2*x3*x4*x5*x7+m2*m3*m4*m5*x2*x3*x4*x5+m2*m3*m4*m7*x2*x3*x4*x7+m2*m3*m5*m7*x2*x3*x5*x7+m2*m4*m5*m7*x2*x4*x5*x7+m3*m4*m5*m7*x3*x4*x5*x7+m2*m3*m4*x2*x3*x4+m2*m3*m5*x2*x3*x5+m2*m3*m7*x2*x3*x7+m2*m4*m5*x2*x4*x5+m2*m4*m7*x2*x4*x7+m2*m5*m7*x2*x5*x7+m3*m4*m5*x3*x4*x5+m3*m4*m7*x3*x4*x7+m3*m5*m7*x3*x5*x7+m4*m5*m7*x4*x5*x7+m2*m3*x2*x3+m2*m4*x2*x4+m2*m5*x2*x5+m2*m7*x2*x7+m3*m4*x3*x4+m3*m5*x3*x5+m3*m7*x3*x7+m4*m5*x4*x5+m4*m7*x4*x7+m5*m7*x5*x7+m2*x2+m3*x3+m4*x4+m5*x5+m7*x7+1)/m_denom;
 +    #m_elseif n == 7;
 +    prm s##n = -m1*s1*x7*(m2*m3*m4*m5*m6*x2*x3*x4*x5*x6+m2*m3*m4*m5*x2*x3*x4*x5+m2*m3*m4*m6*x2*x3*x4*x6+m2*m3*m5*m6*x2*x3*x5*x6+m2*m4*m5*m6*x2*x4*x5*x6+m3*m4*m5*m6*x3*x4*x5*x6+m2*m3*m4*x2*x3*x4+m2*m3*m5*x2*x3*x5+m2*m3*m6*x2*x3*x6+m2*m4*m5*x2*x4*x5+m2*m4*m6*x2*x4*x6+m2*m5*m6*x2*x5*x6+m3*m4*m5*x3*x4*x5+m3*m4*m6*x3*x4*x6+m3*m5*m6*x3*x5*x6+m4*m5*m6*x4*x5*x6+m2*m3*x2*x3+m2*m4*x2*x4+m2*m5*x2*x5+m2*m6*x2*x6+m3*m4*x3*x4+m3*m5*x3*x5+m3*m6*x3*x6+m4*m5*x4*x5+m4*m6*x4*x6+m5*m6*x5*x6+m2*x2+m3*x3+m4*x4+m5*x5+m6*x6+1)/m_denom;
 +    #m_endif
 +   
 +   #m_elseif p == 8;
 +    #m_if n == 1;
 +    prm m_denom = (6*m2*m3*m4*m5*m6*m7*m8*x2*x3*x4*x5*x6*x7*x8+5*m2*m3*m4*m5*m6*m7*x2*x3*x4*x5*x6*x7+5*m2*m3*m4*m5*m6*m8*x2*x3*x4*x5*x6*x8+5*m2*m3*m4*m5*m7*m8*x2*x3*x4*x5*x7*x8+5*m2*m3*m4*m6*m7*m8*x2*x3*x4*x6*x7*x8+5*m2*m3*m5*m6*m7*m8*x2*x3*x5*x6*x7*x8+5*m2*m4*m5*m6*m7*m8*x2*x4*x5*x6*x7*x8+5*m3*m4*m5*m6*m7*m8*x3*x4*x5*x6*x7*x8+4*m2*m3*m4*m5*m6*x2*x3*x4*x5*x6+4*m2*m3*m4*m5*m7*x2*x3*x4*x5*x7+4*m2*m3*m4*m5*m8*x2*x3*x4*x5*x8+4*m2*m3*m4*m6*m7*x2*x3*x4*x6*x7+4*m2*m3*m4*m6*m8*x2*x3*x4*x6*x8+4*m2*m3*m4*m7*m8*x2*x3*x4*x7*x8+4*m2*m3*m5*m6*m7*x2*x3*x5*x6*x7+4*m2*m3*m5*m6*m8*x2*x3*x5*x6*x8+4*m2*m3*m5*m7*m8*x2*x3*x5*x7*x8+4*m2*m3*m6*m7*m8*x2*x3*x6*x7*x8+4*m2*m4*m5*m6*m7*x2*x4*x5*x6*x7+4*m2*m4*m5*m6*m8*x2*x4*x5*x6*x8+4*m2*m4*m5*m7*m8*x2*x4*x5*x7*x8+4*m2*m4*m6*m7*m8*x2*x4*x6*x7*x8+4*m2*m5*m6*m7*m8*x2*x5*x6*x7*x8+4*m3*m4*m5*m6*m7*x3*x4*x5*x6*x7+4*m3*m4*m5*m6*m8*x3*x4*x5*x6*x8+4*m3*m4*m5*m7*m8*x3*x4*x5*x7*x8+4*m3*m4*m6*m7*m8*x3*x4*x6*x7*x8+4*m3*m5*m6*m7*m8*x3*x5*x6*x7*x8+4*m4*m5*m6*m7*m8*x4*x5*x6*x7*x8+3*m2*m3*m4*m5*x2*x3*x4*x5+3*m2*m3*m4*m6*x2*x3*x4*x6+3*m2*m3*m4*m7*x2*x3*x4*x7+3*m2*m3*m4*m8*x2*x3*x4*x8+3*m2*m3*m5*m6*x2*x3*x5*x6+3*m2*m3*m5*m7*x2*x3*x5*x7+3*m2*m3*m5*m8*x2*x3*x5*x8+3*m2*m3*m6*m7*x2*x3*x6*x7+3*m2*m3*m6*m8*x2*x3*x6*x8+3*m2*m3*m7*m8*x2*x3*x7*x8+3*m2*m4*m5*m6*x2*x4*x5*x6+3*m2*m4*m5*m7*x2*x4*x5*x7+3*m2*m4*m5*m8*x2*x4*x5*x8+3*m2*m4*m6*m7*x2*x4*x6*x7+3*m2*m4*m6*m8*x2*x4*x6*x8+3*m2*m4*m7*m8*x2*x4*x7*x8+3*m2*m5*m6*m7*x2*x5*x6*x7+3*m2*m5*m6*m8*x2*x5*x6*x8+3*m2*m5*m7*m8*x2*x5*x7*x8+3*m2*m6*m7*m8*x2*x6*x7*x8+3*m3*m4*m5*m6*x3*x4*x5*x6+3*m3*m4*m5*m7*x3*x4*x5*x7+3*m3*m4*m5*m8*x3*x4*x5*x8+3*m3*m4*m6*m7*x3*x4*x6*x7+3*m3*m4*m6*m8*x3*x4*x6*x8+3*m3*m4*m7*m8*x3*x4*x7*x8+3*m3*m5*m6*m7*x3*x5*x6*x7+3*m3*m5*m6*m8*x3*x5*x6*x8+3*m3*m5*m7*m8*x3*x5*x7*x8+3*m3*m6*m7*m8*x3*x6*x7*x8+3*m4*m5*m6*m7*x4*x5*x6*x7+3*m4*m5*m6*m8*x4*x