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| + | ====== Sum ====== | ||
| + | ---- | ||
| + | |||
| + | ====Basics==== | ||
| + | ''Sum'' represents a sum of terms. Like any other expression, it inherits all properties of [[Tensor]]. ''Sum'' adopts the following convention on its indices: the indices of sum are free sorted indices of its summands: | ||
| + | <sxh groovy; gutter: false> | ||
| + | def t = 'f_ba^c_c + t_ab^d_d'.t | ||
| + | println t.indice | ||
| + | </sxh> | ||
| + | <sxh plain; gutter: false> | ||
| + | > _ab | ||
| + | </sxh> | ||
| + | |||
| + | ''Sum'' sorts its arguments and reduces any equal terms. Additionally, it reduces terms with same tensorial parts as described in [[documentation:guide:standard_form_of_mathematical_expressions]]. | ||
| + | |||
| + | ====Additional features==== | ||
| + | There are several features in addition to those defined in [[Tensor]] that are inherent only in [[Sum]] and [[Product]]: | ||
| + | |||
| + | <html> | ||
| + | <table style="width:600px;" cellpadding="10"> | ||
| + | <tr> | ||
| + | <td valign="top" style="padding: 15px;margin-top: 35px;border: 1px solid gray;"><code>.select(positions)</code></td> | ||
| + | <td valign="top" style="padding: 15px;margin-top: 35px;border: 1px solid gray;">returns a sum of elements at specified positions</td> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <td valign="top" style="padding: 15px;margin-top: 35px;border: 1px solid gray;"><code>.remove(positions)</code></td> | ||
| + | <td valign="top" style="padding: 15px;margin-top: 35px;border: 1px solid gray;">returns a sum with removed elements at specified positions</td> | ||
| + | </tr> | ||
| + | </table> | ||
| + | </html> | ||
| + | |||
| + | Consider examples: | ||
| + | <sxh groovy; gutter: true> | ||
| + | def s = 'a + b + c + d + e + f'.t | ||
| + | println s.select(2, 3, 5) | ||
| + | </sxh> | ||
| + | <sxh plain; gutter: false> | ||
| + | > c+b+a | ||
| + | </sxh> | ||
| + | <sxh groovy; gutter: true;first-line: 3> | ||
| + | println s.remove(2, 3, 5) | ||
| + | </sxh> | ||
| + | <sxh plain; gutter: false> | ||
| + | > d+e+f | ||
| + | </sxh> | ||
| + | ====See also==== | ||
| + | * Related guides: [[documentation:guide:tensors_and_indices]], [[documentation:guide:tree_traversal]] | ||
| + | * Reference: [[documentation:ref:tensor]], [[documentation:ref:product]], [[documentation:ref:indices]], [[documentation:ref:simpletensor]], [[documentation:ref:tensorfield]] | ||
| + | * JavaDocs: [[http://api.redberry.cc/redberry/1.1.9/java-api/cc/redberry/core/tensor/Sum.html| Sum]] | ||
| + | * Source code: [[https://bitbucket.org/redberry/redberry/src/tip/core/src/main/java/cc/redberry/core/tensor/Sum.java|Sum.java]] | ||