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|-
|-
| <math>A\!</math>
| <math>A\!</math>
|
| <math>\langle \mathcal{A} \rangle</math><br>
<math>\langle \mathcal{A} \rangle</math><br>
<math>\langle a_1, \ldots, a_n \rangle</math><br>
<math>\langle a_1, \ldots, a_n \rangle</math><br>
<math>\{ (a_1, \ldots, a_n) \}\!</math>
<math>\{ (a_1, \ldots, a_n) \}\!</math>
<math>A_1 \times \ldots \times A_n</math><br>
<math>A_1 \times \ldots \times A_n</math><br>
<math>\textstyle \prod_i A_i\!</math>
<math>\textstyle \prod_i A_i\!</math>
|
| Set of cells,<br>
Set of cells,<br>
coordinate tuples,<br>
coordinate tuples,<br>
points, or vectors<br>
points, or vectors<br>
|-
|-
| <math>A^\circ</math>
| <math>A^\circ</math>
|
| <math>[ \mathcal{A} ]</math><br>
<math>[ \mathcal{A} ]</math><br>
<math>(A, A^\uparrow)</math><br>
<math>(A, A^\uparrow)</math><br>
<math>(A\ +\!\to \mathbb{B})</math><br>
<math>(A\ +\!\to \mathbb{B})</math><br>
<math>(A, (A \to \mathbb{B}))</math><br>
<math>(A, (A \to \mathbb{B}))</math><br>
<math>[ a_1, \ldots, a_n ]</math>
<math>[ a_1, \ldots, a_n ]</math>
|
| Universe of discourse<br>
Universe of discourse<br>
based on the features<br>
based on the features<br>
<math>\{ a_1, \ldots, a_n \}</math>
<math>\{ a_1, \ldots, a_n \}</math>
|
| <math>(\mathbb{B}^n, (\mathbb{B}^n \to \mathbb{B}))</math><br>
<math>(\mathbb{B}^n, (\mathbb{B}^n \to \mathbb{B}))</math><br>
<math>(\mathbb{B}^n\ +\!\to \mathbb{B})</math><br>
<math>(\mathbb{B}^n\ +\!\to \mathbb{B})</math><br>
<math>[\mathbb{B}^n]</math>
<math>[\mathbb{B}^n]</math>
| <math>\operatorname{d}\mathcal{A}</math>
| <math>\operatorname{d}\mathcal{A}</math>
| <math>\{ \operatorname{d}a_1, \ldots, \operatorname{d}a_n \}</math>
| <math>\{ \operatorname{d}a_1, \ldots, \operatorname{d}a_n \}</math>
|
| Alphabet of<br>
Alphabet of<br>
differential<br>
differential<br>
features
features
| <math>\operatorname{d}A_i</math>
| <math>\operatorname{d}A_i</math>
| <math>\{ (\operatorname{d}a_i), \operatorname{d}a_i \}</math>
| <math>\{ (\operatorname{d}a_i), \operatorname{d}a_i \}</math>
|
| Differential<br>
Differential<br>
dimension <math>i\!</math>
dimension <math>i\!</math>
| <math>\mathbb{D}</math>
| <math>\mathbb{D}</math>
<math>\operatorname{d}A_1 \times \ldots \times \operatorname{d}A_n</math><br>
<math>\operatorname{d}A_1 \times \ldots \times \operatorname{d}A_n</math><br>
<math>\textstyle \prod_i \operatorname{d}A_i</math>
<math>\textstyle \prod_i \operatorname{d}A_i</math>
|
| Tangent space<br>
Tangent space<br>
at a point:<br>
at a point:<br>
Set of changes,<br>
Set of changes,<br>
| <math>\operatorname{d}A^*</math>
| <math>\operatorname{d}A^*</math>
| <math>(\operatorname{hom} : \operatorname{d}A \to \mathbb{B})</math>
| <math>(\operatorname{hom} : \operatorname{d}A \to \mathbb{B})</math>
|
| Linear functions<br>
Linear functions<br>
on <math>\operatorname{d}A</math>
on <math>\operatorname{d}A</math>
| <math>(\mathbb{D}^n)^* \cong \mathbb{D}^n</math>
| <math>(\mathbb{D}^n)^* \cong \mathbb{D}^n</math>
| <math>\operatorname{d}A^\uparrow</math>
| <math>\operatorname{d}A^\uparrow</math>
| <math>(\operatorname{d}A \to \mathbb{B})</math>
| <math>(\operatorname{d}A \to \mathbb{B})</math>
|
| Boolean functions<br>
Boolean functions<br>
on <math>\operatorname{d}A</math>
on <math>\operatorname{d}A</math>
| <math>\mathbb{D}^n \to \mathbb{B}</math>
| <math>\mathbb{D}^n \to \mathbb{B}</math>
|-
|-
| d''A''<sup>•</sup>
| <math>\operatorname{d}A^\circ</math>
|
| <math>[\operatorname{d}\mathcal{A}]</math><br>
[d<font face="lucida calligraphy">A</font>]<br>
<math>(\operatorname{d}A, \operatorname{d}A^\uparrow)</math><br>
(d''A'', d''A''^)<br>
<math>(\operatorname{d}A\ +\!\to \mathbb{B})</math><br>
(d''A'' +→ '''B''')<br>
<math>(\operatorname{d}A, (\operatorname{d}A \to \mathbb{B}))</math><br>
(d''A'', (d''A'' → '''B'''))<br>
<math>[\operatorname{d}a_1, \ldots, \operatorname{d}a_n]</math>
[d''a''<sub>1</sub>, …, d''a''<sub>''n''</sub>]
| Tangent universe<br>
|
at a point of <math>A^\circ,</math><br>
Tangent universe<br>
at a point of ''A''<sup>•</sup>,<br>
based on the<br>
based on the<br>
tangent features<br>
tangent features<br>
{d''a''<sub>1</sub>, …, d''a''<sub>''n''</sub>}
<math>\{ \operatorname{d}a_1, \ldots, \operatorname{d}a_n \}</math>
|
| <math>(\mathbb{D}^n, (\mathbb{D}^n \to \mathbb{B}))</math><br>
('''D'''<sup>''n''</sup>, ('''D'''<sup>''n''</sup> → '''B'''))<br>
<math>(\mathbb{D}^n\ +\!\to \mathbb{B})</math><br>
('''D'''<sup>''n''</sup> +→ '''B''')<br>
<math>[\mathbb{D}^n]</math>
['''D'''<sup>''n''</sup>]
|}
|}
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