5*x6*x8+3*m4*m5*m7*m8*x4*x5*x7*x8+3*m4*m6*m7*m8*x4*x6*x7*x8+3*m5*m6*m7*m8*x5*x6*x7*x8+2*m2*m3*m4*x2*x3*x4+2*m2*m3*m5*x2*x3*x5+2*m2*m3*m6*x2*x3*x6+2*m2*m3*m7*x2*x3*x7+2*m2*m3*m8*x2*x3*x8+2*m2*m4*m5*x2*x4*x5+2*m2*m4*m6*x2*x4*x6+2*m2*m4*m7*x2*x4*x7+2*m2*m4*m8*x2*x4*x8+2*m2*m5*m6*x2*x5*x6+2*m2*m5*m7*x2*x5*x7+2*m2*m5*m8*x2*x5*x8+2*m2*m6*m7*x2*x6*x7+2*m2*m6*m8*x2*x6*x8+2*m2*m7*m8*x2*x7*x8+2*m3*m4*m5*x3*x4*x5+2*m3*m4*m6*x3*x4*x6+2*m3*m4*m7*x3*x4*x7+2*m3*m4*m8*x3*x4*x8+2*m3*m5*m6*x3*x5*x6+2*m3*m5*m7*x3*x5*x7+2*m3*m5*m8*x3*x5*x8+2*m3*m6*m7*x3*x6*x7+2*m3*m6*m8*x3*x6*x8+2*m3*m7*m8*x3*x7*x8+2*m4*m5*m6*x4*x5*x6+2*m4*m5*m7*x4*x5*x7+2*m4*m5*m8*x4*x5*x8+2*m4*m6*m7*x4*x6*x7+2*m4*m6*m8*x4*x6*x8+2*m4*m7*m8*x4*x7*x8+2*m5*m6*m7*x5*x6*x7+2*m5*m6*m8*x5*x6*x8+2*m5*m7*m8*x5*x7*x8+2*m6*m7*m8*x6*x7*x8+m2*m3*x2*x3+m2*m4*x2*x4+m2*m5*x2*x5+m2*m6*x2*x6+m2*m7*x2*x7+m2*m8*x2*x8+m3*m4*x3*x4+m3*m5*x3*x5+m3*m6*x3*x6+m3*m7*x3*x7+m3*m8*x3*x8+m4*m5*x4*x5+m4*m6*x4*x6+m4*m7*x4*x7+m4*m8*x4*x8+m5*m6*x5*x6+m5*m7*x5*x7+m5*m8*x5*x8+m6*m7*x6*x7+m6*m8*x6*x8+m7*m8*x7*x8-1);
 +    #m_elseif n == 2;
 +    prm s##n = -m1*s1*x2*(m3*m4*m5*m6*m7*m8*x3*x4*x5*x6*x7*x8+m3*m4*m5*m6*m7*x3*x4*x5*x6*x7+m3*m4*m5*m6*m8*x3*x4*x5*x6*x8+m3*m4*m5*m7*m8*x3*x4*x5*x7*x8+m3*m4*m6*m7*m8*x3*x4*x6*x7*x8+m3*m5*m6*m7*m8*x3*x5*x6*x7*x8+m4*m5*m6*m7*m8*x4*x5*x6*x7*x8+m3*m4*m5*m6*x3*x4*x5*x6+m3*m4*m5*m7*x3*x4*x5*x7+m3*m4*m5*m8*x3*x4*x5*x8+m3*m4*m6*m7*x3*x4*x6*x7+m3*m4*m6*m8*x3*x4*x6*x8+m3*m4*m7*m8*x3*x4*x7*x8+m3*m5*m6*m7*x3*x5*x6*x7+m3*m5*m6*m8*x3*x5*x6*x8+m3*m5*m7*m8*x3*x5*x7*x8+m3*m6*m7*m8*x3*x6*x7*x8+m4*m5*m6*m7*x4*x5*x6*x7+m4*m5*m6*m8*x4*x5*x6*x8+m4*m5*m7*m8*x4*x5*x7*x8+m4*m6*m7*m8*x4*x6*x7*x8+m5*m6*m7*m8*x5*x6*x7*x8+m3*m4*m5*x3*x4*x5+m3*m4*m6*x3*x4*x6+m3*m4*m7*x3*x4*x7+m3*m4*m8*x3*x4*x8+m3*m5*m6*x3*x5*x6+m3*m5*m7*x3*x5*x7+m3*m5*m8*x3*x5*x8+m3*m6*m7*x3*x6*x7+m3*m6*m8*x3*x6*x8+m3*m7*m8*x3*x7*x8+m4*m5*m6*x4*x5*x6+m4*m5*m7*x4*x5*x7+m4*m5*m8*x4*x5*x8+m4*m6*m7*x4*x6*x7+m4*m6*m8*x4*x6*x8+m4*m7*m8*x4*x7*x8+m5*m6*m7*x5*x6*x7+m5*m6*m8*x5*x6*x8+m5*m7*m8*x5*x7*x8+m6*m7*m8*x6*x7*x8+m3*m4*x3*x4+m3*m5*x3*x5+m3*m6*x3*x6+m3*m7*x3*x7+m3*m8*x3*x8+m4*m5*x4*x5+m4*m6*x4*x6+m4*m7*x4*x7+m4*m8*x4*x8+m5*m6*x5*x6+m5*m7*x5*x7+m5*m8*x5*x8+m6*m7*x6*x7+m6*m8*x6*x8+m7*m8*x7*x8+m3*x3+m4*x4+m5*x5+m6*x6+m7*x7+m8*x8+1)/m_denom;
 +    #m_elseif n == 3;
 +    prm s##n = -(m2*m4*m5*m6*m7*m8*x2*x4*x5*x6*x7*x8+m2*m4*m5*m6*m7*x2*x4*x5*x6*x7+m2*m4*m5*m6*m8*x2*x4*x5*x6*x8+m2*m4*m5*m7*m8*x2*x4*x5*x7*x8+m2*m4*m6*m7*m8*x2*x4*x6*x7*x8+m2*m5*m6*m7*m8*x2*x5*x6*x7*x8+m4*m5*m6*m7*m8*x4*x5*x6*x7*x8+m2*m4*m5*m6*x2*x4*x5*x6+m2*m4*m5*m7*x2*x4*x5*x7+m2*m4*m5*m8*x2*x4*x5*x8+m2*m4*m6*m7*x2*x4*x6*x7+m2*m4*m6*m8*x2*x4*x6*x8+m2*m4*m7*m8*x2*x4*x7*x8+m2*m5*m6*m7*x2*x5*x6*x7+m2*m5*m6*m8*x2*x5*x6*x8+m2*m5*m7*m8*x2*x5*x7*x8+m2*m6*m7*m8*x2*x6*x7*x8+m4*m5*m6*m7*x4*x5*x6*x7+m4*m5*m6*m8*x4*x5*x6*x8+m4*m5*m7*m8*x4*x5*x7*x8+m4*m6*m7*m8*x4*x6*x7*x8+m5*m6*m7*m8*x5*x6*x7*x8+m2*m4*m5*x2*x4*x5+m2*m4*m6*x2*x4*x6