Следствие. Для
![](data:image/gif;base64,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)
имеет место равенство:
![](data:image/gif;base64,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)
.
Теорема. Пусть
![](data:image/gif;base64,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)
и
![](data:image/gif;base64,R0lGODlhHwAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgAZAA8AhQAAAAAAAB4AHh0AHQAAHR0AAAAAMx0AMgAdSAAcSB0dSAAzWgAzWx1GbDIAHTMAADMAHTMAMzIAMjQ0HTNdXTNGbjNbgEgcAEgdAEceM1ozAFszAF1/f113d0Rqe0huf1V7amxGHW5GM3d3XX9/XX9uSHtqRGZ3d2aIiIBbM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZnQIBwSCwaj8YIUqhcAlIGp1DglEiHh+Jg2LgOF8OAGOAopgKEMAJL7EKRYEbxMSwLo8dCd94NDUN4RhdHdACDQ4FFE2BzQlkZQx9mACWRbABoQxtFAXIAGAF7AH5IEF5XVFKFTk1eQQA7)
- два нормированных полинома над GF(p), такие что
![](data:image/gif;base64,R0lGODlhoQAYAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIABACbABAAhQAAAAAAAB0AAB4AHh0AHQAAHR4eAAAAMx0AMx0AMgAdMwAdSAAcSB0dSAAzWgAyWgAzWx1GbB1IbjMAADIAHTMAHTMAMzIAMjMeRzQ0HTMzWzIyWjNGRjNdXTNISDNGbjNZfzNbgEgcAEgdAEgdHUgeNFozAFszAF1/f113d0Rqe0huf0Rqalluf1V7alVmZm5IHWxGHX9ZM25GM39/XXd3XW5/WXtqRH9uSHd3ZmZ3d2aIiIBbM4iIZgECAwECAwb/QIBwSCwaj8ikcslsOp/QqHQ6nHAEEap2y+0SRYHAImlRlolhBtE09g7PR3hRrhVQ6UQ5XbQ8MAcqRWpGEl4yfkk4A0aIXGEhUYdLgEOLQyIOSRdOCEQxg3lum0ydb24AdlF4R6VCrXxENwSBJk8xgkMmAQVasoFCWUy3QrVuNwKQUMFLw0OZQs8AJ2EBABRGu0NiQwlDzV3Tj9ZF2QA820Ld40O8IwEPAO7R7tVr1PVGAtXTjddovELQAVCXTgisXEMaeQLwTciEZAAGTQB4JNy9ABCKFDOnUMithgAeAmikj9c5kwVWADg4AqGQaRCNGBiShUdHhjiLiHRoMNq6/xg3haTS6Q1UF39Cgg4lMoGhwqFDCSQlkkrqkKVFFFxKeAQrzypZDgoBFVRITIfLjCaxeC8jEVBAkZwNmaURDmQA7kLSO5Jp3SF8jWyUpTLuERBGJixrujKa2LIZjjBmqFaL2L5GMvjkaZPq1c/nmJqjiArJKAAm3GIuEjmx6JVJkBIp1ADADMC4mLClphrHEZWzAdS+bUS2AMSokB+Ph6jZBJLIi9SeqoS2bdxE1GHSRnoZDIxC3BVR/clNuZdDvrsVT8TtiWATwnjQF2B+OXptHF40EoN3kRPpgRcPPkKQ59ZlRVTwyxJ0VHZKBU3QseApRQB3BIRMrCIEPElYoirEZB5ReISHSIAoBIkiCjfJEiDuNCCBqpAjUIpCaAiAjTQCEEZ+SNhoYxAAOw==)
,
![](data:image/gif;base64,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)
.
Тогда
![](data:image/gif;base64,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)
Доказательство: Из предположения следует, что
![](data:image/gif;base64,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)
. Поэтому
![](data:image/gif;base64,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)
Помимо этого
![](data:image/gif;base64,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)
для
![](data:image/gif;base64,R0lGODlhIQAQAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAeAAkAhQAAAAAAAB0AHQAAHR0AMx0AMgAAMwAcSB0dSAAzWgAzWx1GbDMAADIAHTMAMzNGbjNZfzNbgEgdHUgcAEgeNFszAFozAFtISEhuf0Rqe113d1V7al1/f2xGHW5IHX9ZM3tqRH9/XX9uSHd3ZmZ3d2aIiIBbM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZHQIBwSCwajaCjkihZCoqMQGApXBwr0kBkmFBmvwqjxUigAsZUjPFARVDZw8vQSvR8s2HiRIk+5pUFABRDUQEGSg5mAQNqAEEAOw==)
, и полиномы
![](data:image/gif;base64,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)
и
![](data:image/gif;base64,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)
также взаимно просты. Поэтому
![](data:image/gif;base64,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)
.
