diff --git a/data/Polynomials/Cyclotomic_polynomials/generate.sage b/data/Polynomials/Cyclotomic_polynomials/generate.sage new file mode 100644 index 0000000..75a641b --- /dev/null +++ b/data/Polynomials/Cyclotomic_polynomials/generate.sage @@ -0,0 +1,10 @@ +from utils.utils import numbers_to_yaml +import yaml +import os + +path = 'data/Polynomials/Cyclotomic_polynomials' + +numbers = {int(n): str(cyclotomic_polynomial(n)) for n in [1..100]} + +filename = os.path.join(path, 'polynomials.yaml') +yaml.dump(numbers, stream = open(filename, 'w'), sort_keys = False) diff --git a/data/Polynomials/Cyclotomic_polynomials/polynomials.yaml b/data/Polynomials/Cyclotomic_polynomials/polynomials.yaml new file mode 100644 index 0000000..f1f00f1 --- /dev/null +++ b/data/Polynomials/Cyclotomic_polynomials/polynomials.yaml @@ -0,0 +1,221 @@ +1: x - 1 +2: x + 1 +3: x^2 + x + 1 +4: x^2 + 1 +5: x^4 + x^3 + x^2 + x + 1 +6: x^2 - x + 1 +7: x^6 + x^5 + x^4 + x^3 + x^2 + x + 1 +8: x^4 + 1 +9: x^6 + x^3 + 1 +10: x^4 - x^3 + x^2 - x + 1 +11: x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1 +12: x^4 - x^2 + 1 +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 +14: x^6 - x^5 + x^4 - x^3 + x^2 - x + 1 +15: x^8 - x^7 + x^5 - x^4 + x^3 - x + 1 +16: x^8 + 1 +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 +18: x^6 - x^3 + 1 +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 +20: x^8 - x^6 + x^4 - x^2 + 1 +21: x^12 - x^11 + x^9 - x^8 + x^6 - x^4 + x^3 - x + 1 +22: x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1 +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 +24: x^8 - x^4 + 1 +25: x^20 + x^15 + x^10 + x^5 + 1 +26: x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1 +27: x^18 + x^9 + 1 +28: x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1 +29: x^28 + x^27 + x^26 + x^25 + x^24 + 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 +30: x^8 + x^7 - x^5 - x^4 - x^3 + x + 1 +31: x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + 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 +32: x^16 + 1 +33: x^20 - x^19 + x^17 - x^16 + x^14 - x^13 + x^11 - x^10 + x^9 - x^7 + x^6 - x^4 + + x^3 - x + 1 +34: 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 +35: x^24 - x^23 + x^19 - x^18 + x^17 - x^16 + x^14 - x^13 + x^12 - x^11 + x^10 - x^8 + + x^7 - x^6 + x^5 - x + 1 +36: x^12 - x^6 + 1 +37: x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + + x^24 + 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 +38: 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 +39: x^24 - x^23 + x^21 - x^20 + x^18 - x^17 + x^15 - x^14 + x^12 - x^10 + x^9 - x^7 + + x^6 - x^4 + x^3 - x + 1 +40: x^16 - x^12 + x^8 - x^4 + 1 +41: x^40 + x^39 + x^38 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + + x^28 + x^27 + x^26 + x^25 + x^24 + 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 +42: x^12 + x^11 - x^9 - x^8 + x^6 - x^4 - x^3 + x + 1 +43: x^42 + x^41 + x^40 + x^39 + x^38 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + 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 +44: x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1 +45: x^24 - x^21 + x^15 - x^12 + x^9 - x^3 + 1 +46: 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 +47: x^46 + x^45 + x^44 + x^43 + x^42 + x^41 + x^40 + x^39 + x^38 + x^37 + x^36 + x^35 + + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + 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 +48: x^16 - x^8 + 1 +49: x^42 + x^35 + x^28 + x^21 + x^14 + x^7 + 1 +50: x^20 - x^15 + x^10 - x^5 + 1 +51: x^32 - x^31 + x^29 - x^28 + x^26 - x^25 + x^23 - x^22 + x^20 - x^19 + x^17 - x^16 + + x^15 - x^13 + x^12 - x^10 + x^9 - x^7 + x^6 - x^4 + x^3 - x + 1 +52: 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 +53: x^52 + x^51 + x^50 + x^49 + x^48 + x^47 + x^46 + x^45 + x^44 + x^43 + x^42 + x^41 + + x^40 + x^39 + x^38 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + + x^28 + x^27 + x^26 + x^25 + x^24 + 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 +54: x^18 - x^9 + 1 +55: x^40 - x^39 + x^35 - x^34 + x^30 - x^28 + x^25 - x^23 + x^20 - x^17 + x^15 - x^12 + + x^10 - x^6 + x^5 - x + 1 +56: x^24 - x^20 + x^16 - x^12 + x^8 - x^4 + 1 +57: x^36 - x^35 + x^33 - x^32 + x^30 - x^29 + x^27 - x^26 + x^24 - x^23 + x^21 - x^20 + + x^18 - x^16 + x^15 - x^13 + x^12 - x^10 + x^9 - x^7 + x^6 - x^4 + x^3 - x + 1 +58: x^28 - x^27 + x^26 - x^25 + x^24 - 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 +59: x^58 + x^57 + x^56 + x^55 + x^54 + x^53 + x^52 + x^51 + x^50 + x^49 + x^48 + x^47 + + x^46 + x^45 + x^44 + x^43 + x^42 + x^41 + x^40 + x^39 + x^38 + x^37 + x^36 + x^35 + + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + 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 +60: x^16 + x^14 - x^10 - x^8 - x^6 + x^2 + 1 +61: x^60 + x^59 + x^58 + x^57 + x^56 + x^55 + x^54 + x^53 + x^52 + x^51 + x^50 + x^49 + + x^48 + x^47 + x^46 + x^45 + x^44 + x^43 + x^42 + x^41 + x^40 + x^39 + x^38 + x^37 + + x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + + x^24 + 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 +62: x^30 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - 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 +63: x^36 - x^33 + x^27 - x^24 + x^18 - x^12 + x^9 - x^3 + 1 +64: x^32 + 1 +65: x^48 - x^47 + x^43 - x^42 + x^38 - x^37 + x^35 - x^34 + x^33 - x^32 + x^30 - x^29 + + x^28 - x^27 + x^25 - x^24 + x^23 - x^21 + x^20 - x^19 + x^18 - x^16 + x^15 - x^14 + + x^13 - x^11 + x^10 - x^6 + x^5 - x + 1 +66: x^20 + x^19 - x^17 - x^16 + x^14 + x^13 - x^11 - x^10 - x^9 + x^7 + x^6 - x^4 + - x^3 + x + 1 +67: x^66 + x^65 + x^64 + x^63 + x^62 + x^61 + x^60 + x^59 + x^58 + x^57 + x^56 + x^55 + + x^54 + x^53 + x^52 + x^51 + x^50 + x^49 + x^48 + x^47 + x^46 + x^45 + x^44 + x^43 + + x^42 + x^41 + x^40 + x^39 + x^38 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + 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 +68: x^32 - x^30 + x^28 - x^26 + 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 +69: x^44 - x^43 + x^41 - x^40 + x^38 - x^37 + x^35 - x^34 + x^32 - x^31 + x^29 - x^28 + + x^26 - x^25 + x^23 - x^22 + x^21 - x^19 + x^18 - x^16 + x^15 - x^13 + x^12 - x^10 + + x^9 - x^7 + x^6 - x^4 + x^3 - x + 1 +70: x^24 + x^23 - x^19 - x^18 - x^17 - x^16 + x^14 + x^13 + x^12 + x^11 + x^10 - x^8 + - x^7 - x^6 - x^5 + x + 1 +71: x^70 + x^69 + x^68 + x^67 + x^66 + x^65 + x^64 + x^63 + x^62 + x^61 + x^60 + x^59 + + x^58 + x^57 + x^56 + x^55 + x^54 + x^53 + x^52 + x^51 + x^50 + x^49 + x^48 + x^47 + + x^46 + x^45 + x^44 + x^43 + x^42 + x^41 + x^40 + x^39 + x^38 + x^37 + x^36 + x^35 + + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + 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 +72: x^24 - x^12 + 1 +73: x^72 + x^71 + x^70 + x^69 + x^68 + x^67 + x^66 + x^65 + x^64 + x^63 + x^62 + x^61 + + x^60 + x^59 + x^58 + x^57 + x^56 + x^55 + x^54 + x^53 + x^52 + x^51 + x^50 + x^49 + + x^48 + x^47 + x^46 + x^45 + x^44 + x^43 + x^42 + x^41 + x^40 + x^39 + x^38 + x^37 + + x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + + x^24 + 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 +74: x^36 - x^35 + x^34 - x^33 + x^32 - x^31 + x^30 - x^29 + x^28 - x^27 + x^26 - x^25 + + x^24 - 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 +75: x^40 - x^35 + x^25 - x^20 + x^15 - x^5 + 1 +76: x^36 - x^34 + x^32 - x^30 + x^28 - x^26 + 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 +77: x^60 - x^59 + x^53 - x^52 + x^49 - x^48 + x^46 - x^45 + x^42 - x^41 + x^39 - x^37 + + x^35 - x^34 + x^32 - x^30 + x^28 - x^26 + x^25 - x^23 + x^21 - x^19 + x^18 - x^15 + + x^14 - x^12 + x^11 - x^8 + x^7 - x + 1 +78: x^24 + x^23 - x^21 - x^20 + x^18 + x^17 - x^15 - x^14 + x^12 - x^10 - x^9 + x^7 + + x^6 - x^4 - x^3 + x + 1 +79: x^78 + x^77 + x^76 + x^75 + x^74 + x^73 + x^72 + x^71 + x^70 + x^69 + x^68 + x^67 + + x^66 + x^65 + x^64 + x^63 + x^62 + x^61 + x^60 + x^59 + x^58 + x^57 + x^56 + x^55 + + x^54 + x^53 + x^52 + x^51 + x^50 + x^49 + x^48 + x^47 + x^46 + x^45 + x^44 + x^43 + + x^42 + x^41 + x^40 + x^39 + x^38 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + 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 +80: x^32 - x^24 + x^16 - x^8 + 1 +81: x^54 + x^27 + 1 +82: x^40 - x^39 + x^38 - x^37 + x^36 - x^35 + x^34 - x^33 + x^32 - x^31 + x^30 - x^29 + + x^28 - x^27 + x^26 - x^25 + x^24 - 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 +83: x^82 + x^81 + x^80 + x^79 + x^78 + x^77 + x^76 + x^75 + x^74 + x^73 + x^72 + x^71 + + x^70 + x^69 + x^68 + x^67 + x^66 + x^65 + x^64 + x^63 + x^62 + x^61 + x^60 + x^59 + + x^58 + x^57 + x^56 + x^55 + x^54 + x^53 + x^52 + x^51 + x^50 + x^49 + x^48 + x^47 + + x^46 + x^45 + x^44 + x^43 + x^42 + x^41 + x^40 + x^39 + x^38 + x^37 + x^36 + x^35 + + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + 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 +84: x^24 + x^22 - x^18 - x^16 + x^12 - x^8 - x^6 + x^2 + 1 +85: x^64 - x^63 + x^59 - x^58 + x^54 - x^53 + x^49 - x^48 + x^47 - x^46 + x^44 - x^43 + + x^42 - x^41 + x^39 - x^38 + x^37 - x^36 + x^34 - x^33 + x^32 - x^31 + x^30 - x^28 + + x^27 - x^26 + x^25 - x^23 + x^22 - x^21 + x^20 - x^18 + x^17 - x^16 + x^15 - x^11 + + x^10 - x^6 + x^5 - x + 1 +86: x^42 - x^41 + x^40 - x^39 + x^38 - x^37 + x^36 - x^35 + x^34 - x^33 + x^32 - x^31 + + x^30 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - 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 +87: x^56 - x^55 + x^53 - x^52 + x^50 - x^49 + x^47 - x^46 + x^44 - x^43 + x^41 - x^40 + + x^38 - x^37 + x^35 - x^34 + x^32 - x^31 + x^29 - x^28 + x^27 - x^25 + x^24 - x^22 + + x^21 - x^19 + x^18 - x^16 + x^15 - x^13 + x^12 - x^10 + x^9 - x^7 + x^6 - x^4 + + x^3 - x + 1 +88: x^40 - x^36 + x^32 - x^28 + x^24 - x^20 + x^16 - x^12 + x^8 - x^4 + 1 +89: x^88 + x^87 + x^86 + x^85 + x^84 + x^83 + x^82 + x^81 + x^80 + x^79 + x^78 + x^77 + + x^76 + x^75 + x^74 + x^73 + x^72 + x^71 + x^70 + x^69 + x^68 + x^67 + x^66 + x^65 + + x^64 + x^63 + x^62 + x^61 + x^60 + x^59 + x^58 + x^57 + x^56 + x^55 + x^54 + x^53 + + x^52 + x^51 + x^50 + x^49 + x^48 + x^47 + x^46 + x^45 + x^44 + x^43 + x^42 + x^41 + + x^40 + x^39 + x^38 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + + x^28 + x^27 + x^26 + x^25 + x^24 + 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 +90: x^24 + x^21 - x^15 - x^12 - x^9 + x^3 + 1 +91: x^72 - x^71 + x^65 - x^64 + x^59 - x^57 + x^52 - x^50 + x^46 - x^43 + x^39 - x^36 + + x^33 - x^29 + x^26 - x^22 + x^20 - x^15 + x^13 - x^8 + x^7 - x + 1 +92: x^44 - x^42 + x^40 - x^38 + x^36 - x^34 + x^32 - x^30 + x^28 - x^26 + 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 +93: x^60 - x^59 + x^57 - x^56 + x^54 - x^53 + x^51 - x^50 + x^48 - x^47 + x^45 - x^44 + + x^42 - x^41 + x^39 - x^38 + x^36 - x^35 + x^33 - x^32 + x^30 - x^28 + x^27 - x^25 + + x^24 - x^22 + x^21 - x^19 + x^18 - x^16 + x^15 - x^13 + x^12 - x^10 + x^9 - x^7 + + x^6 - x^4 + x^3 - x + 1 +94: x^46 - x^45 + x^44 - x^43 + x^42 - x^41 + x^40 - x^39 + x^38 - x^37 + x^36 - x^35 + + x^34 - x^33 + x^32 - x^31 + x^30 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - 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 +95: x^72 - x^71 + x^67 - x^66 + x^62 - x^61 + x^57 - x^56 + x^53 - x^51 + x^48 - x^46 + + x^43 - x^41 + x^38 - x^36 + x^34 - x^31 + x^29 - x^26 + x^24 - x^21 + x^19 - x^16 + + x^15 - x^11 + x^10 - x^6 + x^5 - x + 1 +96: x^32 - x^16 + 1 +97: x^96 + x^95 + x^94 + x^93 + x^92 + x^91 + x^90 + x^89 + x^88 + x^87 + x^86 + x^85 + + x^84 + x^83 + x^82 + x^81 + x^80 + x^79 + x^78 + x^77 + x^76 + x^75 + x^74 + x^73 + + x^72 + x^71 + x^70 + x^69 + x^68 + x^67 + x^66 + x^65 + x^64 + x^63 + x^62 + x^61 + + x^60 + x^59 + x^58 + x^57 + x^56 + x^55 + x^54 + x^53 + x^52 + x^51 + x^50 + x^49 + + x^48 + x^47 + x^46 + x^45 + x^44 + x^43 + x^42 + x^41 + x^40 + x^39 + x^38 + x^37 + + x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + + x^24 + 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 +98: x^42 - x^35 + x^28 - x^21 + x^14 - x^7 + 1 +99: x^60 - x^57 + x^51 - x^48 + x^42 - x^39 + x^33 - x^30 + x^27 - x^21 + x^18 - x^12 + + x^9 - x^3 + 1 +100: x^40 - x^30 + x^20 - x^10 + 1 diff --git a/data/Polynomials/Cyclotomic_polynomials/table.yaml b/data/Polynomials/Cyclotomic_polynomials/table.yaml new file mode 100644 index 0000000..2a8d9f4 --- /dev/null +++ b/data/Polynomials/Cyclotomic_polynomials/table.yaml @@ -0,0 +1,48 @@ +ID: INPUT{id.yaml} + +Title: > + Cyclotomic polynomials + +Definition: > + The $n$'th cyclotomic polynomial $\Phi_n(x)$ is the monic polynomial + whose roots are the primitive $n$'th roots of unity. + +Parameters: + n: + type: Z + constraints: $n \geq 1$ + +Comments: + +Formulas: + formula-via-roots: > + $\Phi_n(x) = \prod_{1\leq k \leq n: \gcd(n,k)=1} (x-\exp(2\pi ik/n)$. + +Programs: + program-sage: + language: Sage + code: | + polynomials = {n: cyclotomic_polynomial(n) for n in [1..100]} + +References: + +Links: + Wiki: + title: "Wikipedia: Cyclotomic polynomial" + url: https://en.wikipedia.org/wiki/Cyclotomic_polynomial + +Similar tables: + +Keywords: + +Tags: +- Polynomial + +Data properties: + type: Z[x] + complete: no + +Display properties: + number-header: $\Phi_n(x)$ + +Data: INPUT{polynomials.yaml}