+m2*m4*m7*x2*x4*x7+m2*m4*m8*x2*x4*x8+m2*m5*m6*x2*x5*x6+m2*m5*m7*x2*x5*x7+m2*m5*m8*x2*x5*x8+m2*m6*m7*x2*x6*x7+m2*m6*m8*x2*x6*x8+m2*m7*m8*x2*x7*x8+m4*m5*m6*x4*x5*x6+m4*m5*m7*x4*x5*x7+m4*m5*m8*x4*x5*x8+m4*m6*m7*x4*x6*x7+m4*m6*m8*x4*x6*x8+m4*m7*m8*x4*x7*x8+m5*m6*m7*x5*x6*x7+m5*m6*m8*x5*x6*x8+m5*m7*m8*x5*x7*x8+m6*m7*m8*x6*x7*x8+m2*m4*x2*x4+m2*m5*x2*x5+m2*m6*x2*x6+m2*m7*x2*x7+m2*m8*x2*x8+m4*m5*x4*x5+m4*m6*x4*x6+m4*m7*x4*x7+m4*m8*x4*x8+m5*m6*x5*x6+m5*m7*x5*x7+m5*m8*x5*x8+m6*m7*x6*x7+m6*m8*x6*x8+m7*m8*x7*x8+m2*x2+m4*x4+m5*x5+m6*x6+m7*x7+m8*x8+1)*m1*s1*x3/m_denom;
 +    #m_elseif n == 4;
 +    prm s##n = -(m2*m3*m5*m6*m7*m8*x2*x3*x5*x6*x7*x8+m2*m3*m5*m6*m7*x2*x3*x5*x6*x7+m2*m3*m5*m6*m8*x2*x3*x5*x6*x8+m2*m3*m5*m7*m8*x2*x3*x5*x7*x8+m2*m3*m6*m7*m8*x2*x3*x6*x7*x8+m2*m5*m6*m7*m8*x2*x5*x6*x7*x8+m3*m5*m6*m7*m8*x3*x5*x6*x7*x8+m2*m3*m5*m6*x2*x3*x5*x6+m2*m3*m5*m7*x2*x3*x5*x7+m2*m3*m5*m8*x2*x3*x5*x8+m2*m3*m6*m7*x2*x3*x6*x7+m2*m3*m6*m8*x2*x3*x6*x8+m2*m3*m7*m8*x2*x3*x7*x8+m2*m5*m6*m7*x2*x5*x6*x7+m2*m5*m6*m8*x2*x5*x6*x8+m2*m5*m7*m8*x2*x5*x7*x8+m2*m6*m7*m8*x2*x6*x7*x8+m3*m5*m6*m7*x3*x5*x6*x7+m3*m5*m6*m8*x3*x5*x6*x8+m3*m5*m7*m8*x3*x5*x7*x8+m3*m6*m7*m8*x3*x6*x7*x8+m5*m6*m7*m8*x5*x6*x7*x8+m2*m3*m5*x2*x3*x5+m2*m3*m6*x2*x3*x6+m2*m3*m7*x2*x3*x7+m2*m3*m8*x2*x3*x8+m2*m5*m6*x2*x5*x6+m2*m5*m7*x2*x5*x7+m2*m5*m8*x2*x5*x8+m2*m6*m7*x2*x6*x7+m2*m6*m8*x2*x6*x8+m2*m7*m8*x2*x7*x8+m3*m5*m6*x3*x5*x6+m3*m5*m7*x3*x5*x7+m3*m5*m8*x3*x5*x8+m3*m6*m7*x3*x6*x7+m3*m6*m8*x3*x6*x8+m3*m7*m8*x3*x7*x8+m5*m6*m7*x5*x6*x7+m5*m6*m8*x5*x6*x8+m5*m7*m8*x5*x7*x8+m6*m7*m8*x6*x7*x8+m2*m3*x2*x3+m2*m5*x2*x5+m2*m6*x2*x6+m2*m7*x2*x7+m2*m8*x2*x8+m3*m5*x3*x5+m3*m6*x3*x6+m3*m7*x3*x7+m3*m8*x3*x8+m5*m6*x5*x6+m5*m7*x5*x7+m5*m8*x5*x8+m6*m7*x6*x7+m6*m8*x6*x8+m7*m8*x7*x8+m2*x2+m3*x3+m5*x5+m6*x6+m7*x7+m8*x8+1)*m1*s1*x4/m_denom;
 +    #m_elseif n == 5;
 +    prm s##n = -(m7*x7+1)*(m2*m3*m4*x2*x3*x4+m2*m3*x2*x3+m2*m4*x2*x4+m3*m4*x3*x4+m2*x2+m3*x3+m4*x4+1)*s1*m1*(m8*x8+1)*x5*(m6*x6+1)/m_denom;
 +    #m_elseif n == 6;
 +    prm s##n = -(m8*x8+1)*m1*s1*(m2*m3*m4*m5*x2*x3*x4*x5+m2*m3*m4*x2*x3*x4+m2*m3*m5*x2*x3*x5+m2*m4*m5*x2*x4*x5+m3*m4*m5*x3*x4*x5+m2*m3*x2*x3+m2*m4*x2*x4+m2*m5*x2*x5+m3*m4*x3*x4+m3*m5*x3*x5+m4*m5*x4*x5+m2*x2+m3*x3+m4*x4+m5*x5+1)*x6*(m7*x7+1)/m_denom;
 +    #m_elseif n == 7;
 +    prm s##n = -(m2*m3*m4*m5*m6*x2*x3*x4*x5*x6+m2*m3*m4*m5*x2*x3*x4*x5+m2*m3*m4*m6*x2*x3*x4*x6+m2*m3*m5*m6*x2*x3*x5*x6+m2*m4*m5*m6*x2*x4*x5*x6+m3*m4*m5*m6*x3*x4*x5*x6+m2*m3*m4*x2*x3*x4+m2*m3*m5*x2*x3*x5+m2*m3*m6*x2*x3*x6+m2*m4*m5*x2*x4*x5+m2*m4*m6*x2*x4*x6+m2*m5*m6*x2*x5*x6+m3*m4*m5*x3*x4*x5+m3*m4*m6*x3*x4*x6+m3*m5*m6*x3*x5*x6+m4*m5*m6*x4*x5*x6+m2*m3*x2*x3+m2*m4*x2*x4+m2*m5*x2*x5+m2*m6*x2*x6+m3*m4*x3*x4+m3*m5*x3*x5+m3*m6*x3*x6+m4*m5*x4*x5+m4*m6*x4*x6+m5*m6*x5*x6+m2*x2+m3*x3+m4*x4+m5*x5+m6*x6+1)*s1*m1*x7*(m8*x8+1)/m_denom;
 +    #m_elseif n == 8;