Таким образом, пусть
![](data:image/gif;base64,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)
- свободный от квадратов полином степени n, который нужно разложить на множители над GF(p), и предположим, удалось найти полиномы
![](data:image/gif;base64,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)
,
![](data:image/gif;base64,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)
, такие что
![](data:image/gif;base64,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)
. По одной из ранее доказанных теорем, полином
![](data:image/gif;base64,R0lGODlhLQAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIABAApAA0AhQAAAAAAAB0AAAAAHQAdSB0dSAAzWgAzWx1GbB1IbjMAADMAMzQeSDQ0HTMzWzIyWjNGRjNZfzNbgEgcAEgdAFozAFszAF1/f0huf0Rqe2xGHW5IHX9ZM25GM39/XW5/WXd3XWp7VX9uSHd3ZmZ3d2aIiIBbM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZaQIBwSCwaj8jkUQERIJTQKLEirUoZ1mwyAlhov8JKYABWmsbDQLk4zgDOhKIBcBAqyGuhQXMUOa0BgYJqRgJJE3lIiEcdAHOJRQ2QWgVsQxQBCYkbAXVChABBADs=)
имеет в
![](data:image/gif;base64,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)
ровно p корней. А именно 0,1…p-1. Значит он раскладывается следующим образом
![](data:image/gif;base64,R0lGODlh5wAYAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIABADiABAAhQAAAAAAAB0AAB4AHgAAHR4eAAAAMx0AMh0AMwAdMwAdSAAcSB0dSR0dSAAzWgAzWx1GbB1IbjMAADIAHTMAHTMAMzIAMjMeRzQ0HTMzWzNGRjNZfzNbgEgcAEgdAEgdHUgeNEceM1ozAFszAFozHUhZf11/f113d0Rqe0huf1luf25IHWxGHW5GM39ZM39ZSH9/XW5/WXd3XX9uSHtqRHd3ZmZ3d2aIiIBbM4iIZgECAwECAwECAwECAwECAwECAwb/QIBwSCwaj8ikcslsOp/QqHRKrR4lGgHEyu16v+CwWCpSjL8Vb2chTB/dXkkgsGlT4Wfp2i7d5qkGcQFsQgNFOIFiK3QAM4ZRiX9RckQDKFB4kk8WYCyEQgdEnGcdDkOhm5pUnwAITSIBBKpRImKsAKZCfme5ACxPtbNHIUm/RMZCsUMBZl3Kyc1QzwABQhNEONPMUMin1kfa0VAdRahM14fhUQLVsJFFxEm35r71QxKyVr/dy3P+1UhMPRjybojAKbckAECEZF+VGUYkcGhSkMhBKgWG7CIS7wg/ABKJCHgy4p+/gUZGctEyhEVFACyNmJxTxFMRCVteClFZZCbA6yYKmbhMEnNIyZm9iCQYQo6IzyMJjUwcM7VKU4JHrkqJOjRJVSlfheCkmEQrrSGOUgwrFnEjhjNvjRw1ibJIC1xEXmJI+sQmkaA6AcQFE5RJ4L1URgmpC09JVI0AGgC4+2WLZMpRcBxBN0QzRCFqocwbErqI5clR/gVWwhlbI9JRJAsJ3NFIMLRCWARA6eGnvt1Cek/52XvXLuAAikORMw3ZiCKLePtuQpcI72YesDcbsZFaLuXc/PF1wjzfYmFnKFxSRWFWJibrwZRGgz7PIzGFh9zPk9/J/i6yEVbfgGe8B4aB9c0hDhd4BAEAOw==)
. Заменив х на
![](data:image/gif;base64,R0lGODlhHwAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgAZAA8AhQAAAAAAAB4AHh0AHQAAHR0AAAAAMx0AMgAdSAAcSB0dSAAzWgAzWx1GbDIAHTMAADMAHTMAMzIAMjQ0HTNdXTNGbjNbgEgcAEgdAEceM1ozAFszAF1/f113d0Rqe0huf1V7amxGHW5GM3d3XX9/XX9uSHtqRGZ3d2aIiIBbM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZnQIBwSCwaj8YIUqhcAlIGp1DglEiHh+Jg2LgOF8OAGOAopgKEMAJL7EKRYEbxMSwLo8dCd94NDUN4RhdHdACDQ4FFE2BzQlkZQx9mACWRbABoQxtFAXIAGAF7AH5IEF5XVFKFTk1eQQA7)
, в кольце
![](data:image/gif;base64,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)
получим
![](data:image/gif;base64,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)
. Так как
![](data:image/gif;base64,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)
, то
![](data:image/gif;base64,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)
. Кроме того поскольку полиномы
