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IntegerRelations[LinearDependency] - find an integer dependence (relation)
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Calling Sequence
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LinearDependency(v,opts)
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Parameters
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v
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list or Vector of (complex) floating-point numbers
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opts
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(optional); equation of the form method=LLL or method=PSLQ specifying the algorithm used
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Description
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By default, Bailey and Ferguson's PSLQ (Partial Sum of Least Squares) algorithm is used.
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The optional argument method=LLL specifies that the LLL (Lenstra-Lenstra-Lovasz) lattice basis reduction algorithm be used.
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Examples
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| (1) |
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![v := expand([seq(r^i, i = 0 .. 4)])](/support/helpjp/helpview.aspx?si=5685/file01986/math88.png)
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![v := [1, 2^(1/2)+3^(1/2), 5+2*2^(1/2)*3^(1/2), 11*2^(1/2)+9*3^(1/2), 49+20*2^(1/2)*3^(1/2)]](/support/helpjp/helpview.aspx?si=5685/file01986/math91.png)
| (2) |
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![v := [1., 3.14626436994, 9.89897948556, 31.1448064542, 97.9897948556]](/support/helpjp/helpview.aspx?si=5685/file01986/math98.png)
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![v := [1., 3.146264370, 9.898979486, 31.14480645, 97.98979486]](/support/helpjp/helpview.aspx?si=5685/file01986/math105.png)
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![u := [1, 0, -10, 0, 1]](/support/helpjp/helpview.aspx?si=5685/file01986/math112.png)
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![add(u[i]*v[i], i = 1 .. 5)](/support/helpjp/helpview.aspx?si=5685/file01986/math116.png)
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| (6) |
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![m := add(u[i]*z^(i-1), i = 1 .. 5)](/support/helpjp/helpview.aspx?si=5685/file01986/math123.png)
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| (8) |
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| (9) |
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![v := Vector(expand([seq(r^i, i = 0 .. 4)], 12))](/support/helpjp/helpview.aspx?si=5685/file01986/math144.png)
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^(1/3)], [1+2*(-2)^(1/3)+(-2)^(2/3)], [-1+3*(-2)^(1/3)+3*(-2)^(2/3)], [-7+2*(-2)^(1/3)+6*(-2)^(2/3)]])](/support/helpjp/helpview.aspx?si=5685/file01986/math147.png)
| (10) |
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](/support/helpjp/helpview.aspx?si=5685/file01986/math155.png)
| (11) |
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](/support/helpjp/helpview.aspx?si=5685/file01986/math162.png)
| (12) |
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![add(u[i]*v[i], i = 1 .. 5)](/support/helpjp/helpview.aspx?si=5685/file01986/math166.png)
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| (13) |
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![m := add(u[i]*z^(i-1), i = 1 .. 5)](/support/helpjp/helpview.aspx?si=5685/file01986/math173.png)
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| (14) |
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| (15) |
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| (16) |
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| (17) |
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