 +    prm s##n = -m1*s1*x8*(m2*m3*m4*m5*m6*m7*x2*x3*x4*x5*x6*x7+m2*m3*m4*m5*m6*x2*x3*x4*x5*x6+m2*m3*m4*m5*m7*x2*x3*x4*x5*x7+m2*m3*m4*m6*m7*x2*x3*x4*x6*x7+m2*m3*m5*m6*m7*x2*x3*x5*x6*x7+m2*m4*m5*m6*m7*x2*x4*x5*x6*x7+m3*m4*m5*m6*m7*x3*x4*x5*x6*x7+m2*m3*m4*m5*x2*x3*x4*x5+m2*m3*m4*m6*x2*x3*x4*x6+m2*m3*m4*m7*x2*x3*x4*x7+m2*m3*m5*m6*x2*x3*x5*x6+m2*m3*m5*m7*x2*x3*x5*x7+m2*m3*m6*m7*x2*x3*x6*x7+m2*m4*m5*m6*x2*x4*x5*x6+m2*m4*m5*m7*x2*x4*x5*x7+m2*m4*m6*m7*x2*x4*x6*x7+m2*m5*m6*m7*x2*x5*x6*x7+m3*m4*m5*m6*x3*x4*x5*x6+m3*m4*m5*m7*x3*x4*x5*x7+m3*m4*m6*m7*x3*x4*x6*x7+m3*m5*m6*m7*x3*x5*x6*x7+m4*m5*m6*m7*x4*x5*x6*x7+m2*m3*m4*x2*x3*x4+m2*m3*m5*x2*x3*x5+m2*m3*m6*x2*x3*x6+m2*m3*m7*x2*x3*x7+m2*m4*m5*x2*x4*x5+m2*m4*m6*x2*x4*x6+m2*m4*m7*x2*x4*x7+m2*m5*m6*x2*x5*x6+m2*m5*m7*x2*x5*x7+m2*m6*m7*x2*x6*x7+m3*m4*m5*x3*x4*x5+m3*m4*m6*x3*x4*x6+m3*m4*m7*x3*x4*x7+m3*m5*m6*x3*x5*x6+m3*m5*m7*x3*x5*x7+m3*m6*m7*x3*x6*x7+m4*m5*m6*x4*x5*x6+m4*m5*m7*x4*x5*x7+m4*m6*m7*x4*x6*x7+m5*m6*m7*x5*x6*x7+m2*m3*x2*x3+m2*m4*x2*x4+m2*m5*x2*x5+m2*m6*x2*x6+m2*m7*x2*x7+m3*m4*x3*x4+m3*m5*x3*x5+m3*m6*x3*x6+m3*m7*x3*x7+m4*m5*x4*x5+m4*m6*x4*x6+m4*m7*x4*x7+m5*m6*x5*x6+m5*m7*x5*x7+m6*m7*x6*x7+m2*x2+m3*x3+m4*x4+m5*x5+m6*x6+m7*x7+1)/m_denom;
 +    #m_endif
 +
 +   #m_elseif p == 9;
 +    #m_if n == 1;
 +    prm m_denom = 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 +    #m_elseif n == 2;
 +    prm s##n = -x2*s1*m1*(m3*m4*m5*m6*m7*m8*m9*x3*x4*x5*x6*x7*x8*x9+m3*m4*m5*m6*m7*m8*x3*x4*x5*x6*x7*x8+m3*m4*m5*m6*m7*m9*x3*x4*x5*x6*x7*x9+m3*m4*m5*m6*m8*m9*x3*x4*x5*x6*x8*x9+m3*m4*m5*m7*m8*m9*x3*x4*x5*x7*x8*x9+m3*m4*m6*m7*m8*m9*x3*x4*x6*x7*x8*x9+m3*m5*m6*m7*m8*m9*x3*x5*x6*x7*x8*x9+m4*m5*m6*m7*m8*m9*x4*x5*x6*x7*x8*x9+m3*m4*m5*m6*m7*x3*x4*x5*x6*x7+m3*m4*m5*m6*m8*x3*x4*x5*x6*x8+m3*m4*m5*m6*m9*x3*x4*x5*x6*x9+m3*m4*m5*m7*m8*x3*x4*x5*x7*x8+m3*m4*m5*m7*m9*x3*x4*x5*x7*x9+m3*m4*m5*m8*m9*x3*x4*x5*x8*x9+m3*m4*m6*m7*m8*x3*x4*x6*x7*x8+m3*m4*m6*m7*m9*x3*x4*x6*x7*x9+m3*m4*m6*m8*m9*x3*x4*x6*x8*x9+m3*m4*m7*m8*m9*x3*x4*x7*x8*x9+m3*m5*m6*m7*m8*x3*x5*x6*x7*x8+m3*m5*m6*m7*m9*x3*x5*x6*x7*x9+m3*m5*m6*m8*m9*x3*x5*x6*x8*x9+m3*m5*m7*m8*m9*x3*x5*x7*x8*x9+m3*m6*m7*m8*m9*x3*x6*x7*x8*x9+m4*m5*m6*m7*m8*x4*x5*x6*x7*x8+m4*m5*m6*m7*m9*x4*x5*x6*x7*x9+m4*m5*m6*m8*m9*x4*x5*x6*x8*x9+m4*m5*m7*m8*m9*x4*x5*x7*x8*x9+m4*m6*m7*m8*m9*x4*x6*x7*x8*x9+m5*m6*m7*m8*m9*x5*x6*x7*x8*x9+m3*m4*m5*m6*x3*x4*x5*x6+m3*m4*m5*m7*x3*x4*x5*x7+m3*m4*m5*m8*x3*x4*x5*x8+m3*m4*m5*m9*x3*x4*x5*x9+m3*m4*m6*m7*x3*x4*x6*x7+m3*m4*m6*m8*x3*x4*x6*x8+m3*m4*m6*m9*x3*x4*x6*x9+m3*m4*m7*m8*x3*x4*x7*x8+m3*m4*m7*m9*x3*x4*x7*x9+m3*m4*m8*m9*x3*x4*x8*x9+m3*m5*m6*m7*x3*x5*x6*x7+m3*m5*m6*m8*x3*x5*x6*x8+m3*m5*m6*m9*x3*x5*x6*x9+m3*m5*m7*m8*x3*x5*x7*x8+m3*m5*m7*m9*x3*x5*x7*x9+m3*m5*m8*m9*x3*x5*x8*x9+m3*m6*m7*m8*x3*x6*x7*x8+m3*m6*m7*m9*x3*x6*x7*x9+m3*m6*m8*m9*x3*x6*x8*x9+m3*m7*m8*m9*x3*x7*x8*x9+m4*m5*m6*m7*x4*x5*x6*x7+m4*m5*m6*m8*x4*x5*x6*x8+m4*m5*m6*m9*x4*x5*x6*x9+m4*m5*m7*m8*x4*x5*x7*x8+m4*m5*m7*m9*x4*x5*x7*x9+m4*m5*m8*m9*x4*x5*x8*x9+m4*m6*m7*m8*x4*x6*x7*x8+m4*m6*m7*m9*x4*x6*x7*x9+m4*m6*m8*m9*x4*x6*x8*x9+m4*m7*m8*m9*x4*x7*x8*x9+m5*