cleanF7_list := [9.*x-1.*y+8.*z-19.*x^3*y+32.*x^3*z+14.*y*z-24.*x^4-8.*x^3-32.
*x^2*y*z-20.*y^2+5.*z^2+7.*x^2+23.*y^3-4.*z^3-14.*x^2*y^2-8.*x^2*y+33.*x^2*z^2
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^4+4.*z^4-33.*z^4*y+28.*z^4*y^3-24.*z^5*y+22.*z^6*y+11.*z^7*y-42.*z^4*y^2+41.*
z^4*y^4+43.*z^5*y^3+29.*z^6*y^2+45.*z^5*y^2+36.*z*y^4+59.*y^3*z^2+33.*y^2*z^3-\
6.*y^5*z+9.*y^3*z^3+7.*y^6*z-24.*y^5*z^2-14.*y^4*z^3+39.*y^4*z^2+5.*z^7-16.*z^
5+2.*z^8-8.*z^6-25.*y^5-13.*y^7+28.*y^6+3.*y^8+24.*y^5*z^3-2.*y^7*z+9.*y^6*z^2
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35.*x*y^3*z-34.*x*y^2*z^2+14.*x*z^4*y+3.*x*z^4*y^3+8.*x*z^5*y-16.*x*z^6*y-21.*
x*z^4*y^2-13.*x*z^5*y^2+26.*x*z*y^4-90.*x*y^3*z^2+40.*x*y^2*z^3+15.*x*y^5*z+98\
.*x*y^3*z^3+23.*x*y^6*z+39.*x*y^5*z^2-2.*x*y^4*z^3+90.*x*y^4*z^2+63.*x^2*y^2*z
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^2*z^5*y-53.*x^2*z^4*y^2+20.*x^2*z*y^4-68.*x^2*y^3*z^2-5.*x^2*y^2*z^3-43.*x^2*
y^5*z-17.*x^2*y^3*z^3-17.*x^2*y^4*z^2-25.*x^3*y*z+3.*x^3*y^2*z-22.*x^3*y*z^2+
17.*x^3*y^3*z-3.*x^3*y^2*z^2-28.*x^3*y*z^3+39.*x^3*z^4*y+19.*x^3*z*y^4-12.*x^3
*y^3*z^2+16.*x^3*y^2*z^3-42.*x^2*y^3-15.*x^2*z^3+19.*x^2*y^4+4.*x^2*z^4-9.*x^2
*z^5+5.*x^2*z^6+22.*x^2*y^5-2.*x^2*y^6+9.*x^3*y^2+34.*x^3*y^3-6.*x^3*z^3-34.*x
^3*y^4-30.*x^3*z^4+10.*x^3*z^5+20.*x^3*y^5+11.*x^5+31.*x^6+42.*x^4*y+15.*x^4*z
-11.*x^4*y^2+2.*x^4*z^2+26.*x^4*z^3-13.*x^4*y^4-8.*x^4*z^4+28.*x^5*y-47.*x^5*z
-14.*x^5*y^2+24.*x^5*z^2-12.*x^5*y^3-2.*x^5*z^3+2.*x^6*z^2-32.*x^6*z-12.*x^6*y
^2-23.*x^6*y-10.*x^7*y+4.*x^7*z+14.*x^4*y*z-24.*x^4*y^2*z-36.*x^4*y*z^2-7.*x^4
*y^3*z-11.*x^4*y^2*z^2+3.*x^4*y*z^3+46.*x^5*y*z+3.*x^5*y^2*z-33.*x^5*y*z^2+17.
