This page contains three views of the steps in the derivation: d3js, graphviz PNG, and a table.
Notes for this derivation:
Index | Inference Rule | Input latex | Feeds latex | Output latex | step validity | dimension check | unit check | notes |
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8 | replace summation notation with vector notation |
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Nothing to split |
7575859310:
7575859312: |
7575859310:
7575859312: |
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2 | replace curl with LeviCevita summation contravariant |
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Nothing to split |
7575859295:
7575859300: |
7575859295:
7575859300: |
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5 | substitute RHS of expr 1 into expr 2 |
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failed |
7575859304:
failed 7575859302: 7575859306: |
7575859304:
N/A 7575859302: 7575859306: |
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7 | simplify |
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Nothing to split |
7575859308:
7575859310: |
7575859308:
7575859310: |
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6 | simplify |
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failed |
7575859306:
7575859308: |
7575859306:
7575859308: |
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3 | replace curl with LeviCevita summation contravariant |
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Nothing to split |
7575859300:
7575859302: |
7575859300:
7575859302: |
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1 | declare identity |
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no validation is available for declarations |
7575859295:
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7575859295:
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9 | claim LHS equals RHS |
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Nothing to split |
7575859312:
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7575859312:
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4 | declare identity |
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no validation is available for declarations |
7575859304:
failed |
7575859304:
N/A |
symbol ID | category | latex | scope | dimension | name | value | Used in derivations | references | |
---|---|---|---|---|---|---|---|---|---|
8304 | variable |
l
\(l\) |
integer | dimensionless | index |
|
3 | ||
9690 | variable |
k
\(k\) |
integer | dimensionless | index |
|
4 | ||
4326 | variable |
\vec{E}
\(\vec{E}\) |
complex | dimensionless | electric field | 9 | |||
1552 | variable |
j
\(j\) |
['integer'] | dimensionless | index | 7 | |||
1567 | variable |
i
\(i\) |
['integer'] | dimensionless | index | 1 | |||
6238 | variable |
E
\(E\) |
real | dimensionless | electric field | 20 | |||
7984 | variable |
i
\(i\) |
integer | dimensionless | index |
|
1 | ||
1434 | variable |
\hat{x}_n
\(\hat{x}_n\) |
real | dimensionless | nth unit vector |
|
1 | ||
2380 | variable |
\hat{x}_m
\(\hat{x}_m\) |
real | dimensionless | mth unit vector |
|
1 | ||
8349 | variable |
\hat{x}_i
\(\hat{x}_i\) |
real | dimensionless | ith unit vector |
|
3 | ||
7930 | variable |
m
\(m\) |
integer | dimensionless | index |
|
5 | ||
1592 | variable |
n
\(n\) |
integer | dimensionless | index | 23 |