m6*m7*m8*x5*x6*x7*x8+m5*m6*m7*m9*x5*x6*x7*x9+m5*m6*m8*m9*x5*x6*x8*x9+m5*m7*m8*m9*x5*x7*x8*x9+m6*m7*m8*m9*x6*x7*x8*x9+m3*m4*m5*x3*x4*x5+m3*m4*m6*x3*x4*x6+m3*m4*m7*x3*x4*x7+m3*m4*m8*x3*x4*x8+m3*m4*m9*x3*x4*x9+m3*m5*m6*x3*x5*x6+m3*m5*m7*x3*x5*x7+m3*m5*m8*x3*x5*x8+m3*m5*m9*x3*x5*x9+m3*m6*m7*x3*x6*x7+m3*m6*m8*x3*x6*x8+m3*m6*m9*x3*x6*x9+m3*m7*m8*x3*x7*x8+m3*m7*m9*x3*x7*x9+m3*m8*m9*x3*x8*x9+m4*m5*m6*x4*x5*x6+m4*m5*m7*x4*x5*x7+m4*m5*m8*x4*x5*x8+m4*m5*m9*x4*x5*x9+m4*m6*m7*x4*x6*x7+m4*m6*m8*x4*x6*x8+m4*m6*m9*x4*x6*x9+m4*m7*m8*x4*x7*x8+m4*m7*m9*x4*x7*x9+m4*m8*m9*x4*x8*x9+m5*m6*m7*x5*x6*x7+m5*m6*m8*x5*x6*x8+m5*m6*m9*x5*x6*x9+m5*m7*m8*x5*x7*x8+m5*m7*m9*x5*x7*x9+m5*m8*m9*x5*x8*x9+m6*m7*m8*x6*x7*x8+m6*m7*m9*x6*x7*x9+m6*m8*m9*x6*x8*x9+m7*m8*m9*x7*x8*x9+m3*m4*x3*x4+m3*m5*x3*x5+m3*m6*x3*x6+m3*m7*x3*x7+m3*m8*x3*x8+m3*m9*x3*x9+m4*m5*x4*x5+m4*m6*x4*x6+m4*m7*x4*x7+m4*m8*x4*x8+m4*m9*x4*x9+m5*m6*x5*x6+m5*m7*x5*x7+m5*m8*x5*x8+m5*m9*x5*x9+m6*m7*x6*x7+m6*m8*x6*x8+m6*m9*x6*x9+m7*m8*x7*x8+m7*m9*x7*x9+m8*m9*x8*x9+m3*x3+m4*x4+m5*x5+m6*x6+m7*x7+m8*x8+m9*x9+1)/m_denom;
 +    #m_elseif n == 3;
 +    prm s##n = -(m2*m4*m5*m6*m7*m8*m9*x2*x4*x5*x6*x7*x8*x9+m2*m4*m5*m6*m7*m8*x2*x4*x5*x6*x7*x8+m2*m4*m5*m6*m7*m9*x2*x4*x5*x6*x7*x9+m2*m4*m5*m6*m8*m9*x2*x4*x5*x6*x8*x9+m2*m4*m5*m7*m8*m9*x2*x4*x5*x7*x8*x9+m2*m4*m6*m7*m8*m9*x2*x4*x6*x7*x8*x9+m2*m5*m6*m7*m8*m9*x2*x5*x6*x7*x8*x9+m4*m5*m6*m7*m8*m9*x4*x5*x6*x7*x8*x9+m2*m4*m5*m6*m7*x2*x4*x5*x6*x7+m2*m4*m5*m6*m8*x2*x4*x5*x6*x8+m2*m4*m5*m6*m9*x2*x4*x5*x6*x9+m2*m4*m5*m7*m8*x2*x4*x5*x7*x8+m2*m4*m5*m7*m9*x2*x4*x5*x7*x9+m2*m4*m5*m8*m9*x2*x4*x5*x8*x9+m2*m4*m6*m7*m8*x2*x4*x6*x7*x8+m2*m4*m6*m7*m9*x2*x4*x6*x7*x9+m2*m4*m6*m8*m9*x2*x4*x6*x8*x9+m2*m4*m7*m8*m9*x2*x4*x7*x8*x9+m2*m5*m6*m7*m8*x2*x5*x6*x7*x8+m2*m5*m6*m7*m9*x2*x5*x6*x7*x9+m2*m5*m6*m8*m9*x2*x5*x6*x8*x9+m2*m5*m7*m8*m9*x2*x5*x7*x8*x9+m2*m6*m7*m8*m9*x2*x6*x7*x8*x9+m4*m5*m6*m7*m8*x4*x5*x6*x7*x8+m4*m5*m6*m7*m9*x4*x5*x6*x7*x9+m4*m5*m6*m8*m9*x4*x5*x6*x8*x9+m4*m5*m7*m8*m9*x4*x5*x7*x8*x9+m4*m6*m7*m8*m9*x4*x6*x7*x8*x9+m5*m6*m7*m8*m9*x5*x6*x7*x8*x9+m2*m4*m5*m6*x2*x4*x5*x6+m2*m4*m5*m7*x2*x4*x5*x7+m2*m4*m5*m8*x2*x4*x5*x8+m2*m4*m5*m9*x2*x4*x5*x9+m2*m4*m6*m7*x2*x4*x6*x7+m2*m4*m6*m8*x2*x4*x6*x8+m2*m4*m6*m9*x2*x4*x6*x9+m2*m4*m7*m8*x2*x4*x7*x8+m2*m4*m7*m9*x2*x4*x7*x9+m2*m4*m8*m9*x2*x4*x8*x9+m2*m5*m6*m7*x2*x5*x6*x7+m2*m5*m6*m8*x2*x5*x6*x8+m2*m5*m6*m9*x2*x5*x6*x9+m2*m5*m7*m8*x2*x5*x7*x8+m2*m5*m7*m9*x2*x5*x7*x9+m2*m5*m8*m9*x2*x5*x8*x9+m2*m6*m7*m8*x2*x6*x7*x8+m2*m6*m7*m9*x2*x6*x7*x9+m2*m6*m8*m9*x2*x6*x8*x9+m2*m7*m8*m9*x2*x7*x8*x9+m4*m5*m6*m7*x4*x5*x6*x7+m4*m5*m6*m8*x4*x5*x6*x8+m4*m5*m6*m9*x4*x5*x6*x9+m4*m5*m7*m8*x4*x5*x7*x8+m4*m5*m7*m9*x4*x5*x7*x9+m4*m5*m8*m9*x4*x5*x8*x9+m4*m6*m7*m8*x4*x6*x7*x8+m4*m6*m7*m9*x4*x6*x7*x9+m4*m6*m8*m9*x4*x6*x8*x9+m4*m7*m8*m9*x4*x7*x8*x9+m5*m6*m7*m8*x5*x6*x7*x8+m5*m6*m7*m9*x5*x6*x7*x9+m5*m6*m8*m9*x5*x6*x8*x9+m5*m7*m8*m9*x5*x7*x8*x9+m6*m7*m8*m9*x6*x7*x8*x9+m2*m4*m5*x2*x4*x5+m2*m4*m6*x2*x4*x6+m2*m4*m7*x2*x4*