*x^6*y*z+9.*x^7-3.*x^8+4., -14.*x-3.*y-4.*z-5.*x^3*y+43.*x^3*z-20.*y*z-27.*x^4
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*z^3-40.*x*z^2+10.*x*z+20.*y^3*z+34.*y^2*z^2+32.*y*z^3+16.*x*y^2*z+81.*x*y*z^2
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.*z^4*y^2-18.*z^4*y^4-8.*z^5*y^3-3.*z^6*y^2-2.*z^5*y^2-17.*z*y^4-20.*y^3*z^2+3\
.*y^2*z^3-29.*y^5*z-25.*y^3*z^3+23.*y^6*z+23.*y^5*z^2-33.*y^4*z^3-15.*y^4*z^2+
z^7-12.*z^5-1.*z^8+z^6+25.*y^5-3.*y^7-3.*y^6+9.*y^8-11.*y^5*z^3+6.*y^7*z-5.*y^
6*z^2+20.*x*y^4+7.*x*z^4+5.*x*z^7+6.*x*z^5-43.*x*y^5-9.*x*y^7+47.*x*y^6-26.*x*
y^3*z+96.*x*y^2*z^2+6.*x*z^4*y-41.*x*z^4*y^3+42.*x*z^5*y-5.*x*z^6*y-62.*x*z^4*
y^2+18.*x*z^5*y^2+50.*x*z*y^4-15.*x*y^3*z^2+24.*x*y^2*z^3-34.*x*y^5*z-18.*x*y^
3*z^3-30.*x*y^6*z-35.*x*y^5*z^2-39.*x*y^4*z^3+x*y^4*z^2+35.*x^2*y^2*z-3.*x^2*y
*z^2-52.*x^2*y^3*z+83.*x^2*y^2*z^2-18.*x^2*y*z^3+27.*x^2*z^4*y+25.*x^2*z^5*y-\
32.*x^2*z^4*y^2+42.*x^2*z*y^4-9.*x^2*y^3*z^2+8.*x^2*y^2*z^3-10.*x^2*y^5*z+34.*
x^2*y^3*z^3-47.*x^2*y^4*z^2+8.*x^3*y*z+58.*x^3*y^2*z-4.*x^3*y*z^2-76.*x^3*y^3*
z+11.*x^3*y^2*z^2-51.*x^3*y*z^3-5.*x^3*z^4*y-29.*x^3*z*y^4-36.*x^3*y^3*z^2-9.*
x^3*y^2*z^3-7.*x^2*y^3-27.*x^2*z^3+22.*x^2*y^4+34.*x^2*z^4-3.*x^2*z^5-4.*x^2*z
^6-5.*x^2*y^5+14.*x^2*y^6+13.*x^3*y^2+2.*x^3*y^3-4.*x^3*z^3+30.*x^3*y^4+6.*x^3
*z^4-8.*x^3*z^5-13.*x^3*y^5+7.*x^5+21.*x^6+43.*x^4*y-23.*x^4*z-28.*x^4*y^2-28.
*x^4*z^2-9.*x^4*z^3-9.*x^4*y^4+3.*x^4*z^4+19.*x^5*y-12.*x^5*z-20.*x^5*y^2-15.*
x^5*z^2-5.*x^5*y^3+8.*x^5*z^3+2.*x^6*z^2+10.*x^6*z-10.*x^6*y^2-2.*x^6*y-6.*x^7
*y-3.*x^7*z+72.*x^4*y*z+6.*x^4*y^2*z-8.*x^4*y*z^2-35.*x^4*y^3*z-28.*x^4*y^2*z^
2+x^4*y*z^3+19.*x^5*y*z-23.*x^5*y^2*z+2.*x^5*y*z^2-13.*x^6*y*z+x^7-1.*x^8-3.-\
10.*x*y*z^3+59.*x^3*z^2+35.*x^4*y^3];
noiseF7_list := [-.9862740964e-4*y+.8145865692e-3*z-.5475385048e-3*x^3*z-.\
2259497400e-3*x^3-.5816639313e-3*z^2+.8819269824e-3*y^3-.7975452780e-3*x*z^3+.\
4932334476e-3*y^3*z-.6009331222e-3*x*y^2*z-.5765868904e-3*z^5*y+.5968200765e-3
*z^7*y-.8174464213e-3*z^5*y^3+.4798339157e-3*z*y^4+.7800862557e-3*y^3*z^2+.\
6327663826e-3*y^3*z^3-.8785208665e-4*y^4*z^3-.1753185752e-3*y^4*z^2+.\
9383635402e-3*z^8+.4954185031e-3*x*z^6+.2035850537e-3*x*y^3*z-.9511632525e-3*x
