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sorted([g.monic() for f in polys for g, e in f.factor() if g.degree() > 1], key=str)[:10]'-Numbers: []+Numbers:+- params:+ r: '1'+ number: x^3 - x - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#1}[$\theta_{1}$] is the root+ in $(1,\varphi)$; this polynomial is selected from $P_{2}$.+- params:+ r: '2'+ number: x^4 - x^3 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#2}[$\theta_{2}$] is the root+ in $(1,\varphi)$; this polynomial is selected from $Q_{2}$.+- params:+ r: '3'+ number: x^5 - x^4 - x^3 + x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#3}[$\theta_{3}$] is the root+ in $(1,\varphi)$; this polynomial is selected from $Q_{3}$.+- params:+ r: '4'+ number: x^3 - x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#4}[$\theta_{4}$] is the root+ in $(1,\varphi)$; this polynomial is selected from $P_{3}$.+- params:+ r: '5'+ number: x^6 - x^5 - x^4 + x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#5}[$\theta_{5}$] is the root+ in $(1,\varphi)$; this polynomial is selected from $Q_{4}$.+- params:+ r: '6'+ number: x^5 - x^3 - x^2 - x - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#6}[$\theta_{6}$] is the root+ in $(1,\varphi)$; this polynomial is selected from $P_{4}$.+- params:+ r: '7'+ number: x^7 - x^6 - x^5 + x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#7}[$\theta_{7}$] is the root+ in $(1,\varphi)$; this polynomial is selected from $Q_{5}$.+- params:+ r: '8'+ number: x^6 - 2*x^5 + x^4 - x^2 + x - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#8}[$\theta_{8}$] is the root+ in $(1,\varphi)$; this polynomial is selected from $E$.+- params:+ r: '9'+ number: x^5 - x^4 - x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#9}[$\theta_{9}$] is the root+ in $(1,\varphi)$; this polynomial is selected from $P_{5}$.+- params:+ r: '10'+ number: x^8 - x^7 - x^6 + x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#10}[$\theta_{10}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $Q_{6}$.+- params:+ r: '11'+ number: x^7 - x^5 - x^4 - x^3 - x^2 - x - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#11}[$\theta_{11}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $P_{6}$.+- params:+ r: '12'+ number: x^9 - x^8 - x^7 + x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#12}[$\theta_{12}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $Q_{7}$.+- params:+ r: '13'+ number: x^7 - x^6 - x^4 - x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#13}[$\theta_{13}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $P_{7}$.+- params:+ r: '14'+ number: x^10 - x^9 - x^8 + x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#14}[$\theta_{14}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $Q_{8}$.+- params:+ r: '15'+ number: x^9 - x^7 - x^6 - x^5 - x^4 - x^3 - x^2 - x - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#15}[$\theta_{15}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $P_{8}$.+- params:+ r: '16'+ number: x^11 - x^10 - x^9 + x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#16}[$\theta_{16}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $Q_{9}$.+- params:+ r: '17'+ number: x^9 - x^8 - x^6 - x^4 - x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#17}[$\theta_{17}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $P_{9}$.+- params:+ r: '18'+ number: x^12 - x^11 - x^10 + x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#18}[$\theta_{18}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $Q_{10}$.+- params:+ r: '19'+ number: x^11 - x^9 - x^8 - x^7 - x^6 - x^5 - x^4 - x^3 - x^2 - x - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#19}[$\theta_{19}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $P_{10}$.+- params:+ r: '20'+ number: x^13 - x^12 - x^11 + x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#20}[$\theta_{20}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $Q_{11}$.+- params:+ r: '21'+ number: x^11 - x^10 - x^8 - x^6 - x^4 - x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#21}[$\theta_{21}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $P_{11}$.+- params:+ r: '22'+ number: x^14 - x^13 - x^12 + x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#22}[$\theta_{22}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $Q_{12}$.+- params:+ r: '23'+ number: x^13 - x^11 - x^10 - x^9 - x^8 - x^7 - x^6 - x^5 - x^4 - x^3 - x^2 - x -+ 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#23}[$\theta_{23}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $P_{12}$.+- params:+ r: '24'+ number: x^15 - x^14 - x^13 + x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#24}[$\theta_{24}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $Q_{13}$.+- params:+ r: '25'+ number: x^13 - x^12 - x^10 - x^8 - x^6 - x^4 - x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#25}[$\theta_{25}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $P_{13}$.+- params:+ r: '26'+ number: x^16 - x^15 - x^14 + x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#26}[$\theta_{26}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $Q_{14}$.