Changes

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<pre>

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Table 66-ii.  Computation Summary for g<u, v> = ((u, v))

o--------------------------------------------------------------------------------o

|+ Table 66-ii.  Computation Summary for g‹''u'', ''v''› = ((''u'', ''v''))

|                                                                               |

| !e!g  = uv.    1     + u(v).    0     + (u)v.    0     + (u)(v).    1     |

{| align="left" border="0" cellpadding="1" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%"

|                                                                               |

| <math>\epsilon</math>''g''

|   Eg  = uv.((du, dv)) + u(v). (du, dv) + (u)v. (du, dv) + (u)(v).((du, dv)) |

| = || ''uv''        || <math>\cdot</math> || 1

|                                                                               |

| + || ''u''(''v'')   || <math>\cdot</math> || 0

|   Dg  = uv. (du, dv) + u(v). (du, dv) + (u)v. (du, dv) + (u)(v). (du, dv) |

| + || (''u'')''v''  || <math>\cdot</math> || 0

|                                                                               |

| + || (''u'')(''v'') || <math>\cdot</math> || 1

|   dg  = uv. (du, dv) + u(v). (du, dv) + (u)v. (du, dv) + (u)(v). (du, dv) |

|-

|                                                                               |

| E''g''

|   rg  = uv.    0     + u(v).    0     + (u)v.    0     + (u)(v).    0     |

| = || ''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'')

</pre>

| + || (''u'')(''v'') || <math>\cdot</math> || ((d''u'', d''v''))

|-

| 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'')

|-

| 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'')

|-

| r''g''

| = || ''uv''        || <math>\cdot</math> || 0

| + || ''u''(''v'')   || <math>\cdot</math> || 0

| + || (''u'')''v''  || <math>\cdot</math> || 0

| + || (''u'')(''v'') || <math>\cdot</math> || 0

|}

|}

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Table&nbsp;67 shows how to compute the analytic series for ''F''&nbsp;=&nbsp;‹''f'',&nbsp;''g''›&nbsp;=&nbsp;‹((''u'')(''v'')),&nbsp;((''u'',&nbsp;''v''))› in terms of coordinates, and Table&nbsp;68 recaps these results in symbolic terms, agreeing with earlier derivations.

Table&nbsp;67 shows how to compute the analytic series for ''F''&nbsp;=&nbsp;‹''f'',&nbsp;''g''›&nbsp;=&nbsp;‹((''u'')(''v'')),&nbsp;((''u'',&nbsp;''v''))› in terms of coordinates, and Table&nbsp;68 recaps these results in symbolic terms, agreeing with earlier derivations.