![](data:image/gif;base64,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)
и
![](data:image/gif;base64,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)
- взаимно простые при
![](data:image/gif;base64,R0lGODlhIQAQAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAeAAkAhQAAAAAAAB0AHQAAHR0AMx0AMgAAMwAcSB0dSAAzWgAzWx1GbDMAADIAHTMAMzNGbjNZfzNbgEgdHUgcAEgeNFszAFozAFtISEhuf0Rqe113d1V7al1/f2xGHW5IHX9ZM3tqRH9/XX9uSHd3ZmZ3d2aIiIBbM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZHQIBwSCwajaCjkihZCoqMQGApXBwr0kBkmFBmvwqjxUigAsZUjPFARVDZw8vQSvR8s2HiRIk+5pUFABRDUQEGSg5mAQNqAEEAOw==)
, то
![](data:image/gif;base64,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)
- нетривиальное разложение полинома над GF(p).
Теперь задача состоит в определении полиномов
![](data:image/gif;base64,R0lGODlhHwAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgAZAA8AhQAAAAAAAB4AHh0AHQAAHR0AAAAAMx0AMgAdSAAcSB0dSAAzWgAzWx1GbDIAHTMAADMAHTMAMzIAMjQ0HTNdXTNGbjNbgEgcAEgdAEceM1ozAFszAF1/f113d0Rqe0huf1V7amxGHW5GM3d3XX9/XX9uSHtqRGZ3d2aIiIBbM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZnQIBwSCwaj8YIUqhcAlIGp1DglEiHh+Jg2LgOF8OAGOAopgKEMAJL7EKRYEbxMSwLo8dCd94NDUN4RhdHdACDQ4FFE2BzQlkZQx9mACWRbABoQxtFAXIAGAF7AH5IEF5XVFKFTk1eQQA7)
. Это можно осуществить с помощью решения систем линейных уравнений, получаемой следующим образом. Пусть
![](data:image/gif;base64,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)
, где коэффициенты требуется найти. Нужно сначала проверить делит ли
![](data:image/gif;base64,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)
полином
![](data:image/gif;base64,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)
. Ранее доказано, что
![](data:image/gif;base64,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)
.
Разделив
![](data:image/gif;base64,R0lGODlhFQAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgARAA8AhQAAAAAAAB0AAAAAHQAdSB0dSAAzWgAzWx1GbB1IbjMAADMAMzMeRzQ0HTMzWzIyWjNGRjNZfzNbgEgcAEgdAFozAFszM0gzSF1/f0huf0Rqe2xGHW5IHX9ZM25GM25/WX9/XXd3XX9uSHd3ZmZ3d2aIiIBbM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwY+QIBwSCwaj8ik0lghABQQAWIpAVSWQksxgQVEAItlwBoYDE3l4RhrAByICrNRJO0KJ3aAB9DOd9cAFAFcSEEAOw==)
на
![](data:image/gif;base64,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)
получаем
![](data:image/gif;base64,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)
, где
![](data:image/gif;base64,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)
. Теперь, заменив
![](data:image/gif;base64,R0lGODlhFQAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgARAA8AhQAAAAAAAB0AAAAAHQAdSB0dSAAzWgAzWx1GbB1IbjMAADMAMzMeRzQ0HTMzWzIyWjNGRjNZfzNbgEgcAEgdAFozAFszM0gzSF1/f0huf0Rqe2xGHW5IHX9ZM25GM25/WX9/XXd3XX9uSHd3ZmZ3d2aIiIBbM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwY+QIBwSCwaj8ik0lghABQQAWIpAVSWQksxgQVEAItlwBoYDE3l4RhrAByICrNRJO0KJ3aAB9DOd9cAFAFcSEEAOw==)
на соответствующие выражения, получим
![](data:image/gif;base64,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)
+[кратное
![](data:image/gif;base64,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)
].
