Différences
Ci-dessous, les différences entre deux révisions de la page.
Prochaine révision | Révision précédenteDernière révisionLes deux révisions suivantes | ||
teaching:progappchim:math_nombres [2020/01/14 12:22] – créée villersd | teaching:progappchim:math_nombres [2020/01/14 13:58] – villersd | ||
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Ligne 11: | Ligne 11: | ||
===== Calculs en précision arbitraire ===== | ===== Calculs en précision arbitraire ===== | ||
<note tip> | <note tip> | ||
- | Ces évaluations | + | Les calculs suivants |
* 1/9² = 0.0123456790123456790123456790123456790123456790123457... | * 1/9² = 0.0123456790123456790123456790123456790123456790123457... | ||
Ligne 30: | Ligne 30: | ||
$$1/(1-x)^2 \approx 1 + 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 + 7x^6 + 8x^7 + 9x^8 + ...$$ | $$1/(1-x)^2 \approx 1 + 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 + 7x^6 + 8x^7 + 9x^8 + ...$$ | ||
+ | Ce développement va introduire des décimales particulières si x = 0.1, 0.01 ou 0.001 | ||
+ | |||
+ | ==== Programme ==== | ||
+ | |||
+ | <code python> | ||
+ | # | ||
+ | # -*- coding: utf-8 -*- | ||
+ | """ | ||
+ | ' | ||
+ | consécutives | ||
+ | |||
+ | Librairie de multiprécision : http:// | ||
+ | |||
+ | """ | ||
+ | |||
+ | from mpmath import mp # multiprecision library | ||
+ | n = 41 | ||
+ | mp.dps = n | ||
+ | #mp.pretty = True | ||
+ | print(' | ||
+ | |||
+ | print(' | ||
+ | sumt = mp.mpf(0) | ||
+ | for i in range(40, 0, -1): | ||
+ | t = mp.mpf(i) * (mp.mpf(1)/ | ||
+ | | ||
+ | sumt += t | ||
+ | print(mp.nstr(t, | ||
+ | mp.nstr(sumt, | ||
+ | |||
+ | print(100/ | ||
+ | |||
+ | n = 51 | ||
+ | mp.dps = n | ||
+ | #mp.pretty = True | ||
+ | print(' | ||
+ | |||
+ | print(' | ||
+ | sumt = mp.mpf(0) | ||
+ | for i in range(25, 0, -1): | ||
+ | t = mp.mpf(i) * (mp.mpf(1)/ | ||
+ | | ||
+ | sumt += t | ||
+ | print(mp.nstr(t, | ||
+ | mp.nstr(sumt, | ||
+ | |||
+ | print(10000/ | ||
+ | </ | ||
+ | |||
+ | |||
+ | |||
+ | ==== Résultats ==== | ||
+ | < | ||
+ | standard float value : 1.2345679012345678 | ||
+ | |||
+ | Multiprécision : | ||
+ | |||
+ | 0.000000000000000000000000000000000000040 0.000000000000000000000000000000000000040 | ||
+ | 0.000000000000000000000000000000000000390 0.000000000000000000000000000000000000430 | ||
+ | 0.000000000000000000000000000000000003800 0.000000000000000000000000000000000004230 | ||
+ | 0.000000000000000000000000000000000037000 0.000000000000000000000000000000000041230 | ||
+ | 0.000000000000000000000000000000000360000 0.000000000000000000000000000000000401230 | ||
+ | 0.000000000000000000000000000000003500000 0.000000000000000000000000000000003901230 | ||
+ | 0.000000000000000000000000000000034000000 0.000000000000000000000000000000037901230 | ||
+ | 0.000000000000000000000000000000330000000 0.000000000000000000000000000000367901230 | ||
+ | 0.000000000000000000000000000003200000000 0.000000000000000000000000000003567901230 | ||
+ | 0.000000000000000000000000000031000000000 0.000000000000000000000000000034567901230 | ||
+ | 0.000000000000000000000000000300000000000 0.000000000000000000000000000334567901230 | ||
+ | 0.000000000000000000000000002900000000000 0.000000000000000000000000003234567901230 | ||
+ | 0.000000000000000000000000028000000000000 0.000000000000000000000000031234567901230 | ||
+ | 0.000000000000000000000000270000000000000 0.000000000000000000000000301234567901230 | ||
+ | 0.000000000000000000000002600000000000000 0.000000000000000000000002901234567901230 | ||
+ | 0.000000000000000000000025000000000000000 0.000000000000000000000027901234567901230 | ||
+ | 0.000000000000000000000240000000000000000 0.000000000000000000000267901234567901230 | ||
+ | 0.000000000000000000002300000000000000000 0.000000000000000000002567901234567901230 | ||
+ | 0.000000000000000000022000000000000000000 0.000000000000000000024567901234567901230 | ||
+ | 0.000000000000000000210000000000000000000 0.000000000000000000234567901234567901230 | ||
+ | 0.000000000000000002000000000000000000000 0.000000000000000002234567901234567901230 | ||
+ | 0.000000000000000019000000000000000000000 0.000000000000000021234567901234567901230 | ||
+ | 0.000000000000000180000000000000000000000 0.000000000000000201234567901234567901230 | ||
+ | 0.000000000000001700000000000000000000000 0.000000000000001901234567901234567901230 | ||
+ | 0.000000000000016000000000000000000000000 0.000000000000017901234567901234567901230 | ||
