Douglas Blumeyer's RTT How-To: Difference between revisions

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And so our results are <math>-2</math>, <math>3</math>, <math>1</math>, <math>-11</math>. There's no GCD to extract. We prefer for the first term to be positive; this doesn’t make a difference in how things behave, but is done because it normalizes things (we could have found the result where the first term came out positive by simply changing the order of the rows of our mapping, which doesn’t affect how the mapping works at all). And so we flip the signs<ref>If it helps you, you could think of this sign-flipping step as paired with the GCD extraction step, if you think of it like extracting a GCD of -1.</ref>, and our list ends up as <math>2</math>, <math>-3</math>, <math>-1</math>, <math>11</math>. Finally, set these inside triply-nested brackets, because it’s a trimap for a rank-3 temperament, and we get {{multicovector|rank=3|2 -3 -1 11}}.

And so our results are <math>-2</math>, <math>3</math>, <math>1</math>, <math>-11</math>. There's no GCD to extract. We prefer for the first term to be positive; this doesn’t make a difference in how things behave, but is done because it normalizes things (we could have found the result where the first term came out positive by simply changing the order of the rows of our mapping, which doesn’t affect how the mapping works at all, or mean there's anything different about the temperament). And so we flip the signs<ref>If it helps you, you could think of this sign-flipping step as paired with the GCD extraction step, if you think of it like extracting a GCD of -1.</ref>, and our list ends up as <math>2</math>, <math>-3</math>, <math>-1</math>, <math>11</math>. Finally, set these inside triply-nested brackets, because it’s a trimap for a rank-3 temperament, and we get {{multicovector|rank=3|2 -3 -1 11}}.

As for getting from the multimap back to the mapping, you can solve a system of equations for that. Though it’s not easy and there may not be a unique solution. And you probably will never have the multimap without the mapping anyway.

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-And so our results are <span><math>-2</math></span>, <span><math>3</math></span>, <span><math>1</math></span>, <span><math>-11</math></span>. There's no GCD to extract. We prefer for the first term to be positive; this doesn’t make a difference in how things behave, but is done because it normalizes things (we could have found the result where the first term came out positive by simply changing the order of the rows of our mapping, which doesn’t affect how the mapping works at all). And so we flip the signs<ref>If it helps you, you could think of this sign-flipping step as paired with the GCD extraction step, if you think of it like extracting a GCD of -1.</ref>, and our list ends up as <span><math>2</math></span>, <span><math>-3</math></span>, <span><math>-1</math></span>, <span><math>11</math></span>. Finally, set these inside triply-nested brackets, because it’s a trimap for a rank-3 temperament, and we get {{multicovector|rank=3|2 -3 -1 11}}.
+And so our results are <span><math>-2</math></span>, <span><math>3</math></span>, <span><math>1</math></span>, <span><math>-11</math></span>. There's no GCD to extract. We prefer for the first term to be positive; this doesn’t make a difference in how things behave, but is done because it normalizes things (we could have found the result where the first term came out positive by simply changing the order of the rows of our mapping, which doesn’t affect how the mapping works at all, or mean there's anything different about the temperament). And so we flip the signs<ref>If it helps you, you could think of this sign-flipping step as paired with the GCD extraction step, if you think of it like extracting a GCD of -1.</ref>, and our list ends up as <span><math>2</math></span>, <span><math>-3</math></span>, <span><math>-1</math></span>, <span><math>11</math></span>. Finally, set these inside triply-nested brackets, because it’s a trimap for a rank-3 temperament, and we get {{multicovector|rank=3|2 -3 -1 11}}.
 As for getting from the multimap back to the mapping, you can solve a system of equations for that. Though it’s not easy and there may not be a unique solution. And you probably will never have the multimap without the mapping anyway.