Таким образом
![](data:image/gif;base64,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)
тогда и только тогда когда
![](data:image/gif;base64,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)
делит полином
![](data:image/gif;base64,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)
, степень которого
![](data:image/gif;base64,R0lGODlhLwATAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAqAAwAhQAAAAAAAB0AABwcHAAAHQAcSB0dSAAdSAAzWwAzWh1Ibh1GbDMAADMAHTIAHTIAMjNGbjNbgEgcAEgdAEgdHVozAFszAFszM0hbSFl/WUhuf11/f2xGHW5IHX9/XX9uSHd3ZmZ3d2aIiIBbM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZmQIBwSCwaj8ikcskcFpSIphTACDyNnEB0Or0SA9wwxysJRJIfAVi4DnsD7eQD0BAuwgCv0BK4IxNDFEV8cIVaRXpfRxUDeERjSR1GDApDfm5cBkMOABBhFW+GcEWSQwIHYVUBBABBADs=)
. Поэтому полином степени n будет делить этот полином если только он равен нулю. Приравняв его нулю и собрав коэффициенты при степенях
х, получаем систему из n линейных уравнений
![](data:image/gif;base64,R0lGODlhSAAYAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIABgBEAA4AhQAAAAAAAB0AHQAAHR0AAAAAMx0AMh0AMwAcSAAdSB0zWgAzWx1IXx1GbB1IbjIAHTMAADMzWzNGbjNdgDNbgEgcAEgdAEgdHUgeNEceM1szAFozAFozHUgzM1oyMlszM0ZGRlV7VVl/WURqe0huf11/f1V7al13d2xGHW5GM39ZSHtqRHd3XX9uSH9/XXd3ZmaIiIBdM4BbM4BuboiIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwagQIBwSCwaj8ikcllcMYuSp1TonA4FVqz1qZ1qAuDJExzYKr9h60bdMC/XbtL04WbKt4gpKl9P8q0VRWVKDkMFfUSBUodCBgAYQgoAHEmOkAAZiEOWWwEDcihDbS0EjAAxnkOZQqVCFkOvrkOtQ553ACEQbUarmr5HIEq9RKFCuxALSb0QU8xKYgwAZKpIkpRPw79DHmaDY9pDH0IQCUeDQQA7)
. Это и есть коэффициенты того полинома
![](data:image/gif;base64,R0lGODlhHwAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgAZAA8AhQAAAAAAAB4AHh0AHQAAHR0AAAAAMx0AMgAdSAAcSB0dSAAzWgAzWx1GbDIAHTMAADMAHTMAMzIAMjQ0HTNdXTNGbjNbgEgcAEgdAEceM1ozAFszAF1/f113d0Rqe0huf1V7amxGHW5GM3d3XX9/XX9uSHtqRGZ3d2aIiIBbM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZnQIBwSCwaj8YIUqhcAlIGp1DglEiHh+Jg2LgOF8OAGOAopgKEMAJL7EKRYEbxMSwLo8dCd94NDUN4RhdHdACDQ4FFE2BzQlkZQx9mACWRbABoQxtFAXIAGAF7AH5IEF5XVFKFTk1eQQA7)
.
Пусть
![](data:image/gif;base64,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)
- матрица, строки которой образуют
коэффициенты полиномов остатков. По этому всему имеет место
Теорема. Полином
![](data:image/gif;base64,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)
является решением сравнения
![](data:image/gif;base64,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)
тогда и только тогда, когда
![](data:image/gif;base64,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)
.
