Temperament addition: Difference between revisions

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====3. Addabiliziation defactoring====

But it is not quite as simple as determining the <math>L_{\text{dep}}</math> and then supplying the remaining vectors necessary to match the grade of the original matrix, because the results may then be [[enfactored]]. And defactoring them without compromising the explicit <math>L_{\text{dep}}</math> cannot be done using existing [[defactoring algorithms]]; it's a tricky process, or at least computationally intensive. This is called '''addabilization defactoring'''.

But it is not quite as simple as determining the <math>L_{\text{dep}}</math> and then supplying the remaining vectors necessary to match the grade of the original matrix, because the results may then be [[enfactoring|enfactored]]. And defactoring them without compromising the explicit <math>L_{\text{dep}}</math> cannot be done using existing [[defactoring algorithms]]; it's a tricky process, or at least computationally intensive. This is called '''addabilization defactoring'''.

Most established defactoring algorithms will alter any or all of the entries of a matrix. This is not an option if we still want to be able to add temperaments, however, because these matrices must retain their explicit <math>L_{\text{dep}}</math>. And we can't defactor and then paste the <math>L_{\text{dep}}</math> back over the first vector or something, because then we might just be enfactored again. We need to find a defactoring algorithm that manages to work without altering any of the vectors in the <math>L_{\text{dep}}</math>.

@@ Line 307: / Line 307: @@
 ====3. Addabiliziation defactoring====
-But it is not quite as simple as determining the <span style="color: #3C8031;"><math>L_{\text{dep}}</math></span> and then supplying the remaining vectors necessary to match the grade of the original matrix, because the results may then be [[enfactored]]. And defactoring them without compromising the explicit <span style="color: #3C8031;"><math>L_{\text{dep}}</math></span> cannot be done using existing [[defactoring algorithms]]; it's a tricky process, or at least computationally intensive. This is called '''addabilization defactoring'''.
+But it is not quite as simple as determining the <span style="color: #3C8031;"><math>L_{\text{dep}}</math></span> and then supplying the remaining vectors necessary to match the grade of the original matrix, because the results may then be [[enfactoring|enfactored]]. And defactoring them without compromising the explicit <span style="color: #3C8031;"><math>L_{\text{dep}}</math></span> cannot be done using existing [[defactoring algorithms]]; it's a tricky process, or at least computationally intensive. This is called '''addabilization defactoring'''.
 Most established defactoring algorithms will alter any or all of the entries of a matrix. This is not an option if we still want to be able to add temperaments, however, because these matrices must retain their explicit <span style="color: #3C8031;"><math>L_{\text{dep}}</math></span>. And we can't defactor and then paste the <span style="color: #3C8031;"><math>L_{\text{dep}}</math></span> back over the first vector or something, because then we might just be enfactored again. We need to find a defactoring algorithm that manages to work without altering any of the vectors in the <span style="color: #3C8031;"><math>L_{\text{dep}}</math></span>.