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 documentation:ref:expandtensors [2015/11/20 20:45]poslavskysv [Examples] documentation:ref:expandtensors [2015/11/21 12:33] Line 1: Line 1: - ====== ExpandTensors ====== - ---- - ====Description==== - * ''​ExpandTensors''​ expands out products of tensors leaving unexpended all symbolic terms. - * ''​ExpandTensors[transformations]''​ or ''​%%ExpandTensors[[Simplifications:​ transformations]]%%''​ applies ''​transformations''​ at each level of expand procedure. - - * ''​%%ExpandTensors[[LeaveScalars:​ true]]%%''​ will not expand expressions like ''​(A_a^a + B_a^a)*(C_b^b + D_b^b)''​. - - ====Examples==== - ---- - Expand tensors in expressions:​ - - println ExpandTensors >> '​(a+b)**10*(x_n + y_n)*(f_m - r_m)'​.t - ​ - - > (a+b)**10*x_{n}*f_{m}+(a+b)**10*f_{m}*y_{n}-(a+b)**10*r_{m}*y_{n}-(a+b)**10*x_{n}*r_{m} - ​ - - - println ExpandTensors >> '(1 + x)**4*(A_a + B_a)'​.t - ​ - - > (1 + x)**4 * A_a + (1 + x)**4 * B_a - ​ - - - println ExpandTensors >> '(1 + x)**4*(A_a + B_a)*(A^a + B^a)'​.t - ​ - - > (x+1)**4*B^{a}*B_{a}+2*(x+1)**4*B^{a}*A_{a}+(x+1)**4*A^{a}*A_{a} - ​ - ---- - - Symbolic parts will be kept on all levels: - - - def t = '​((a+b)*(c+d)*(f_a + (k+i)*t_a) + (a + c)*t_a)*(c+r)*((a+b)*f^a + (c+d)*t^a)'​.t - println ExpandTensors >> t - ​ - - > (c+r)*(c+d)*(a+b)**2*f_a*f^a + (c+r)*((a+b)*(c+d)*(k+i) + - (a + c))*(a+b)*t_a*f^a + (c+r)*(a+b)*(c+d)*(c+d)*f_a*t^a ​ - + (c+r)*((a+b)*(c+d)*(k+i) + (a + c))*(c+d)*t_a*t^a - ​ - - ---- - Specify additional simplifications:​ - - - def simplify = '​f_a*f^a = a'.t & '​f_a*t^a = b'.t & '​t_a*t^a = c'.t - def t = '​(2*(c+a)-164*a)*(f_{a}+t_{a})*f^{a}'​.t - println ExpandTensors[simplify] >> t - ​ - - > a*(-164*a+2*(c+a))+b*(-164*a+2*(c+a)) - ​ - - ====See also==== - * Related guides: [[documentation:​guide:​applying_and_manipulating_transformations]],​ [[documentation:​guide:​list_of_transformations]] - * Related transformations:​ [[documentation:​ref:​expand]], ​ [[documentation:​ref:​expandall]],​ [[documentation:​ref:​expandnumerator]],​ [[documentation:​ref:​expanddenominator]] - * JavaDocs: [[http://​api.redberry.cc/​redberry/​1.1.8/​java-api/​cc/​redberry/​core/​transformations/​expand/​ExpandTensorsTransformation.html|ExpandTensorsTransformation]] - * Source code: [[https://​bitbucket.org/​redberry/​redberry/​src/​tip/​core/​src/​main/​java/​cc/​redberry/​core/​transformations/​expand/​ExpandTensorsTransformation.java|ExpandTensorsTransformation.java]]