+- params:+ r: '27'+ number: x^15 - x^13 - x^12 - x^11 - x^10 - x^9 - x^8 - x^7 - x^6 - x^5 - x^4 - x^3+ - x^2 - x - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#27}[$\theta_{27}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $P_{14}$.+- params:+ r: '28'+ number: x^17 - x^16 - x^15 + x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#28}[$\theta_{28}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $Q_{15}$.+- params:+ r: '29'+ number: x^15 - x^14 - x^12 - x^10 - x^8 - x^6 - x^4 - x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#29}[$\theta_{29}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $P_{15}$.+- params:+ r: '30'+ number: x^18 - x^17 - x^16 + x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#30}[$\theta_{30}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $Q_{16}$.+- params:+ r: '31'+ number: x^17 - x^15 - x^14 - x^13 - x^12 - x^11 - x^10 - x^9 - x^8 - x^7 - x^6 -+ x^5 - x^4 - x^3 - x^2 - x - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#31}[$\theta_{31}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $P_{16}$.+- params:+ r: '32'+ number: x^19 - x^18 - x^17 + x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#32}[$\theta_{32}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $Q_{17}$.+- params:+ r: '33'+ number: x^17 - x^16 - x^14 - x^12 - x^10 - x^8 - x^6 - x^4 - x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#33}[$\theta_{33}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $P_{17}$.+- params:+ r: '34'+ number: x^20 - x^19 - x^18 + x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#34}[$\theta_{34}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $Q_{18}$.+- params:+ r: '35'+ number: x^19 - x^17 - x^16 - x^15 - x^14 - x^13 - x^12 - x^11 - x^10 - x^9 - x^8+ - x^7 - x^6 - x^5 - x^4 - x^3 - x^2 - x - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#35}[$\theta_{35}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $P_{18}$.+- params:+ r: '36'+ number: x^21 - x^20 - x^19 + x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#36}[$\theta_{36}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $Q_{19}$.+- params:+ r: '37'+ number: x^19 - x^18 - x^16 - x^14 - x^12 - x^10 - x^8 - x^6 - x^4 - x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#37}[$\theta_{37}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $P_{19}$.+- params:+ r: '38'+ number: x^22 - x^21 - x^20 + x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#38}[$\theta_{38}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $Q_{20}$.+- params:+ r: '39'+ number: x^21 - x^19 - x^18 - x^17 - x^16 - x^15 - x^14 - x^13 - x^12 - x^11 - x^10+ - x^9 - x^8 - x^7 - x^6 - x^5 - x^4 - x^3 - x^2 - x - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#39}[$\theta_{39}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $P_{20}$.+- params:+ r: '40'+ number: x^23 - x^22 - x^21 + x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#40}[$\theta_{40}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $Q_{21}$.+- params:+ r: '41'+ number: x^21 - x^20 - x^18 - x^16 - x^14 - x^12 - x^10 - x^8 - x^6 - x^4 - x^2 -+ 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#41}[$\theta_{41}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $P_{21}$.+- params:+ r: '42'+ number: x^24 - x^23 - x^22 + x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#42}[$\theta_{42}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $Q_{22}$.+- params:+ r: '43'+ number: x^23 - x^21 - x^20 - x^19 - x^18 - x^17 - x^16 - x^15 - x^14 - x^13 - x^12+ - x^11 - x^10 - x^9 - x^8 - x^7 - x^6 - x^5 - x^4 - x^3 - x^2 - x - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#43}[$\theta_{43}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $P_{22}$.+- params:+ r: '44'+ number: x^25 - x^24 - x^23 + x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#44}[$\theta_{44}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $Q_{23}$.+- params:+ r: '45'+ number: x^23 - x^22 - x^20 - x^18 - x^16 - x^14 - x^12 - x^10 - x^8 - x^6 - x^4+ - x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#45}[$\theta_{45}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $P_{23}$.+- params:+ r: '46'+ number: x^26 - x^25 - x^24 + x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#46}[$\theta_{46}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $Q_{24}$.+- params:+ r: '47'+ number: x^25 - x^23 - x^22 - x^21 - x^20 - x^19 - x^18 - x^17 - x^16 - x^15 - x^14+ - x^13 - x^12 - x^11 - x^10 - x^9 - x^8 - x^7 - x^6 - x^5 - x^4 - x^3 - x^2 -+ x - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#47}[$\theta_{47}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $P_{24}$.+- params:+ r: '48'+ number: x^27 - x^26 - x^25 + x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#48}[$\theta_{48}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $Q_{25}$.+- params:+ r: '49'+ number: x^25 - x^24 - x^22 - x^20 - x^18 - x^16 - x^14 - x^12 - x^10 - x^8 - x^6+ - x^4 - x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#49}[$\theta_{49}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $P_{25}$.+- params:+ r: '50'+ number: x^28 - x^27 - x^26 + x^2 - 1+ comment: HREF{Pisot_numbers_less_than_the_golden_ratio#50}[$\theta_{50}$] is the+ root in $(1,\varphi)$; this polynomial is selected from $Q_{26}$.
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