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Revision as of 18:42, 27 June 2008
, 18:42, 27 June 2008→Differential Forms: add table descriptions
===Differential Forms===
===Differential Forms===
The actions of the difference operator <math>\operatorname{D}</math> and the tangent operator <math>\operatorname{d}</math> on each of the 16 propositional forms on two variables are shown in the Tables below.
Table A7 expands the resulting differential forms over a so-called "logical basis":
<center>
<math>\{ (\operatorname{d}x)(\operatorname{d}y),\ \operatorname{d}x\,(\operatorname{d}y),\ (\operatorname{d}x)\,\operatorname{d}y,\ \operatorname{d}x\,\operatorname{d}y \}.</math>
</center>
This is a set of singular propositions indicating mutually exclusive and exhaustive "cells" or coordinate points of the universe of discourse. For this reason, it may also be referred to as a cell-basis, point-basis, or singular basis. In this setting it is frequently convenient to use the following abbreviations:
<center>
<math>\partial x = \operatorname{d}x\,(\operatorname{d}y)</math> and <math>\partial y = (\operatorname{d}x)\,\operatorname{d}y.</math>
</center>
Table A8 expands the resulting differential forms over a so-called "algebraic basis":
<center>
<math>\{ 1,\ \operatorname{d}x,\ \operatorname{d}y,\ \operatorname{d}x\,\operatorname{d}y \}.</math>
</center>
====Table A7. Differential Forms Expanded on a Logical Basis====
====Table A7. Differential Forms Expanded on a Logical Basis====
