SHINTANI-ML.sage

var('x');
examples = [
[
[
1646,
x^4 - x^3 - x^2 + x + 1,
0.5435350724978695499,
117,
x^2 - 1,
4,
39
],
[
8/33*x^3 - 1/6*x^2 - 14/25*x + 12/17,
-19/25*x^3 + 15/11*x^2 - 5/21*x - 17/22,
-8/33*x^3 + 1/6*x^2 + 14/25*x + 5/17,
-13/33*x^3 - 5/24*x^2 + 5/21*x + 1/5
],
[
[
[
-3484967077*x^3 + 9568658891*x^2 + 897523984*x - 6529633395,
1
],
[
54090804856038*x^3 + 11299587334121*x^2 - 56912687041471*x + 80288844196480,
1
],
[
-235559422324*x^3 + 3930210800317*x^2 + 5739653809983*x + 2450015545210,
-1
],
[
-2587443093*x^3 + 5626468589*x^2 + 445941581*x - 9568658891,
-1
],
[
83068766785678*x^3 - 229045377543419*x^2 + 53945636087474*x + 148605419642436,
-1
],
[
2616584*x^3 - 4909115*x^2 + 904191*x + 1549723,
-1
]
],
[
[
1046690613883*x^3 - 1147207991039*x^2 + 772391666414*x + 405635423205,
1
],
[
27164263*x^3 + 14293796*x^2 - 16507671*x - 13384495,
1
],
[
54090804856038*x^3 + 11299587334121*x^2 - 56912687041471*x + 80288844196480,
1
],
[
-235559422324*x^3 + 3930210800317*x^2 + 5739653809983*x + 2450015545210,
-1
],
[
-2587443093*x^3 + 5626468589*x^2 + 445941581*x - 9568658891,
-1
],
[
-9242949657044*x^3 + 7254115153237*x^2 + 6789052507748*x - 9896501297178,
-1
],
[
-216816651410612*x^3 + 344744786005843*x^2 - 31141837624999*x - 251280299694285,
-1
],
[
-137014402873152*x^3 + 217454360774135*x^2 + 2628808884695*x - 229045377543419,
-1
]
],
[
[
54090804856038*x^3 + 11299587334121*x^2 - 56912687041471*x + 80288844196480,
1
],
[
216816651410612*x^3 - 344744786005843*x^2 + 31141837624999*x + 251280299694285,
1
],
[
-2587443093*x^3 + 5626468589*x^2 + 445941581*x - 9568658891,
-1
],
[
-137014402873152*x^3 + 217454360774135*x^2 + 2628808884695*x - 229045377543419,
-1
],
[
-9242949657044*x^3 + 7254115153237*x^2 + 6789052507748*x - 9896501297178,
-1
],
[
100967239337*x^3 - 260103654318*x^2 + 146851157549*x + 15141694310,
-1
]
],
[
[
-83068766785678*x^3 + 229045377543419*x^2 - 53945636087474*x - 148605419642436,
1
],
[
54090804856038*x^3 + 11299587334121*x^2 - 56912687041471*x + 80288844196480,
1
],
[
137014402873152*x^3 - 217454360774135*x^2 - 2628808884695*x + 229045377543419,
1
],
[
-2587443093*x^3 + 5626468589*x^2 + 445941581*x - 9568658891,
-1
],
[
-9242949657044*x^3 + 7254115153237*x^2 + 6789052507748*x - 9896501297178,
-1
],
[
2616584*x^3 - 4909115*x^2 + 904191*x + 1549723,
-1
]
],
[
[
1046690613883*x^3 - 1147207991039*x^2 + 772391666414*x + 405635423205,
1
],
[
9242949657044*x^3 - 7254115153237*x^2 - 6789052507748*x + 9896501297178,
1
],
[
-235559422324*x^3 + 3930210800317*x^2 + 5739653809983*x + 2450015545210,
-1
],
[
-2587443093*x^3 + 5626468589*x^2 + 445941581*x - 9568658891,
-1
],
[
