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 help from Alan

The equations were calculated in Maple from the standard Hill/Howard quantification algorithm.

The Maple syntax used was

> 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]);

where

mn = cell_mass * cell_volume
xn = wn / (mn (100 - wn))

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

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)

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
}