*z^4*y^2+.5259128815e-5*x*y^2*z^3-.1509080772e-3*x*y^5*z-.5239956023e-3*x*y^3*
z^3-.6231157206e-3*x*y^6*z+.1416001689e-3*x*y^4*z^3+.3931600453e-3*x^2*y^4*z^2
-.5382627297e-3*x^3*y*z+.2095725344e-3*x^3*y^3*z-.1061240781e-2*x^3*y*z^3+.\
4457941777e-3*x^3*z*y^4+.1009945531e-3*x^2*z^5+.1254800286e-3*x^2*y^5-.\
1045731172e-2*x^3*z^3-.4400637624e-3*x^5+.5774223529e-3*x^5*y+.3222100061e-3*x
^6*z-.6278821408e-4*x^4*y*z+.2960214726e-3*x^4*y^2*z^2+.7849169422e-3*x^4*y*z^
3-.7358067475e-3*x^6*y*z, .2863196771e-3*x-.3993739628e-3*y+.4620013286e-3*z+.\
2125927653e-3*x^3*y+.1956789444e-3*x^3*z-.4594325630e-3*y*z+.1526104181e-3*x^4
-.2981293272e-3*x^3-.3507008570e-3*x^2*y*z-.3759881867e-3*y^2-.1981476283e-3*z
^2-.3299458019e-3*x^2-.2951316396e-3*y^3+.2224532036e-3*z^3+.1399762847e-3*x^2
*y^2+.3207954676e-3*x^2*y-.3034050668e-3*x^2*z^2+.1609886929e-3*x^2*z-.\
2667227113e-3*y^2*z+.8626096334e-6*y*z^2+.1490265372e-4*x*y^3-.3782710045e-3*x
*y^2-.4717235586e-3*x*y+.4418229354e-3*x*z^3+.6147880811e-4*x*z^2+.8202893374e\
-4*x*z+.1542784478e-3*y^3*z+.1259171775e-3*y^2*z^2+.1067967916e-3*y*z^3+.\
1720310494e-3*x*y^2*z-.8013691150e-4*x*y*z^2+.9487752806e-4*x*y*z-.2332525043e\
-3*y^4+.4470128904e-3*z^4-.2890266510e-3*z^4*y+.6136919475e-4*z^4*y^3+.\
2092662376e-4*z^5*y-.1790367740e-3*z^6*y+.2916097141e-3*z^7*y-.2709928672e-3*z
^4*y^2+.2222006163e-3*z^4*y^4-.1841647738e-3*z^5*y^3-.3536508864e-3*z^6*y^2-.\
3011889702e-3*z^5*y^2-.3949751304e-3*z*y^4+.3155483229e-3*y^3*z^2+.3029141895e\
-4*y^2*z^3+.2234826162e-3*y^5*z+.2326424821e-3*y^3*z^3+.4748165624e-3*y^6*z-.\
3879026845e-3*y^5*z^2+.3127555646e-3*y^4*z^3-.1688427298e-3*y^4*z^2+.\
3351548202e-3*z^7+.7706773690e-4*z^5-.2235064452e-3*z^8-.4019331969e-3*z^6+.\
5819993835e-4*y^5+.3645312059e-3*y^7-.3086093194e-3*y^6+.1814244393e-3*y^8-.\
4596899161e-3*y^5*z^3-.3800438816e-3*y^7*z-.4581029050e-3*y^6*z^2-.1636766036e\
-3*x*y^4-.2047291968e-3*x*z^4-.3055163158e-3*x*z^7-.1622420981e-3*x*z^5+.\
8190978876e-4*x*z^6+.4520455742e-3*x*y^5+.1211942706e-4*x*y^7-.3308608353e-3*x
*y^6-.3520019199e-3*x*y^3*z+.2190027651e-3*x*y^2*z^2+.1245827537e-3*x*z^4*y-.\