x7+m2*m4*m8*x2*x4*x8+m2*m4*m9*x2*x4*x9+m2*m5*m6*x2*x5*x6+m2*m5*m7*x2*x5*x7+m2*m5*m8*x2*x5*x8+m2*m5*m9*x2*x5*x9+m2*m6*m7*x2*x6*x7+m2*m6*m8*x2*x6*x8+m2*m6*m9*x2*x6*x9+m2*m7*m8*x2*x7*x8+m2*m7*m9*x2*x7*x9+m2*m8*m9*x2*x8*x9+m4*m5*m6*x4*x5*x6+m4*m5*m7*x4*x5*x7+m4*m5*m8*x4*x5*x8+m4*m5*m9*x4*x5*x9+m4*m6*m7*x4*x6*x7+m4*m6*m8*x4*x6*x8+m4*m6*m9*x4*x6*x9+m4*m7*m8*x4*x7*x8+m4*m7*m9*x4*x7*x9+m4*m8*m9*x4*x8*x9+m5*m6*m7*x5*x6*x7+m5*m6*m8*x5*x6*x8+m5*m6*m9*x5*x6*x9+m5*m7*m8*x5*x7*x8+m5*m7*m9*x5*x7*x9+m5*m8*m9*x5*x8*x9+m6*m7*m8*x6*x7*x8+m6*m7*m9*x6*x7*x9+m6*m8*m9*x6*x8*x9+m7*m8*m9*x7*x8*x9+m2*m4*x2*x4+m2*m5*x2*x5+m2*m6*x2*x6+m2*m7*x2*x7+m2*m8*x2*x8+m2*m9*x2*x9+m4*m5*x4*x5+m4*m6*x4*x6+m4*m7*x4*x7+m4*m8*x4*x8+m4*m9*x4*x9+m5*m6*x5*x6+m5*m7*x5*x7+m5*m8*x5*x8+m5*m9*x5*x9+m6*m7*x6*x7+m6*m8*x6*x8+m6*m9*x6*x9+m7*m8*x7*x8+m7*m9*x7*x9+m8*m9*x8*x9+m2*x2+m4*x4+m5*x5+m6*x6+m7*x7+m8*x8+m9*x9+1)*x3*s1*m1/m_denom;
 +    #m_elseif n == 4;
 +    prm s##n = -(m2*m3*m5*m6*m7*m8*m9*x2*x3*x5*x6*x7*x8*x9+m2*m3*m5*m6*m7*m8*x2*x3*x5*x6*x7*x8+m2*m3*m5*m6*m7*m9*x2*x3*x5*x6*x7*x9+m2*m3*m5*m6*m8*m9*x2*x3*x5*x6*x8*x9+m2*m3*m5*m7*m8*m9*x2*x3*x5*x7*x8*x9+m2*m3*m6*m7*m8*m9*x2*x3*x6*x7*x8*x9+m2*m5*m6*m7*m8*m9*x2*x5*x6*x7*x8*x9+m3*m5*m6*m7*m8*m9*x3*x5*x6*x7*x8*x9+m2*m3*m5*m6*m7*x2*x3*x5*x6*x7+m2*m3*m5*m6*m8*x2*x3*x5*x6*x8+m2*m3*m5*m6*m9*x2*x3*x5*x6*x9+m2*m3*m5*m7*m8*x2*x3*x5*x7*x8+m2*m3*m5*m7*m9*x2*x3*x5*x7*x9+m2*m3*m5*m8*m9*x2*x3*x5*x8*x9+m2*m3*m6*m7*m8*x2*x3*x6*x7*x8+m2*m3*m6*m7*m9*x2*x3*x6*x7*x9+m2*m3*m6*m8*m9*x2*x3*x6*x8*x9+m2*m3*m7*m8*m9*x2*x3*x7*x8*x9+m2*m5*m6*m7*m8*x2*x5*x6*x7*x8+m2*m5*m6*m7*m9*x2*x5*x6*x7*x9+m2*m5*m6*m8*m9*x2*x5*x6*x8*x9+m2*m5*m7*m8*m9*x2*x5*x7*x8*x9+m2*m6*m7*m8*m9*x2*x6*x7*x8*x9+m3*m5*m6*m7*m8*x3*x5*x6*x7*x8+m3*m5*m6*m7*m9*x3*x5*x6*x7*x9+m3*m5*m6*m8*m9*x3*x5*x6*x8*x9+m3*m5*m7*m8*m9*x3*x5*x7*x8*x9+m3*m6*m7*m8*m9*x3*x6*x7*x8*x9+m5*m6*m7*m8*m9*x5*x6*x7*x8*x9+m2*m3*m5*m6*x2*x3*x5*x6+m2*m3*m5*m7*x2*x3*x5*x7+m2*m3*m5*m8*x2*x3*x5*x8+m2*m3*m5*m9*x2*x3*x5*x9+m2*m3*m6*m7*x2*x3*x6*x7+m2*m3*m6*m8*x2*x3*x6*x8+m2*m3*m6*m9*x2*x3*x6*x9+m2*m3*m7*m8*x2*x3*x7*x8+m2*m3*m7*m9*x2*x3*x7*x9+m2*m3*m8*m9*x2*x3*x8*x9+m2*m5*m6*m7*x2*x5*x6*x7+m2*m5*m6*m8*x2*x5*x6*x8+m2*m5*m6*m9*x2*x5*x6*x9+m2*m5*m7*m8*x2*x5*x7*x8+m2*m5*m7*m9*x2*x5*x7*x9+m2*m5*m8*m9*x2*x5*x8*x9+m2*m6*m7*m8*x2*x6*x7*x8+m2*m6*m7*m9*x2*x6*x7*x9+m2*m6*m8*m9*x2*x6*x8*x9+m2*m7*m8*m9*x2*x7*x8*x9+m3*m5*m6*m7*x3*x5*x6*x7+m3*m5*m6*m8*x3*x5*x6*x8+m3*m5*m6*m9*x3*x5*x6*x9+m3*m5*m7*m8*x3*x5*x7*x8+m3*m5*m7*m9*x3*x5*x7*x9+m3*m5*m8*m9*x3*x5*x8*x9+m3*m6*m7*m8*x3*x6*x7*x8+m3*m6*m7*m9*x3*x6*x7*x9+m3*m6*m8*m9*x3*x6*x8*x9+m3*m7*m8*m9*x3*x7*x8*x9+m5*m6*m7*m8*x5*x6*x7*x8+m5*m6*m7*m9*x5*x6*x7*x9+m5*m6*m8*m9*x5*x6*x8*x9+m5*m7*m8*m9*x5*x7*x8*x9+m6*m7*m8*m9*x6*x7*x8*x9+m2*m3*m5*x2*x3*x5+m2*m3*m6*x2*x3*x6+m2*m3*m7*x2*x3*x7+m2*m3*m8*x2*x3*x8+m2*m3*m9*x2*x3*x9+m2*m5*m6*x2*x5*x6+m2*m5*m7*x2*x5*x7+m2*m5*m8*x2*x5*x8+m2*m5*m9*x2*x5*x9+m2*m6*m7*x2*x6*x7+m2*m6*m8*x2*x6*x8+m2*m6*m9*x2*