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Directory:Jon Awbrey/Papers/Differential Logic and Dynamic Systems (view source)
Revision as of 16:46, 19 June 2007
, 16:46, 19 June 2007→Transformations of Type '''B'''<sup>2</sup> → '''B'''<sup>2</sup>: wiki table
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Figure 69 gives a graphical picture of the difference map D''F'' = ‹D''f'', D''g''› for the transformation ''F'' = ‹''f'', ''g''› = ‹((''u'')(''v'')), ((''u'', ''v''))›. This depicts the same information about D''f'' and D''g'' that was given in the corresponding rows of the computation summary in Tables 66-i and 66-ii, excerpted here:
Figure 69 gives a graphical picture of the difference map D''F'' = ‹D''f'', D''g''› for the transformation ''F'' = ‹''f'', ''g''› = ‹((''u'')(''v'')), ((''u'', ''v''))›. This depicts the same information about D''f'' and D''g'' that was given in the corresponding rows of the computation summary in Tables 66-i and 66-ii, excerpted here:
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| Df = uv. du dv + u(v). du (dv) + (u)v.(du) dv + (u)(v).((du)(dv)) |
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| D''f''
| Dg = uv.(du, dv) + u(v).(du, dv) + (u)v.(du, dv) + (u)(v). (du, dv) |
| = || ''uv'' || <math>\cdot</math> || d''u'' d''v''
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| + || ''u''(''v'') || <math>\cdot</math> || d''u'' (d''v'')
| + || (''u'')''v'' || <math>\cdot</math> || (d''u'') d''v''
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| + || (''u'')(''v'') || <math>\cdot</math> || ((d''u'')(d''v''))
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| D''g''
| = || ''uv'' || <math>\cdot</math> || (d''u'', d''v'')
| + || ''u''(''v'') || <math>\cdot</math> || (d''u'', d''v'')
| + || (''u'')''v'' || <math>\cdot</math> || (d''u'', d''v'')
| + || (''u'')(''v'') || <math>\cdot</math> || (d''u'', d''v'')
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