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documentation:ref:collect [2015/11/20 20:32] poslavskysv [Description] |
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| - | ====== Collect ====== | ||
| - | ---- | ||
| - | ====Description==== | ||
| - | * ''Collect[var1, var2]'' collects together terms involving the same powers of specified vars. | ||
| - | * ''Collect[var1, var2, ..., transformations]'' or ''%%Collect[var1, var2, ..., [Simplifications: transformations]]%%'' additionally applies specified transformations to the expression that forms the coefficient of each term obtained. | ||
| - | |||
| - | * In the case of tensorial vars, ''Collect'' will insert [[documentation:ref:Kronecker delta|Kronecker deltas]] or [[documentation:ref:metric tensor|metric tensors]] in order to "uncontract" indices and factor out tensorial parts. | ||
| - | |||
| - | |||
| - | * In the case of scalar vars, the behaviour of ''Collect'' is similar to other CASs. | ||
| - | |||
| - | * To prevent expand of symbolic terms when collecting tensors one can use option ''%%Collect[[var1, var2, ..., [ExpandSymbolic: true]]%%'' | ||
| - | ====Examples==== | ||
| - | |||
| - | ---- | ||
| - | |||
| - | Collect terms involving ''x'': | ||
| - | <sxh groovy; gutter: false> | ||
| - | println Collect['x'] >> 'a*x + b*x + с*x**2 + d*x**2 + f*e'.t | ||
| - | </sxh> | ||
| - | <sxh plain; gutter: false> | ||
| - | > (a + b)*x + (c + d)*x**2 + f*e | ||
| - | </sxh> | ||
| - | |||
| - | ---- | ||
| - | |||
| - | Collect powers of ''x'' and factor coefficients: | ||
| - | <sxh groovy; gutter: false> | ||
| - | println Collect['x', Factor] >> '(1 + a + x)**4'.t | ||
| - | </sxh> | ||
| - | <sxh plain; gutter: false> | ||
| - | > x**4 + 4*x**3*(a+1) + 6*x**2*(a+1)**2 + 4*(a+1)**3*x + (a+1)**4 | ||
| - | </sxh> | ||
| - | |||
| - | ---- | ||
| - | |||
| - | Collect terms involving tensor ''A_i'': | ||
| - | <sxh groovy; gutter: false> | ||
| - | println Collect['A_i'] >> 'A_m*B_n + A_n*C_m + B_n*C_m'.t | ||
| - | </sxh> | ||
| - | <sxh plain; gutter: false> | ||
| - | > A_{a}*(C_{m}*d_{n}^{a} + B_{n}*d_{m}^{a}) + B_{n}*C_{m} | ||
| - | </sxh> | ||
| - | |||
| - | ---- | ||
| - | |||
| - | Collect terms involving same tensorial function ''F_ij[x_ab]'': | ||
| - | <sxh groovy; gutter: false> | ||
| - | def t = 'F_ij[t_ab]*t^ij + F_ab[t_pq]*f^ba + F_ij[f_ij]*t^ij + F_ij[f_ij]*f^ji'.t | ||
| - | println Collect['F_ij[a_ij]'] >> t | ||
| - | </sxh> | ||
| - | <sxh plain; gutter: false> | ||
| - | > (t^{ij}+f^{ji})*F_{ij}[t_{ab}]+(t^{ij}+f^{ji})*F_{ij}[f_{ij}] | ||
| - | </sxh> | ||
| - | |||
| - | ---- | ||
| - | |||
| - | |||
| - | Collect with respect to two variables: | ||
| - | <sxh groovy; gutter: false> | ||
| - | def t = 'A_a * B^b + A^b * B_a + A_a * C^b + A^b * D_a'.t | ||
| - | println Collect['A_m', 'B_m'] >> t | ||
| - | </sxh> | ||
| - | <sxh plain; gutter: false> | ||
| - | > A_c*B^d*(d_a^c*d^b_d+g_ad*g^bc)+(C^b*d_a^c+g^bc*D_a)*A_c | ||
| - | </sxh> | ||
| - | |||
| - | ---- | ||
| - | |||
| - | |||
| - | By default ''Collect'' will expand all expressions: | ||
| - | <sxh groovy; gutter: true> | ||
| - | def t = '(a+b)**2 * A_a * B^b + A^b * B_a'.t | ||
| - | println Collect['B_m'] >> t | ||
| - | </sxh> | ||
| - | <sxh plain; gutter: false> | ||
| - | > B_{c}*((b**2+a**2+2*b*a)*A_{a}*g^{bc}+A^{b}*d_{a}^{c}) | ||
| - | </sxh> | ||
| - | To prevent this overhead one can use: | ||
| - | <sxh groovy; gutter: true; first-line: 3> | ||
| - | println Collect['B_m', [ExpandSymbolic: false]] >> t | ||
| - | </sxh> | ||
| - | <sxh plain; gutter: false> | ||
| - | > B_{c}*((a+b)**2*A_{a}*g^{bc}+A^{b}*d_{a}^{c}) | ||
| - | </sxh> | ||
| - | |||
| - | |||
| - | ---- | ||
| - | |||
| - | ====See also==== | ||
| - | * Related guides: [[documentation:guide:applying_and_manipulating_transformations]], [[documentation:guide:list_of_transformations]] | ||
| - | * Related transformations: [[documentation:ref:collectnonscalars]] | ||
| - | * JavaDocs: [[http://api.redberry.cc/redberry/1.1.8/java-api/cc/redberry/core/transformations/collect/CollectTransformation.html| CollectTransformation]] | ||
| - | * Source code: [[https://bitbucket.org/redberry/redberry/src/tip/core/src/main/java/cc/redberry/core/transformations/collect/CollectTransformation.java|CollectTransformation.java]] | ||