3116260702e-3*x*z^4*y^3+.2859479448e-4*x*z^5*y+.1055862786e-3*x*z^6*y+.\
2750390307e-3*x*z^4*y^2+.2610752394e-3*x*z^5*y^2-.3157103600e-3*x*z*y^4-.\
3132464419e-3*x*y^3*z^2+.3314136680e-3*x*y^2*z^3+.4193140663e-3*x*y^5*z-.\
8575102284e-4*x*y^3*z^3+.8015597473e-4*x*y^6*z+.2446570615e-3*x*y^5*z^2+.\
4677155215e-3*x*y^4*z^3-.2409349725e-3*x*y^4*z^2-.2647687336e-3*x^2*y^2*z-.\
8800048000e-4*x^2*y*z^2+.3771176813e-4*x^2*y^3*z+.1922999929e-4*x^2*y^2*z^2-.\
4179605792e-3*x^2*y*z^3+.4096442597e-3*x^2*z^4*y+.1548026857e-3*x^2*z^5*y+.\
2352589057e-3*x^2*z^4*y^2+.1703820829e-3*x^2*z*y^4-.4017092044e-3*x^2*y^3*z^2+
.1584437562e-3*x^2*y^2*z^3-.3328005155e-3*x^2*y^5*z+.1712065661e-3*x^2*y^3*z^3
-.4383677309e-3*x^2*y^4*z^2+.1245636905e-3*x^3*y*z+.3602705813e-3*x^3*y^2*z+.\
3568678009e-3*x^3*y*z^2+.2431987270e-3*x^3*y^3*z+.1246494749e-3*x^3*y^2*z^2-.\
3017227397e-3*x^3*y*z^3+.3381000841e-3*x^3*z^4*y+.1321889691e-3*x^3*z*y^4-.\
3517636299e-3*x^3*y^3*z^2+.3512155633e-3*x^3*y^2*z^3+.3936168774e-3*x^2*y^3+.\
1634955032e-3*x^2*z^3-.2346441177e-3*x^2*y^4-.1621324847e-4*x^2*z^4-.\
3063979886e-3*x^2*z^5-.2299069134e-3*x^2*z^6-.4940227326e-4*x^2*y^5+.\
1703677855e-3*x^2*y^6+.4358942812e-3*x^3*y^2+.2997687621e-4*x^3*y^3-.\
3803584245e-4*x^3*z^3+.3047251931e-4*x^3*y^4-.4610719978e-3*x^3*z^4-.\
8186689660e-4*x^3*z^5+.1700961349e-3*x^3*y^5-.3863537996e-3*x^5-.4565540201e-3
*x^6+.1441749538e-3*x^4*y+.3352120098e-3*x^4*z+.4386870394e-3*x^4*y^2+.\
1975757324e-3*x^4*z^2+.1311214301e-3*x^4*z^3-.4700364659e-3*x^4*y^4-.\
4118555907e-3*x^4*z^4-.1435935263e-4*x^5*y-.2079890034e-3*x^5*z+.2655741537e-3
*x^5*y^2-.3428229910e-3*x^5*z^2+.2884642867e-3*x^5*y^3-.4538947044e-3*x^5*z^3-
.7919804911e-4*x^6*z^2+.3727331460e-4*x^6*z+.2830503389e-3*x^6*y^2-.1311166643\
e-3*x^6*y+.2979720558e-3*x^7*y-.1035083902e-3*x^7*z-.3416744334e-3*x^4*y*z-.\
3454632438e-3*x^4*y^2*z-.1894977030e-3*x^4*y*z^2+.1512426338e-3*x^4*y^3*z-.\
4384773444e-3*x^4*y^2*z^2-.4661332763e-3*x^4*y*z^3+.3938646990e-3*x^5*y*z-.\
2826881382e-3*x^5*y^2*z-.2352350768e-3*x^5*y*z^2+.2749151199e-3*x^6*y*z-.\
4600711799e-3*x^7+.2993589034e-3*x^8-.9145091853e-4*x*y*z^3+.2552990909e-3*x^3
*z^2+.1638672355e-3*x^4*y^3-.3953849889e-3];
gcd_F7 := 4;