-1388340*x^3 + 1549723*x^2 - 1228244*x + 742808,
-1
]
],
[
[
1046690613883*x^3 - 1147207991039*x^2 + 772391666414*x + 405635423205,
1
],
[
2587443093*x^3 - 5626468589*x^2 - 445941581*x + 9568658891,
1
],
[
-3484967077*x^3 + 9568658891*x^2 + 897523984*x - 6529633395,
1
],
[
-235559422324*x^3 + 3930210800317*x^2 + 5739653809983*x + 2450015545210,
-1
],
[
1819082280297*x^3 - 2560654848131*x^2 - 305118046049*x + 1147207991039,
-1
],
[
-1388340*x^3 + 1549723*x^2 - 1228244*x + 742808,
-1
],
[
2453897149296*x^3 + 188488994645*x^2 - 11885335800985*x + 7254115153237,
-1
]
],
[
[
2587443093*x^3 - 5626468589*x^2 - 445941581*x + 9568658891,
1
],
[
1388340*x^3 - 1549723*x^2 + 1228244*x - 742808,
1
],
[
-3484967077*x^3 + 9568658891*x^2 + 897523984*x - 6529633395,
1
],
[
1819082280297*x^3 - 2560654848131*x^2 - 305118046049*x + 1147207991039,
-1
],
[
83068766785678*x^3 - 229045377543419*x^2 + 53945636087474*x + 148605419642436,
-1
],
[
2453897149296*x^3 + 188488994645*x^2 - 11885335800985*x + 7254115153237,
-1
]
],
[
[
-2453897149296*x^3 - 188488994645*x^2 + 11885335800985*x - 7254115153237,
1
],
[
27164263*x^3 + 14293796*x^2 - 16507671*x - 13384495,
1
],
[
-3484967077*x^3 + 9568658891*x^2 + 897523984*x - 6529633395,
1
],
[
2587443093*x^3 - 5626468589*x^2 - 445941581*x + 9568658891,
1
],
[
1819082280297*x^3 - 2560654848131*x^2 - 305118046049*x + 1147207991039,
-1
],
[
83068766785678*x^3 - 229045377543419*x^2 + 53945636087474*x + 148605419642436,
-1
],
[
2616584*x^3 - 4909115*x^2 + 904191*x + 1549723,
-1
],
[
113562845237*x^3 - 156822393168*x^2 - 149683533901*x + 245092500560,
-1
]
],
[
[
54090804856038*x^3 + 11299587334121*x^2 - 56912687041471*x + 80288844196480,
1
],
[
27164263*x^3 + 14293796*x^2 - 16507671*x - 13384495,
1
],
[
2587443093*x^3 - 5626468589*x^2 - 445941581*x + 9568658891,
1
],
[
-3484967077*x^3 + 9568658891*x^2 + 897523984*x - 6529633395,
1
],
[
-113562845237*x^3 + 156822393168*x^2 + 149683533901*x - 245092500560,
1
],
[
1819082280297*x^3 - 2560654848131*x^2 - 305118046049*x + 1147207991039,
-1
],
[
83068766785678*x^3 - 229045377543419*x^2 + 53945636087474*x + 148605419642436,
-1
],
[
2616584*x^3 - 4909115*x^2 + 904191*x + 1549723,
-1
],
[
100967239337*x^3 - 260103654318*x^2 + 146851157549*x + 15141694310,
-1
]
],
[
[
2587443093*x^3 - 5626468589*x^2 - 445941581*x + 9568658891,
1
],
[
-1819082280297*x^3 + 2560654848131*x^2 + 305118046049*x - 1147207991039,
1
],
[
1046690613883*x^3 - 1147207991039*x^2 + 772391666414*x + 405635423205,
1
],
[
27164263*x^3 + 14293796*x^2 - 16507671*x - 13384495,
1
],
[
-1388340*x^3 + 1549723*x^2 - 1228244*x + 742808,
-1
],
[
-2821882185433*x^3 + 94410313716034*x^2 - 145679236386639*x - 11299587334121,