x6*x9+m2*m7*m8*x2*x7*x8+m2*m7*m9*x2*x7*x9+m2*m8*m9*x2*x8*x9+m3*m5*m6*x3*x5*x6+m3*m5*m7*x3*x5*x7+m3*m5*m8*x3*x5*x8+m3*m5*m9*x3*x5*x9+m3*m6*m7*x3*x6*x7+m3*m6*m8*x3*x6*x8+m3*m6*m9*x3*x6*x9+m3*m7*m8*x3*x7*x8+m3*m7*m9*x3*x7*x9+m3*m8*m9*x3*x8*x9+m5*m6*m7*x5*x6*x7+m5*m6*m8*x5*x6*x8+m5*m6*m9*x5*x6*x9+m5*m7*m8*x5*x7*x8+m5*m7*m9*x5*x7*x9+m5*m8*m9*x5*x8*x9+m6*m7*m8*x6*x7*x8+m6*m7*m9*x6*x7*x9+m6*m8*m9*x6*x8*x9+m7*m8*m9*x7*x8*x9+m2*m3*x2*x3+m2*m5*x2*x5+m2*m6*x2*x6+m2*m7*x2*x7+m2*m8*x2*x8+m2*m9*x2*x9+m3*m5*x3*x5+m3*m6*x3*x6+m3*m7*x3*x7+m3*m8*x3*x8+m3*m9*x3*x9+m5*m6*x5*x6+m5*m7*x5*x7+m5*m8*x5*x8+m5*m9*x5*x9+m6*m7*x6*x7+m6*m8*x6*x8+m6*m9*x6*x9+m7*m8*x7*x8+m7*m9*x7*x9+m8*m9*x8*x9+m2*x2+m3*x3+m5*x5+m6*x6+m7*x7+m8*x8+m9*x9+1)*m1*s1*x4/m_denom;
 +    #m_elseif n == 5;
 +    prm s##n = -(m7*x7+1)*(m9*x9+1)*s1*m1*(m2*m3*m4*x2*x3*x4+m2*m3*x2*x3+m2*m4*x2*x4+m3*m4*x3*x4+m2*x2+m3*x3+m4*x4+1)*(m8*x8+1)*x5*(m6*x6+1)/m_denom;
 +    #m_elseif n == 6;
 +    prm s##n = -(m8*x8+1)*(m2*m3*m4*m5*x2*x3*x4*x5+m2*m3*m4*x2*x3*x4+m2*m3*m5*x2*x3*x5+m2*m4*m5*x2*x4*x5+m3*m4*m5*x3*x4*x5+m2*m3*x2*x3+m2*m4*x2*x4+m2*m5*x2*x5+m3*m4*x3*x4+m3*m5*x3*x5+m4*m5*x4*x5+m2*x2+m3*x3+m4*x4+m5*x5+1)*m1*s1*(m9*x9+1)*x6*(m7*x7+1)/m_denom;
 +    #m_elseif n == 7;
 +    prm s##n = -(m9*x9+1)*s1*m1*(m2*m3*m4*m5*m6*x2*x3*x4*x5*x6+m2*m3*m4*m5*x2*x3*x4*x5+m2*m3*m4*m6*x2*x3*x4*x6+m2*m3*m5*m6*x2*x3*x5*x6+m2*m4*m5*m6*x2*x4*x5*x6+m3*m4*m5*m6*x3*x4*x5*x6+m2*m3*m4*x2*x3*x4+m2*m3*m5*x2*x3*x5+m2*m3*m6*x2*x3*x6+m2*m4*m5*x2*x4*x5+m2*m4*m6*x2*x4*x6+m2*m5*m6*x2*x5*x6+m3*m4*m5*x3*x4*x5+m3*m4*m6*x3*x4*x6+m3*m5*m6*x3*x5*x6+m4*m5*m6*x4*x5*x6+m2*m3*x2*x3+m2*m4*x2*x4+m2*m5*x2*x5+m2*m6*x2*x6+m3*m4*x3*x4+m3*m5*x3*x5+m3*m6*x3*x6+m4*m5*x4*x5+m4*m6*x4*x6+m5*m6*x5*x6+m2*x2+m3*x3+m4*x4+m5*x5+m6*x6+1)*x7*(m8*x8+1)/m_denom;
 +    #m_elseif n == 8;
 +    prm s##n = -(m2*m3*m4*m5*m6*m7*x2*x3*x4*x5*x6*x7+m2*m3*m4*m5*m6*x2*x3*x4*x5*x6+m2*m3*m4*m5*m7*x2*x3*x4*x5*x7+m2*m3*m4*m6*m7*x2*x3*x4*x6*x7+m2*m3*m5*m6*m7*x2*x3*x5*x6*x7+m2*m4*m5*m6*m7*x2*x4*x5*x6*x7+m3*m4*m5*m6*m7*x3*x4*x5*x6*x7+m2*m3*m4*m5*x2*x3*x4*x5+m2*m3*m4*m6*x2*x3*x4*x6+m2*m3*m4*m7*x2*x3*x4*x7+m2*m3*m5*m6*x2*x3*x5*x6+m2*m3*m5*m7*x2*x3*x5*x7+m2*m3*m6*m7*x2*x3*x6*x7+m2*m4*m5*m6*x2*x4*x5*x6+m2*m4*m5*m7*x2*x4*x5*x7+m2*m4*m6*m7*x2*x4*x6*x7+m2*m5*m6*m7*x2*x5*x6*x7+m3*m4*m5*m6*x3*x4*x5*x6+m3*m4*m5*m7*x3*x4*x5*x7+m3*m4*m6*m7*x3*x4*x6*x7+m3*m5*m6*m7*x3*x5*x6*x7+m4*m5*m6*m7*x4*x5*x6*x7+m2*m3*m4*x2*x3*x4+m2*m3*m5*x2*x3*x5+m2*m3*m6*x2*x3*x6+m2*m3*m7*x2*x3*x7+m2*m4*m5*x2*x4*x5+m2*m4*m6*x2*x4*x6+m2*m4*m7*x2*x4*x7+m2*m5*m6*x2*x5*x6+m2*m5*m7*x2*x5*x7+m2*m6*m7*x2*x6*x7+m3*m4*m5*x3*x4*x5+m3*m4*m6*x3*x4*x6+m3*m4*m7*x3*x4*x7+m3*m5*m6*x3*x5*x6+m3*m5*m7*x3*x5*x7+m3*m6*m7*x3*x6*x7+m4*m5*m6*x4*x5*x6+m4*m5*m7*x4*x5*x7+m4*m6*m7*x4*x6*x7+m5*m6*m7*x5*x6*x7+m2*m3*x2*x3+m2*m4*x2*x4+m2*m5*x2*x5+m2*m6*x2*x6+m2*m7*x2*x7+m3*m4*x3*x4+m3*m5*x3*x5+m3*m6*x3*x6+m3*m7*x3*x7+m4*m5*x4*x5+m4*m6*x4*x6+m4*m7*x4*x7+m5*m6*x5*x6+m5*m7*x5*x7+m6*m7*x6*x7+m2*x2+m3*x3+m4*x4+m5*x5+m6*x6+m7*x7+1)*m1*s1*x8*(m9*x9+1)/m_denom;
