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shangxj金蟲 (正式寫手)
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[求助]
如何用mathematica8解這一方程的所有整數(shù)解?
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如題 方程為0.91x+0.45y+0.75z=70 請(qǐng)大俠不吝相助,并另有獎(jiǎng)勵(lì)奉上。 |
金蟲 (正式寫手)
金蟲 (正式寫手)
鐵桿木蟲 (職業(yè)作家)
木蟲 (著名寫手)
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雖然你要求用mathematica8解這個(gè)方程的整數(shù)解。但是我不會(huì)mathematica8這個(gè)軟件。我用Fortran編寫了一段小程序,給你解了一下。為了減小計(jì)算量,首先解了一下非負(fù)整數(shù)解如下: x = 10 y = 2 z = 80 x = 10 y = 7 z = 77 x = 10 y = 12 z = 74 x = 10 y = 17 z = 71 x = 10 y = 22 z = 68 x = 10 y = 27 z = 65 x = 10 y = 32 z = 62 x = 10 y = 37 z = 59 x = 10 y = 42 z = 56 x = 10 y = 47 z = 53 x = 10 y = 52 z = 50 x = 10 y = 57 z = 47 x = 10 y = 62 z = 44 x = 10 y = 67 z = 41 x = 10 y = 72 z = 38 x = 10 y = 77 z = 35 x = 10 y = 82 z = 32 x = 10 y = 87 z = 29 x = 10 y = 92 z = 26 x = 10 y = 97 z = 23 x = 10 y = 102 z = 20 x = 10 y = 107 z = 17 x = 10 y = 112 z = 14 x = 10 y = 117 z = 11 x = 10 y = 122 z = 8 x = 10 y = 127 z = 5 x = 10 y = 132 z = 2 x = 25 y = 0 z = 63 x = 25 y = 5 z = 60 x = 25 y = 10 z = 57 x = 25 y = 15 z = 54 x = 25 y = 20 z = 51 x = 25 y = 25 z = 48 x = 25 y = 30 z = 45 x = 25 y = 35 z = 42 x = 25 y = 40 z = 39 x = 25 y = 45 z = 36 x = 25 y = 50 z = 33 x = 25 y = 55 z = 30 x = 25 y = 60 z = 27 x = 25 y = 65 z = 24 x = 25 y = 70 z = 21 x = 25 y = 75 z = 18 x = 25 y = 80 z = 15 x = 25 y = 85 z = 12 x = 25 y = 90 z = 9 x = 25 y = 95 z = 6 x = 25 y = 100 z = 3 x = 25 y = 105 z = 0 x = 40 y = 3 z = 43 x = 40 y = 8 z = 40 x = 40 y = 13 z = 37 x = 40 y = 18 z = 34 x = 40 y = 23 z = 31 x = 40 y = 28 z = 28 x = 40 y = 33 z = 25 x = 40 y = 38 z = 22 x = 40 y = 43 z = 19 x = 40 y = 48 z = 16 x = 40 y = 53 z = 13 x = 40 y = 58 z = 10 x = 40 y = 63 z = 7 x = 40 y = 68 z = 4 x = 40 y = 73 z = 1 x = 55 y = 1 z = 26 x = 55 y = 6 z = 23 x = 55 y = 11 z = 20 x = 55 y = 16 z = 17 x = 55 y = 21 z = 14 x = 55 y = 26 z = 11 x = 55 y = 31 z = 8 x = 55 y = 36 z = 5 x = 55 y = 41 z = 2 x = 70 y = 4 z = 6 x = 70 y = 9 z = 3 x = 70 y = 14 z = 0 在[-1000,1000]這個(gè)區(qū)間內(nèi)的整數(shù)就有33177組。估計(jì)你的這個(gè)問(wèn)題也是有實(shí)際應(yīng)用的,所以我覺(jué)得你肯定是有區(qū)間界定的。因此我把我的代碼放在這兒,你可以通過(guò)調(diào)整這個(gè)區(qū)間的上下線來(lái)尋找你想要的結(jié)果: program sovl integer*4 i, j, k integer*4 max_x, max_y, max_z real*8 resu,EPS parameter (EPS=1.d-300) max_x=int(70d0/0.91d0)+1 max_y=int(70d0/0.45d0)+1 max_z=int(70d0/0.75d0)+1 open(unit=100,file="solv.dat" ![]() do i=-1000,1000,1 do j=-1000,1000,1 do k=-1000,1000,1 resu=(real(i)*0.91d0+real(j)*0.45d0+real(k)*0.75d0) if(abs(resu-70d0) write(100,'(a4,I5,2x,a4,I5,2x,a4,I5)')"x = ",i,"y = ",j,"z = ",k endif enddo enddo enddo end program sovl |

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