Пусть N – множество векторов
![](data:image/gif;base64,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)
, таких что
![](data:image/gif;base64,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)
называется
нуль-пространством матрицы
![](data:image/gif;base64,R0lGODlhJwAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgAjAA8AhQAAAAAAAAAAHR0AHR0AAAAAMwAcSAAdSB0dSQAzWgAzWwAyWh1Ibh1GbDMAADNZfzNbgEgcAFozAFszAFlZakhuf11/f113d2xGHW5IHX9ZM3d3XX9/XX9uSHtqRHd3ZmaIiIBbM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZnQIBwSCwaj8hiYJlsCifLAFETYAylziRGoCxKDNlkguhQeAvho6PINaLTxQExooYbwUNHw4glRv9HdEQERwd2Qx0DFWQLbIdEeEMZAQ9Xj3lHUEtmlwBRRxSdYQ4Bb6JIaB0En6dEQQA7)
. У этого пространства имеется базис и размерность.
Теорема. Число различных неприводимых сомножителей
![](data:image/gif;base64,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)
полинома
![](data:image/gif;base64,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)
в
![](data:image/gif;base64,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)
равно размерности нуль-пространства матрицы
![](data:image/gif;base64,R0lGODlhJwAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgAjAA8AhQAAAAAAAAAAHR0AHR0AAAAAMwAcSAAdSB0dSQAzWgAzWwAyWh1Ibh1GbDMAADNZfzNbgEgcAFozAFszAFlZakhuf11/f113d2xGHW5IHX9ZM3d3XX9/XX9uSHtqRHd3ZmaIiIBbM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZnQIBwSCwaj8hiYJlsCifLAFETYAylziRGoCxKDNlkguhQeAvho6PINaLTxQExooYbwUNHw4glRv9HdEQERwd2Qx0DFWQLbIdEeEMZAQ9Xj3lHUEtmlwBRRxSdYQ4Bb6JIaB0En6dEQQA7)
.
Доказательство: Полином
![](data:image/gif;base64,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)
тогда и только тогда когда каждый
![](data:image/gif;base64,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)
,
![](data:image/gif;base64,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)
. По ранее доказанным фактам для набора
![](data:image/gif;base64,R0lGODlhDwAYAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIACAALAAwAhAAAAAAAAB0AMwAAMwAcSAAdSAAzWgAzWx1GbB1IbjMAADIyWjNZfzNbgEgcAFozAFszM0gzSFtISF13d11/f2xGHXd3XX9uSH9/XWaIiIBbM4iIZgECAwECAwECAwECAwUkICCOJKkEQTkaKim0JNFKIzJGoiM+7RkMpAJsSCQthppAAhACADs=)
существует единственный
![](data:image/gif;base64,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)
, такой что
![](data:image/gif;base64,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)
. Существует
![](data:image/gif;base64,R0lGODlhFAAYAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIABAAQABAAhQAAAAAAAAAAHR0AAB4eAB0AHQAAMwAdMx0dSAAdSAAzWx1GbDIAHTQdNDIAMjVIWzNZfzNbgEgcAEgdHVozAFszAFszM0ZGM1tINVluf11/f0huf2xGHX9/XX9uSHtqRGZ3d2aIiIBbM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwY4QIBwSCwajwABQIFsOoWNp3QKGAQAlIBBShgunIehxEkZfgqbpmNIYTYRw22TE6i7nekpfFpPSIMAOw==)
решений сравнения
![](data:image/gif;base64,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)
.
![](data:image/gif;base64,R0lGODlhHwAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgAZAA8AhQAAAAAAAB4AHh0AHQAAHR0AAAAAMx0AMgAdSAAcSB0dSAAzWgAzWx1GbDIAHTMAADMAHTMAMzIAMjQ0HTNdXTNGbjNbgEgcAEgdAEceM1ozAFszAF1/f113d0Rqe0huf1V7amxGHW5GM3d3XX9/XX9uSHtqRGZ3d2aIiIBbM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZnQIBwSCwaj8YIUqhcAlIGp1DglEiHh+Jg2LgOF8OAGOAopgKEMAJL7EKRYEbxMSwLo8dCd94NDUN4RhdHdACDQ4FFE2BzQlkZQx9mACWRbABoQxtFAXIAGAF7AH5IEF5XVFKFTk1eQQA7)
является решением сравнения если
![](data:image/gif;base64,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)
. Для вопроса о неприводимости получен
Тест3. Полином
![](data:image/gif;base64,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)
степени
n>1 неприводим в
![](data:image/gif;base64,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)
тогда и только тогда когда нуль-пространство матрицы
![](data:image/gif;base64,R0lGODlhJwAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgAjAA8AhQAAAAAAAAAAHR0AHR0AAAAAMwAcSAAdSB0dSQAzWgAzWwAyWh1Ibh1GbDMAADNZfzNbgEgcAFozAFszAFlZakhuf11/f113d2xGHW5IHX9ZM3d3XX9/XX9uSHtqRHd3ZmaIiIBbM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZnQIBwSCwaj8hiYJlsCifLAFETYAylziRGoCxKDNlkguhQeAvho6PINaLTxQExooYbwUNHw4glRv9HdEQERwd2Qx0DFWQLbIdEeEMZAQ9Xj3lHUEtmlwBRRxSdYQ4Bb6JIaB0En6dEQQA7)
одномерно и
![](data:image/gif;base64,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)
.