 +    #m_elseif n == 9;
 +    prm s##n = -x9*s1*m1*(m2*m3*m4*m5*m6*m7*m8*x2*x3*x4*x5*x6*x7*x8+m2*m3*m4*m5*m6*m7*x2*x3*x4*x5*x6*x7+m2*m3*m4*m5*m6*m8*x2*x3*x4*x5*x6*x8+m2*m3*m4*m5*m7*m8*x2*x3*x4*x5*x7*x8+m2*m3*m4*m6*m7*m8*x2*x3*x4*x6*x7*x8+m2*m3*m5*m6*m7*m8*x2*x3*x5*x6*x7*x8+m2*m4*m5*m6*m7*m8*x2*x4*x5*x6*x7*x8+m3*m4*m5*m6*m7*m8*x3*x4*x5*x6*x7*x8+m2*m3*m4*m5*m6*x2*x3*x4*x5*x6+m2*m3*m4*m5*m7*x2*x3*x4*x5*x7+m2*m3*m4*m5*m8*x2*x3*x4*x5*x8+m2*m3*m4*m6*m7*x2*x3*x4*x6*x7+m2*m3*m4*m6*m8*x2*x3*x4*x6*x8+m2*m3*m4*m7*m8*x2*x3*x4*x7*x8+m2*m3*m5*m6*m7*x2*x3*x5*x6*x7+m2*m3*m5*m6*m8*x2*x3*x5*x6*x8+m2*m3*m5*m7*m8*x2*x3*x5*x7*x8+m2*m3*m6*m7*m8*x2*x3*x6*x7*x8+m2*m4*m5*m6*m7*x2*x4*x5*x6*x7+m2*m4*m5*m6*m8*x2*x4*x5*x6*x8+m2*m4*m5*m7*m8*x2*x4*x5*x7*x8+m2*m4*m6*m7*m8*x2*x4*x6*x7*x8+m2*m5*m6*m7*m8*x2*x5*x6*x7*x8+m3*m4*m5*m6*m7*x3*x4*x5*x6*x7+m3*m4*m5*m6*m8*x3*x4*x5*x6*x8+m3*m4*m5*m7*m8*x3*x4*x5*x7*x8+m3*m4*m6*m7*m8*x3*x4*x6*x7*x8+m3*m5*m6*m7*m8*x3*x5*x6*x7*x8+m4*m5*m6*m7*m8*x4*x5*x6*x7*x8+m2*m3*m4*m5*x2*x3*x4*x5+m2*m3*m4*m6*x2*x3*x4*x6+m2*m3*m4*m7*x2*x3*x4*x7+m2*m3*m4*m8*x2*x3*x4*x8+m2*m3*m5*m6*x2*x3*x5*x6+m2*m3*m5*m7*x2*x3*x5*x7+m2*m3*m5*m8*x2*x3*x5*x8+m2*m3*m6*m7*x2*x3*x6*x7+m2*m3*m6*m8*x2*x3*x6*x8+m2*m3*m7*m8*x2*x3*x7*x8+m2*m4*m5*m6*x2*x4*x5*x6+m2*m4*m5*m7*x2*x4*x5*x7+m2*m4*m5*m8*x2*x4*x5*x8+m2*m4*m6*m7*x2*x4*x6*x7+m2*m4*m6*m8*x2*x4*x6*x8+m2*m4*m7*m8*x2*x4*x7*x8+m2*m5*m6*m7*x2*x5*x6*x7+m2*m5*m6*m8*x2*x5*x6*x8+m2*m5*m7*m8*x2*x5*x7*x8+m2*m6*m7*m8*x2*x6*x7*x8+m3*m4*m5*m6*x3*x4*x5*x6+m3*m4*m5*m7*x3*x4*x5*x7+m3*m4*m5*m8*x3*x4*x5*x8+m3*m4*m6*m7*x3*x4*x6*x7+m3*m4*m6*m8*x3*x4*x6*x8+m3*m4*m7*m8*x3*x4*x7*x8+m3*m5*m6*m7*x3*x5*x6*x7+m3*m5*m6*m8*x3*x5*x6*x8+m3*m5*m7*m8*x3*x5*x7*x8+m3*m6*m7*m8*x3*x6*x7*x8+m4*m5*m6*m7*x4*x5*x6*x7+m4*m5*m6*m8*x4*x5*x6*x8+m4*m5*m7*m8*x4*x5*x7*x8+m4*m6*m7*m8*x4*x6*x7*x8+m5*m6*m7*m8*x5*x6*x7*x8+m2*m3*m4*x2*x3*x4+m2*m3*m5*x2*x3*x5+m2*m3*m6*x2*x3*x6+m2*m3*m7*x2*x3*x7+m2*m3*m8*x2*x3*x8+m2*m4*m5*x2*x4*x5+m2*m4*m6*x2*x4*x6+m2*m4*m7*x2*x4*x7+m2*m4*m8*x2*x4*x8+m2*m5*m6*x2*x5*x6+m2*m5*m7*x2*x5*x7+m2*m5*m8*x2*x5*x8+m2*m6*m7*x2*x6*x7+m2*m6*m8*x2*x6*x8+m2*m7*m8*x2*x7*x8+m3*m4*m5*x3*x4*x5+m3*m4*m6*x3*x4*x6+m3*m4*m7*x3*x4*x7+m3*m4*m8*x3*x4*x8+m3*m5*m6*x3*x5*x6+m3*m5*m7*x3*x5*x7+m3*m5*m8*x3*x5*x8+m3*m6*m7*x3*x6*x7+m3*m6*m8*x3*x6*x8+m3*m7*m8*x3*x7*x8+m4*m5*m6*x4*x5*x6+m4*m5*m7*x4*x5*x7+m4*m5*m8*x4*x5*x8+m4*m6*m7*x4*x6*x7+m4*m6*m8*x4*x6*x8+m4*m7*m8*x4*x7*x8+m5*m6*m7*x5*x6*x7+m5*m6*m8*x5*x6*x8+m5*m7*m8*x5*x7*x8+m6*m7*m8*x6*x7*x8+m2*m3*x2*x3+m2*m4*x2*x4+m2*m5*x2*x5+m2*m6*x2*x6+m2*m7*x2*x7+m2*m8*x2*x8+m3*m4*x3*x4+m3*m5*x3*x5+m3*m6*x3*x6+m3*m7*x3*x7+m3*m8*x3*x8+m4*m5*x4*x5+m4*m6*x4*x6+m4*m7*x4*x7+m4*m8*x4*x8+m5*m6*x5*x6+m5*m7*x5*x7+m5*m8*x5*x8+m6*m7*x6*x7+m6*m8*x6*x8+m7*m8*x7*x8+m2*x2+m3*x3+m4*x4+m5*x5+m6*x6+m7*x7+m8*x8+1)/m_denom;
 +    #m_endif
 +   
 +   
 +   #m_endif
 +   
 +   scale = s##n; : sc
 +}
 +</code>