refine_weight_percentage
Differences
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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: | ||
+ | |||
+ | 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, | ||
+ | </ | ||
+ | where | ||
+ | < | ||
+ | mn = cell_mass * cell_volume | ||
+ | xn = wn / (mn (100 - wn)) | ||
+ | </ | ||
+ | |||
+ | ===== To use the macro ===== | ||
+ | |||
+ | The first phase must have a scale factor: s1. | ||
+ | The remaining phases must have weight percentages: | ||
+ | |||
+ | 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 '' | ||
+ | prm !w2 20 | ||
+ | prm w3 30 | ||
+ | prm w4 30 | ||
+ | |||
+ | str | ||
+ | wt_dets(1, | ||
+ | str | ||
+ | wt_dets(2, | ||
+ | str | ||
+ | wt_dets(3, | ||
+ | str | ||
+ | wt_dets(4, | ||
+ | </ | ||
+ | |||
+ | |||
+ | <code topas> | ||
+ | macro wt_dets(n, | ||
+ | macro wt_dets(n, | ||
+ | { | ||
+ | prm m##n = Get(cell_mass) Get(cell_volume); | ||
+ | prm x##n = w##n / (m##n (100 - w##n)); | ||
+ | |||
+ | |||
+ | #m_if p == 2; '' | ||
+ | | ||
+ | | ||
+ | | ||
+ | prm s##n = x2*s1*m1; | ||
+ | | ||
+ | |||
+ | # | ||
+ | | ||
+ | prm m_denom = (m2*m3*x2*x3-1); | ||
+ | | ||
+ | prm s##n = -m1*s1*x2*(m3*x3+1)/ | ||
+ | | ||
+ | prm s##n = -m1*s1*x3*(m2*x2+1)/ | ||
+ | | ||
+ | |||
+ | # | ||
+ | | ||
+ | prm m_denom = (2*m2*m3*m4*x2*x3*x4+m2*m3*x2*x3+m2*m4*x2*x4+m3*m4*x3*x4-1); | ||
+ | | ||
+ | prm s##n = -m1*s1*x2*(m3*m4*x3*x4+m3*x3+m4*x4+1)/ | ||
+ | | ||
+ | prm s##n = -m1*s1*x3*(m2*m4*x2*x4+m2*x2+m4*x4+1)/ | ||
+ | | ||
+ | prm s##n = -m1*s1*x4*(m2*m3*x2*x3+m2*x2+m3*x3+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); | ||
+ | | ||
+ | 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)/ | ||
+ | | ||
+ | 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)/ | ||
+ | | ||
+ | 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)/ | ||
+ | | ||
+ | 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)/ | ||
+ | | ||
+ | |||
+ | # | ||
+ | | ||
+ | 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); | ||
+ | | ||
+ | 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)/ | ||
+ | | ||
+ | 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)/ | ||
+ | | ||
+ | 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)/ | ||
+ | | ||
+ | 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)/ | ||
+ | | ||
+ | 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)/ | ||
+ | | ||
+ | |||
+ | # | ||
+ | | ||
+ | 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); | ||
+ | | ||
+ | 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/ | ||
+ | | ||
+ | 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/ | ||
+ | | ||
+ | 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)/ | ||
+ | | ||
+ | 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)/ | ||
+ | | ||
+ | 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)/ | ||
+ | | ||
+ | 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)/ | ||
+ | | ||
+ | |||
+ | # | ||
+ | | ||
+ | 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); | ||
+ | | ||
+ | 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)/ | ||
+ | | ||
+ | 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/ | ||
+ | | ||
+ | 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/ | ||
+ | | ||
+ | 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)/ | ||
+ | | ||
+ | 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)/ | ||
+ | | ||
+ | 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)/ | ||
+ | | ||
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+ | | ||
+ | |||
+ | # | ||
+ | | ||
+ | prm m_denom = 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| ||
+ | | ||
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+ | | ||
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+ | | ||
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+ | | ||
+ | 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)/ | ||
+ | | ||
+ | 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)/ | ||
+ | | ||
+ | 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)/ | ||
+ | | ||
+ | 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)/ | ||
+ | | ||
+ | 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)/ | ||
+ | | ||
+ | |||
+ | |||
+ | # | ||
+ | |||
+ | scale = s##n; : sc | ||
+ | } | ||
+ | </ |