Доказательство: Нуль-пространство матрицы
![](data:image/gif;base64,R0lGODlhJwAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgAjAA8AhQAAAAAAAAAAHR0AHR0AAAAAMwAcSAAdSB0dSQAzWgAzWwAyWh1Ibh1GbDMAADNZfzNbgEgcAFozAFszAFlZakhuf11/f113d2xGHW5IHX9ZM3d3XX9/XX9uSHtqRHd3ZmaIiIBbM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZnQIBwSCwaj8hiYJlsCifLAFETYAylziRGoCxKDNlkguhQeAvho6PINaLTxQExooYbwUNHw4glRv9HdEQERwd2Qx0DFWQLbIdEeEMZAQ9Xj3lHUEtmlwBRRxSdYQ4Bb6JIaB0En6dEQQA7)
одномерно тогда и только тогда когда
![](data:image/gif;base64,R0lGODlhZwAYAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgBiABMAhQAAAAAAAAAAHR4AHh0AAB4eAB0AHQAAMx0AMgAdMwAdSAAcSB0dSAAzWgAzWx1GbB1IbjIAHTMAADMAHTMAMzIAMjQ0HTNZfzNbgEgdAEgcAEgdHUceM1ozAFszAE80AFszM0YzRl1dM0ZGWVtbW0huf11/f113d0Rqe0Rublluf25IHWxGHX9ZM25GM39ZSHd3XX9/XX9uSHtqRGZ3d3d3ZmaIiIBbM4iIZgECAwECAwECAwECAwECAwECAwECAwb/QIBwSCwaj8ikcslsOp/QqHQqzFCv2CyzpO16ryCAAEpJlrGBgOJLPA/TiyEJelgOrhps3W6MAwhQFU0IVw1sR4REcS4AIU4dT4ZSGpJRHQ+RQyx+Qg5EBAEXAAF7ABFcRAECKAA3agAyiVKVQqCipEgRRa5jQgFDMkWcRxEFQnlCpUQsACyeQxJGHmnUac/HxMYAyLvKRIbXQtFDw7tFmCzeQ4BFEpiz5kTvReq189Dz5UkGQ/XbRuOiUFLCz0g6JNyIBNyURJAQSEJu+LMAEEORadWsFaEFwCEAiAAyKKvHiCMACRaF6BvC4KEyXUYgAGjJSIgsKAmFtPyojAMRX5hEbug0cnOlrzRH5q0IcO2XEGZUOFJb4qGI05AB5kElh2SDkglN3Aik5RWJTyJgwy5bOWOJjAGskqAsNKQtlDtL5iqSlmaNErFsMvT90NfsEcBFxC59dahxkml+GwcBADs=)
- степень неприводимого полинома. Тогда берём r(x)=1.
