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lines changed Original file line number Diff line number Diff line change @@ -119,7 +119,7 @@ install:
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- ninja --version
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before_script :
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- - ${CMAKE} -G Ninja -DCMAKE_BUILD_TYPE=${BUILD_TYPE} -DKLEIN_ENABLE_BENCH =OFF
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+ - ${CMAKE} -G Ninja -DCMAKE_BUILD_TYPE=${BUILD_TYPE} -DKLEIN_ENABLE_PERF =OFF
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- ${CMAKE} --build .
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script :
Original file line number Diff line number Diff line change @@ -26,7 +26,7 @@ platform:
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build_script :
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- cmake --version
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- - cmake -G "Visual Studio 16 2019" -A x64 -DCMAKE_BUILD_TYPE=%configuration% -DKLEIN_ENABLE_BENCH =OFF
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+ - cmake -G "Visual Studio 16 2019" -A x64 -DCMAKE_BUILD_TYPE=%configuration% -DKLEIN_ENABLE_PERF =OFF
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- cmake --build .
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- dir
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- C:\projects\klein\%configuration%\klein_test.exe
Original file line number Diff line number Diff line change @@ -41,6 +41,13 @@ The first element squares to $0$ ($\ee_0 \ee_0 =
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0$) while the latter 3 elements square to $1$ ($\ee_1\ee_1 = \ee_2\ee_2 = \ee_3\ee_3 = 1$).
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As we now immediately have a means to create $1$, we can generate all the numbers this way,
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so let's declare $1$ as our grade-0 basis element.
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+
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+ !!! question "Grade?"
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+
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+ Very non-mathematically, the "grade" of an element is the number of subscripts it possesses.
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+ Soon, you should get a good feel of what grades result from what operations, and what information
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+ the grades present in a multivector quantity conveys.
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+
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When we write elements adjacent to one another as in $\ee_1\ee_1$, the operation being represented
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here is the _ geometric product_ . In code, the geometric product is expressed as the multiplication
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(` * ` ) operator. So far, we've written down what the geometric product does when the
@@ -152,7 +159,8 @@ swaps as necessary to write terms with the canonical subscript ordering.
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Written as $a \cdot b$.
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- The _ symmetric inner product_ (inner product for short) is similar to the geometric product except
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+ The _ symmetric inner product_ (inner product for short) is a bilinear binary operation like the
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+ geometric product except
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it _ is always grade decreasing_ such that the final grade is the absolute value of the difference of
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the operand grades. If the grade of the element resulting from a geometric product
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would have been greater than this difference, the inner product extinguishes it to zero. In other
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