-1
],
[
2453897149296*x^3 + 188488994645*x^2 - 11885335800985*x + 7254115153237,
-1
],
[
-216816651410612*x^3 + 344744786005843*x^2 - 31141837624999*x - 251280299694285,
-1
]
],
[
[
-3484967077*x^3 + 9568658891*x^2 + 897523984*x - 6529633395,
1
],
[
27164263*x^3 + 14293796*x^2 - 16507671*x - 13384495,
1
],
[
-1819082280297*x^3 + 2560654848131*x^2 + 305118046049*x - 1147207991039,
1
],
[
1046690613883*x^3 - 1147207991039*x^2 + 772391666414*x + 405635423205,
1
],
[
216816651410612*x^3 - 344744786005843*x^2 + 31141837624999*x + 251280299694285,
1
],
[
-2821882185433*x^3 + 94410313716034*x^2 - 145679236386639*x - 11299587334121,
-1
],
[
-1388340*x^3 + 1549723*x^2 - 1228244*x + 742808,
-1
],
[
2453897149296*x^3 + 188488994645*x^2 - 11885335800985*x + 7254115153237,
-1
],
[
113562845237*x^3 - 156822393168*x^2 - 149683533901*x + 245092500560,
-1
]
],
[
[
2587443093*x^3 - 5626468589*x^2 - 445941581*x + 9568658891,
1
],
[
1046690613883*x^3 - 1147207991039*x^2 + 772391666414*x + 405635423205,
1
],
[
-2453897149296*x^3 - 188488994645*x^2 + 11885335800985*x - 7254115153237,
1
],
[
-2821882185433*x^3 + 94410313716034*x^2 - 145679236386639*x - 11299587334121,
-1
],
[
-1388340*x^3 + 1549723*x^2 - 1228244*x + 742808,
-1
],
[
-137014402873152*x^3 + 217454360774135*x^2 + 2628808884695*x - 229045377543419,
-1
]
],
[
[
1066861*x^3 - 742808*x^2 - 2455201*x + 904191,
1
],
[
-192943081832*x^3 + 245092500560*x^2 + 79380236595*x - 201832952629,
-1
],
[
131529655323*x^3 - 201832952629*x^2 + 61413426509*x + 149683533901,
-1
],
[
-9242949657044*x^3 + 7254115153237*x^2 + 6789052507748*x - 9896501297178,
-1
]
],
[
[
-4800218003941*x^3 + 9896501297178*x^2 - 4442731653103*x - 11885335800985,
1
],
[
1066861*x^3 - 742808*x^2 - 2455201*x + 904191,
1
],
[
192943081832*x^3 - 245092500560*x^2 - 79380236595*x + 201832952629,
1
],
[
83718945475072*x^3 - 8651315445001*x^2 - 123630406416399*x - 71591712331630,
-1
],
[
-9242949657044*x^3 + 7254115153237*x^2 + 6789052507748*x - 9896501297178,
-1
],
[
131529655323*x^3 - 201832952629*x^2 + 61413426509*x + 149683533901,
-1
],
[
96786296970232*x^3 - 251280299694285*x^2 + 120030354440380*x + 123352165099054,
-1
]
],
[
[
235559422324*x^3 - 3930210800317*x^2 - 5739653809983*x - 2450015545210,
1
],
[
92030974670267*x^3 - 148605419642436*x^2 - 8962207884589*x + 2628808884695,
1
],
[
1066861*x^3 - 742808*x^2 - 2455201*x + 904191,
1
],
[
83718945475072*x^3 - 8651315445001*x^2 - 123630406416399*x - 71591712331630,
-1
],
[
-85825545027*x^3 + 143994720671*x^2 + 98110802459*x - 146851157549,
-1
],
[
-9242949657044*x^3 + 7254115153237*x^2 + 6789052507748*x - 9896501297178,
-1
],
[