+ | 0.000000000000150000000000000000000000000 0.000000000000167901234567901234567901230 | ||
+ | 0.000000000001400000000000000000000000000 0.000000000001567901234567901234567901230 | ||
+ | 0.000000000013000000000000000000000000000 0.000000000014567901234567901234567901230 | ||
+ | 0.000000000120000000000000000000000000000 0.000000000134567901234567901234567901230 | ||
+ | 0.000000001100000000000000000000000000000 0.000000001234567901234567901234567901230 | ||
+ | 0.000000010000000000000000000000000000000 0.000000011234567901234567901234567901230 | ||
+ | 0.000000090000000000000000000000000000000 0.000000101234567901234567901234567901230 | ||
+ | 0.000000800000000000000000000000000000000 0.000000901234567901234567901234567901230 | ||
+ | 0.000007000000000000000000000000000000000 0.000007901234567901234567901234567901230 | ||
+ | 0.000060000000000000000000000000000000000 0.000067901234567901234567901234567901230 | ||
+ | 0.000500000000000000000000000000000000000 0.000567901234567901234567901234567901230 | ||
+ | 0.004000000000000000000000000000000000000 0.004567901234567901234567901234567901230 | ||
+ | 0.030000000000000000000000000000000000000 0.034567901234567901234567901234567901230 | ||
+ | 0.200000000000000000000000000000000000000 0.234567901234567901234567901234567901230 | ||
+ | 1.000000000000000000000000000000000000000 1.234567901234567901234567901234567901230 | ||
+ | |||
+ | 1.2345679012345679012345679012345679012346 | ||
+ | |||
+ | ---- | ||
+ | |||
+ | standard float value : 1.0203040506070808 | ||
+ | |||
+ | Multiprécision : | ||
+ | |||
+ | 0.0000000000000000000000000000000000000000000000250 0.0000000000000000000000000000000000000000000000250 | ||
+ | 0.0000000000000000000000000000000000000000000024000 0.0000000000000000000000000000000000000000000024250 | ||
+ | 0.0000000000000000000000000000000000000000002300000 0.0000000000000000000000000000000000000000002324250 | ||
+ | 0.0000000000000000000000000000000000000000220000000 0.0000000000000000000000000000000000000000222324250 | ||
+ | 0.0000000000000000000000000000000000000021000000000 0.0000000000000000000000000000000000000021222324250 | ||
+ | 0.0000000000000000000000000000000000002000000000000 0.0000000000000000000000000000000000002021222324250 | ||
+ | 0.0000000000000000000000000000000000190000000000000 0.0000000000000000000000000000000000192021222324250 | ||
+ | 0.0000000000000000000000000000000018000000000000000 0.0000000000000000000000000000000018192021222324250 | ||
+ | 0.0000000000000000000000000000001700000000000000000 0.0000000000000000000000000000001718192021222324250 | ||
+ | 0.0000000000000000000000000000160000000000000000000 0.0000000000000000000000000000161718192021222324250 | ||
+ | 0.0000000000000000000000000015000000000000000000000 0.0000000000000000000000000015161718192021222324250 | ||
+ | 0.0000000000000000000000001400000000000000000000000 0.0000000000000000000000001415161718192021222324250 | ||
+ | 0.0000000000000000000000130000000000000000000000000 0.0000000000000000000000131415161718192021222324250 | ||
+ | 0.0000000000000000000012000000000000000000000000000 0.0000000000000000000012131415161718192021222324250 | ||
+ | 0.0000000000000000001100000000000000000000000000000 0.0000000000000000001112131415161718192021222324250 | ||
+ | 0.0000000000000000100000000000000000000000000000000 0.0000000000000000101112131415161718192021222324250 | ||
+ | 0.0000000000000009000000000000000000000000000000000 0.0000000000000009101112131415161718192021222324250 | ||
+ | 0.0000000000000800000000000000000000000000000000000 0.0000000000000809101112131415161718192021222324250 | ||
+ | 0.0000000000070000000000000000000000000000000000000 0.0000000000070809101112131415161718192021222324250 | ||
+ | 0.0000000006000000000000000000000000000000000000000 0.0000000006070809101112131415161718192021222324250 | ||
+ | 0.0000000500000000000000000000000000000000000000000 0.0000000506070809101112131415161718192021222324250 | ||
+ | 0.0000040000000000000000000000000000000000000000000 0.0000040506070809101112131415161718192021222324250 | ||
+ | 0.0003000000000000000000000000000000000000000000000 0.0003040506070809101112131415161718192021222324250 | ||
+ | 0.0200000000000000000000000000000000000000000000000 0.0203040506070809101112131415161718192021222324250 | ||
+ | 1.0000000000000000000000000000000000000000000000000 1.0203040506070809101112131415161718192021222324250 | ||
+ | |||
+ | 1.02030405060708091011121314151617181920212223242526 | ||
+ | </ | ||