Теорема. Пусть
![](data:image/gif;base64,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)
в
![](data:image/gif;base64,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)
и
![](data:image/gif;base64,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)
- базис нуль-пространства. Тогда для каждого
![](data:image/gif;base64,R0lGODlhKQAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAgAmAA8AhQAAAAAAAAAAMx0AMh0AMwAcSB0dSAAdSAAzWgAzWx1GbDIAHTMAADMAMzMeRzNbgEgcAEgdHVszAFozHVozAEZGbl1/f1l/bkhuf0Rqe2xGHW5IHX9ZM39/XX9uSHtqRHd3ZmZ3d2aIiIBbM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZYQIBwSCwaj8gkUaBsOiVMAMLZhDYh1KwWGdkSA4WspglOKpKbgHodSJiRkyzFGT96tIbm3ftlq/lYThxUgUcDVA1Uh0hnfIxFC0IEjpCSRgwBB5RFmJpFQQA7)
,
![](data:image/gif;base64,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)
, существует k
![](data:image/gif;base64,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)
и
![](data:image/gif;base64,R0lGODlhLAAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIABAAoABIAhQAAAAAAAAAAHR0AAB0AHQAAMx0AMwAdSAAcSAAzWwAzWh1Ibh1GbDMAADMAMzMeRzMzWzIyWjNGRjNGbjNZfzNbgEgcAEgdHVozAEYzRltISEhZf11/f0huf113d0Rqe2xGHX9ZM39/XX9uSHtqRHd3XW5/WWZ3d3d3ZmaIiIBbM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZ0QIBwSCwaj8ikUokJOJ+FpXQKwAioWOJmCApUssUBdDmYNpxFVbaRkILAR8uBajien4EoUk9FGB9UV1MaQwxFF1MBRRNJFkIYbUV8SAMKRARKd5NEeJt3eEYNEgOGcGAYc6aqAKWrWA6uVE2CsbW2Qg20AEEAOw==)
, такие что
![](data:image/gif;base64,R0lGODlhKQAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIABAAlABIAhQAAAAAAAB4AHh0AAAAAHR4eAB0AHQAAMx0AMx0AMgAdMwAdSB0dSAAzWgAzWx0zWh1GbB1IbjIAHTMAADMAHTMAMzIAMjQ0HTNZfzNbgEgcAEgdAEgdHUgeNFozAFszAFszM0YzRltISF1/f113d0Rqe0huf1luf2xGHX9ZM25GM39ZSHd3XX9/XX9uSHtqRHd3ZmZ3d2Z/ZmaIiIBbM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwaSQIBwSCwaj8ikclhZOp0Hp+CZtDxd1KMnC2gQBwEMIBBNmooBQgmQCiyGiaKkINQky0UUAOUoTog0CkQQRyh4RQNHf0MeGUMGd0gajn6EQlZCW0g0h0QXikQMmZ1yRxEAoipEcUMBrkcbRZZ7AX1CAUW2ABxcFFRNVCJFLlNLiwAfrm9cwEjNVJRc0h3S1QTVR0EAOw==)
делит, а
![](data:image/gif;base64,R0lGODlhLAAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIABAAnABIAhQAAAAAAAB4AHh0AAAAAHR4eAB0AHQAAMx0AMx0AMgAdMwAdSB0dSAAzWgAzWx0zWh1GbB1IbjIAHTMAADMAHTMAMzIAMjQ0HTNZfzNbgEgcAEgdAEgdHUgeNFozAFszAFszM0YzRl1dM1tISF1/f113d0Rqe0huf1luf2xGHX9ZM25GM25dXX9ZSHd3XX9/XX9uSHtqRHd3ZmZ3d2Z/ZmaIiIBbM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwaTQIBwSCwaj8ik8lhZOp+Ag1MAVVqeMET16KmmioMABhCQbskEoSqwGCaKkoJQszQXU41vcUK0KYgQSSl2YEd8Qx4ZQwZ1SHRGE4FCV0JdRiJDNoREF4ZEDJWbRxJHEQCgRW9DAaxHGwAsRZIAKQEOq0W3QhxnABRQTVAjSAImS4cAH6xtvcFIzlCKvb0d071p1kZBADs=)
не делит
![](data:image/gif;base64,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)
.
Доказательство: В нуль-пространстве существует вектор,
![](data:image/gif;base64,R0lGODlhDQAUAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAgAKAA4AhAAAAAAAAAAAMx0AMh0AMwAcSB0dSAAdSB1GbDIAHTMAADNbgEgcAFszAFozHV1/f0huf0Rqe2xGHX9uSH9/XXtqRGaIiIBbM4iIZgECAwECAwECAwECAwECAwECAwECAwUdICCOZCk2gqmuZlCwyOqsE2sz7ACXiUiYisDBFAIAOw==)
-ая компонента которой отлична от
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-ой. Значит найдётся такое k,
![](data:image/gif;base64,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)
,
![](data:image/gif;base64,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)
. Положим
![](data:image/gif;base64,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)
.