-228789962768552*x^3 + 365991494006503*x^2 + 11299587334121*x - 231611844953985,
-1
],
[
-192943081832*x^3 + 245092500560*x^2 + 79380236595*x - 201832952629,
-1
]
],
[
[
-131529655323*x^3 + 201832952629*x^2 - 61413426509*x - 149683533901,
1
],
[
1066861*x^3 - 742808*x^2 - 2455201*x + 904191,
1
],
[
228789962768552*x^3 - 365991494006503*x^2 - 11299587334121*x + 231611844953985,
1
],
[
-9242949657044*x^3 + 7254115153237*x^2 + 6789052507748*x - 9896501297178,
-1
],
[
-85825545027*x^3 + 143994720671*x^2 + 98110802459*x - 146851157549,
-1
],
[
-192943081832*x^3 + 245092500560*x^2 + 79380236595*x - 201832952629,
-1
],
[
4388131883*x^3 - 11815289262*x^2 + 9568658891*x + 1800688790,
-1
]
],
[
[
1066861*x^3 - 742808*x^2 - 2455201*x + 904191,
1
],
[
-131529655323*x^3 + 201832952629*x^2 - 61413426509*x - 149683533901,
1
],
[
192943081832*x^3 - 245092500560*x^2 - 79380236595*x + 201832952629,
1
],
[
-9242949657044*x^3 + 7254115153237*x^2 + 6789052507748*x - 9896501297178,
-1
],
[
-85825545027*x^3 + 143994720671*x^2 + 98110802459*x - 146851157549,
-1
],
[
96786296970232*x^3 - 251280299694285*x^2 + 120030354440380*x + 123352165099054,
-1
]
],
[
[
92030974670267*x^3 - 148605419642436*x^2 - 8962207884589*x + 2628808884695,
1
],
[
85825545027*x^3 - 143994720671*x^2 - 98110802459*x + 146851157549,
1
],
[
83718945475072*x^3 - 8651315445001*x^2 - 123630406416399*x - 71591712331630,
-1
],
[
-9242949657044*x^3 + 7254115153237*x^2 + 6789052507748*x - 9896501297178,
-1
],
[
-34463648283673*x^3 + 123352165099054*x^2 - 62322648686559*x + 31141837624999,
-1
]
],
[
[
9242949657044*x^3 - 7254115153237*x^2 - 6789052507748*x + 9896501297178,
1
],
[
92030974670267*x^3 - 148605419642436*x^2 - 8962207884589*x + 2628808884695,
1
],
[
-4800218003941*x^3 + 9896501297178*x^2 - 4442731653103*x - 11885335800985,
1
],
[
83718945475072*x^3 - 8651315445001*x^2 - 123630406416399*x - 71591712331630,
-1
],
[
83068766785678*x^3 - 229045377543419*x^2 + 53945636087474*x + 148605419642436,
-1
],
[
-34463648283673*x^3 + 123352165099054*x^2 - 62322648686559*x + 31141837624999,
-1
],
[
-12285257432*x^3 + 15141694310*x^2 - 88681981905*x + 143994720671,
-1
]
],
[
[
-4800218003941*x^3 + 9896501297178*x^2 - 4442731653103*x - 11885335800985,
1
],
[
12285257432*x^3 - 15141694310*x^2 + 88681981905*x - 143994720671,
1
],
[
83068766785678*x^3 - 229045377543419*x^2 + 53945636087474*x + 148605419642436,
-1
],
[
-34463648283673*x^3 + 123352165099054*x^2 - 62322648686559*x + 31141837624999,
-1
],
[
96786296970232*x^3 - 251280299694285*x^2 + 120030354440380*x + 123352165099054,
-1
]
],
[
[
9242949657044*x^3 - 7254115153237*x^2 - 6789052507748*x + 9896501297178,
1
],
[
-4800218003941*x^3 + 9896501297178*x^2 - 4442731653103*x - 11885335800985,
