# Differences

This shows you the differences between two versions of the page.

 documentation:ref:expand [2015/11/21 11:03]poslavskysv [See also] documentation:ref:expand [2015/11/21 12:33] Line 1: Line 1: - ====== Expand ====== - ---- - ====Description==== - * ''​Expand''​ expands out products and positive integer powers. - * ''​Expand[transformations]''​ expands out products and positive integer powers and applies ''​transformations''​ at each level of expand procedure. - - ====Examples==== - ---- - Expand a polynomial expressions:​ - - println Expand >> '(x_n + y_n)*(f_m - r_m)'​.t - ​ - - > x_{n}*f_{m}+f_{m}*y_{n}-r_{m}*y_{n}-x_{n}*r_{m} - ​ - - - println Expand >> '(1 + x)**4'​.t - ​ - - > x**4+1+4*x**3+6*x**2+4*x - ​ - - ---- - - println Expand >> '(x + y)/​z'​.t - ​ - - > x/z+y/z - ​ - - ---- - ''​Expand''​ relabels dummies when necessary: - - println Expand >> '​(A_m^m + 1)**3'​.t - ​ - - > 3*A_{m}^{m}*A_{a}^{a}+A_{m}^{m}*A_{a}^{a}*A_{b}^{b}+1+3*A_{b}^{b} - ​ - - - ---- - - - ''​Expand''​ does not go inside functions and denominators;​ ''​ExpandAll''​ does: - - println Expand >> 'f[(x + y)**2]'​.t - ​ - - > f[(x + y)**2] - ​ - - println ExpandAll >> 'f[(x + y)**2]'​.t - ​ - - > f[x**2 + 2*x*y + y**2] - ​ - - ---- - ====Details==== - ''​Expand[transformations]''​ will additionally apply ''​transformations''​ during expand procedure: - - println Expand['​k_a*k^a = 0'.t] >> '(k_a + t_a)*(k^a + t^a)'​.t - ​ - - > 2*k_a*t^a + t_a*t^a - ​ - - Passing additional ''​transformations''​ can significantly improve the performance when expanding huge expressions. For example, when a huge expression involves many metric tensors, one can pass ''​EliminateMetrics''​ in order to reduce the number of processed terms. Consider a random example: - - //create random generator, which generates - // random tensors consisting of metric and A_m - RandomTensor randomTensor = new RandomTensor();​ - randomTensor.clearNamespace() - randomTensor.addToNamespace('​g_mn'​.t,​ '​A_m'​.t) - - //loop to warm up JVM - for (def i in 1..1000) { - def a, b - //next random tensor - def t = randomTensor.nextTensorTree(4,​ 3, 8, '​_a'​.si) - def simplify = EliminateMetrics & '​A_a*A^a = 1'.t & 'd^i_i = 10'.t - - //this will typically 10 times faster - timing { - a = Expand[simplify] >> t - } - //then this - timing { - b = (Expand & simplify) >> t - } - - assert a == b - println ''​ - } - ​ - The sample output will looks like: - - Time: 10 ms. - Time: 1015 ms. - - Time: 7 ms. - Time: 6566 ms. - - Time: 66 ms. - Time: 983 ms. - ... - ​ - - ====See also==== - * Related guides: [[documentation:​guide:​applying_and_manipulating_transformations]],​ [[documentation:​guide:​list_of_transformations]] - * Related transformations:​ [[documentation:​ref:​expandtensors]],​ [[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/​ExpandTransformation.html|ExpandTransformation]] - * Source code: [[https://​bitbucket.org/​redberry/​redberry/​src/​tip/​core/​src/​main/​java/​cc/​redberry/​core/​transformations/​expand/​ExpandTransformation.java|ExpandTransformation.java]]