Defactoring: Difference between revisions
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=== cases temperaments can be regarding which of their mapping forms equal each other === | === cases temperaments can be regarding which of their mapping forms equal each other === | ||
[[File:Cases for temperament mapping | [[File:Cases for temperament mapping forms3.png|300px|thumb|right]] | ||
Considering only full-rank, integer mappings, we find three cases for a given temperament which is not enfactored. In all three cases, HNF is the same as DCF: | Considering only full-rank, integer mappings, we find three cases for a given temperament which is not enfactored. In all three cases, HNF is the same as DCF: | ||
# The RREF, IRREF, and HNF are all ''different''. Example: [[Porcupine_family#Porcupine|porcupine]] with RREF of {{vector|{{map|1 0 <span><math>-\frac13</math></span>}} {{map|0 1 <span><math>\frac53</math></span>}}}}, IRREF of {{vector|{{map|3 0 -1}} {{map|0 3 5}}}}, and HNF of {{vector|{{map|1 2 3}} {{map|0 3 5}}}}. | # The RREF, IRREF, and HNF are all ''different''. Example: [[Porcupine_family#Porcupine|porcupine]] with RREF of {{vector|{{map|1 0 <span><math>-\frac13</math></span>}} {{map|0 1 <span><math>\frac53</math></span>}}}}, IRREF of {{vector|{{map|3 0 -1}} {{map|0 3 5}}}}, and HNF of {{vector|{{map|1 2 3}} {{map|0 3 5}}}}. | ||