1
],
[
34463648283673*x^3 - 123352165099054*x^2 + 62322648686559*x - 31141837624999,
1
],
[
131529655323*x^3 - 201832952629*x^2 + 61413426509*x + 149683533901,
-1
],
[
83068766785678*x^3 - 229045377543419*x^2 + 53945636087474*x + 148605419642436,
-1
],
[
-12285257432*x^3 + 15141694310*x^2 - 88681981905*x + 143994720671,
-1
]
],
[
[
34463648283673*x^3 - 123352165099054*x^2 + 62322648686559*x - 31141837624999,
1
],
[
12285257432*x^3 - 15141694310*x^2 + 88681981905*x - 143994720671,
1
],
[
235559422324*x^3 - 3930210800317*x^2 - 5739653809983*x - 2450015545210,
1
],
[
-4800218003941*x^3 + 9896501297178*x^2 - 4442731653103*x - 11885335800985,
1
],
[
9242949657044*x^3 - 7254115153237*x^2 - 6789052507748*x + 9896501297178,
1
],
[
83068766785678*x^3 - 229045377543419*x^2 + 53945636087474*x + 148605419642436,
-1
],
[
131529655323*x^3 - 201832952629*x^2 + 61413426509*x + 149683533901,
-1
],
[
96786296970232*x^3 - 251280299694285*x^2 + 120030354440380*x + 123352165099054,
-1
],
[
1108328811043*x^3 - 1475085054252*x^2 - 1147207991039*x + 2927411091340,
-1
]
],
[
[
1066861*x^3 - 742808*x^2 - 2455201*x + 904191,
1
],
[
235559422324*x^3 - 3930210800317*x^2 - 5739653809983*x - 2450015545210,
1
],
[
-4800218003941*x^3 + 9896501297178*x^2 - 4442731653103*x - 11885335800985,
1
],
[
9242949657044*x^3 - 7254115153237*x^2 - 6789052507748*x + 9896501297178,
1
],
[
-1108328811043*x^3 + 1475085054252*x^2 + 1147207991039*x - 2927411091340,
1
],
[
83068766785678*x^3 - 229045377543419*x^2 + 53945636087474*x + 148605419642436,
-1
],
[
131529655323*x^3 - 201832952629*x^2 + 61413426509*x + 149683533901,
-1
],
[
96786296970232*x^3 - 251280299694285*x^2 + 120030354440380*x + 123352165099054,
-1
],
[
4388131883*x^3 - 11815289262*x^2 + 9568658891*x + 1800688790,
-1
]
],
[
[
9242949657044*x^3 - 7254115153237*x^2 - 6789052507748*x + 9896501297178,
1
],
[
-83068766785678*x^3 + 229045377543419*x^2 - 53945636087474*x - 148605419642436,
1
],
[
92030974670267*x^3 - 148605419642436*x^2 - 8962207884589*x + 2628808884695,
1
],
[
235559422324*x^3 - 3930210800317*x^2 - 5739653809983*x - 2450015545210,
1
],
[
-34463648283673*x^3 + 123352165099054*x^2 - 62322648686559*x + 31141837624999,
-1
],
[
-1388340*x^3 + 1549723*x^2 - 1228244*x + 742808,
-1
],
[
-12285257432*x^3 + 15141694310*x^2 - 88681981905*x + 143994720671,
-1
],
[
-228789962768552*x^3 + 365991494006503*x^2 + 11299587334121*x - 231611844953985,
-1
]
],
[
[
-4800218003941*x^3 + 9896501297178*x^2 - 4442731653103*x - 11885335800985,
1
],
[
235559422324*x^3 - 3930210800317*x^2 - 5739653809983*x - 2450015545210,
1
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