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documentation:ref:collect [2015/11/20 20:28] poslavskysv [Description] |
documentation:ref:collect [2015/11/20 20:32] poslavskysv [Description] |
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| ---- | ---- | ||
| ====Description==== | ====Description==== | ||
| - | * ''Collect[var1, var2, ..., [transformations]]'' collects together terms involving the same powers of specified vars and applies specified transformations to the expression that forms the coefficient of each term obtained. | + | * ''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 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. | ||
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| * In the case of scalar vars, the behaviour of ''Collect'' is similar to other CASs. | * 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[[vars, [ExpandSymbolic: true]]%%'' | + | * To prevent expand of symbolic terms when collecting tensors one can use option ''%%Collect[[var1, var2, ..., [ExpandSymbolic: false]]%%'' |
| ====Examples==== | ====Examples==== | ||
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| > 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 | > 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> | </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> | ||
| + | |||
| ---- | ---- | ||