From ca9ae43c7d94076ee6eb417091dd5c55429f553d Mon Sep 17 00:00:00 2001 From: Tschijnmo TSCHAU Date: Sat, 9 Sep 2017 21:45:56 -0500 Subject: [PATCH] Update CCSD example for the new gristmill interface --- docs/examples/ccsd.ipynb | 166 ++++++++++++++++----------------------- 1 file changed, 66 insertions(+), 100 deletions(-) diff --git a/docs/examples/ccsd.ipynb b/docs/examples/ccsd.ipynb index 7389de7..13c890c 100644 --- a/docs/examples/ccsd.ipynb +++ b/docs/examples/ccsd.ipynb @@ -117,7 +117,7 @@ { "data": { "text/latex": [ - "$$\\sum_{i \\in O} \\sum_{a \\in V} t_{a,i} c^{\\dagger}_{a} c^{}_{i} + \\sum_{i \\in O} \\sum_{j \\in O} \\sum_{a \\in V} \\sum_{b \\in V} \\frac{1}{4} t_{a,b,i,j} c^{\\dagger}_{a} c^{\\dagger}_{b} c^{}_{j} c^{}_{i}$$" + "$$\\sum_{i \\in O} \\sum_{a \\in V} t_{a,i} c^{\\dagger}_{a} c^{}_{i} + \\sum_{i \\in O} \\sum_{j \\in O} \\sum_{a \\in V} \\sum_{b \\in V} \\frac{1}{4} t_{a,b,i,j} c^{\\dagger}_{a} c^{\\dagger}_{b} c^{}_{j} c^{}_{i}$$" ], "text/plain": [ "" @@ -170,8 +170,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "CPU times: user 352 ms, sys: 50.9 ms, total: 403 ms\n", - "Wall time: 26.4 s\n" + "CPU times: user 348 ms, sys: 50.3 ms, total: 398 ms\n", + "Wall time: 30.4 s\n" ] } ], @@ -251,7 +251,7 @@ { "data": { "text/latex": [ - "$$\\sum_{i \\in O} \\sum_{j \\in O} \\sum_{a \\in V} \\sum_{b \\in V} \\frac{1}{4} t_{a,b,i,j} u_{i,j,a,b} + \\sum_{i \\in O} \\sum_{j \\in O} \\sum_{a \\in V} \\sum_{b \\in V} \\frac{1}{2} t_{a,i} t_{b,j} u_{i,j,a,b} + \\sum_{i \\in O} \\sum_{a \\in V} f_{i,a} t_{a,i} $$" + "$$\\sum_{i \\in O} \\sum_{a \\in V} f_{i,a} t_{a,i} + \\sum_{i \\in O} \\sum_{j \\in O} \\sum_{a \\in V} \\sum_{b \\in V} \\frac{1}{4} t_{a,b,i,j} u_{i,j,a,b} + \\sum_{i \\in O} \\sum_{j \\in O} \\sum_{a \\in V} \\sum_{b \\in V} \\frac{1}{2} t_{a,i} t_{b,j} u_{i,j,a,b} $$" ], "text/plain": [ "" @@ -300,7 +300,7 @@ { "data": { "text/latex": [ - "$$- \\sum_{j \\in O} f_{j,i} t_{a,j} + \\sum_{j \\in O} \\sum_{b \\in V} \\sum_{c \\in V} \\frac{1}{2} t_{b,c,i,j} u_{a,j,b,c} + \\sum_{j \\in O} \\sum_{b \\in V} \\sum_{c \\in V} t_{b,i} t_{c,j} u_{a,j,b,c} + \\sum_{j \\in O} \\sum_{b \\in V} f_{j,b} t_{a,b,i,j} + \\sum_{j \\in O} \\sum_{b \\in V} t_{b,j} u_{a,j,i,b} - \\sum_{j \\in O} \\sum_{b \\in V} f_{j,b} t_{a,j} t_{b,i} + \\sum_{j \\in O} \\sum_{k \\in O} \\sum_{b \\in V} \\sum_{c \\in V} t_{c,k} t_{a,b,i,j} u_{j,k,b,c} + \\sum_{j \\in O} \\sum_{k \\in O} \\sum_{b \\in V} \\sum_{c \\in V} \\frac{1}{2} t_{a,k} t_{b,c,i,j} u_{j,k,b,c} + \\sum_{j \\in O} \\sum_{k \\in O} \\sum_{b \\in V} \\sum_{c \\in V} \\frac{1}{2} t_{c,i} t_{a,b,j,k} u_{j,k,b,c} - \\sum_{j \\in O} \\sum_{k \\in O} \\sum_{b \\in V} \\sum_{c \\in V} t_{a,j} t_{b,i} t_{c,k} u_{j,k,b,c} + f_{a,i} + \\sum_{b \\in V} f_{a,b} t_{b,i} - \\sum_{j \\in O} \\sum_{k \\in O} \\sum_{b \\in V} \\frac{1}{2} t_{a,b,j,k} u_{j,k,i,b} - \\sum_{j \\in O} \\sum_{k \\in O} \\sum_{b \\in V} t_{a,j} t_{b,k} u_{j,k,i,b} $$" + "$$\\sum_{j \\in O} \\sum_{b \\in V} \\sum_{c \\in V} \\frac{1}{2} t_{b,c,i,j} u_{a,j,b,c} + \\sum_{j \\in O} \\sum_{b \\in V} \\sum_{c \\in V} t_{b,i} t_{c,j} u_{a,j,b,c} + \\sum_{j \\in O} \\sum_{b \\in V} f_{j,b} t_{a,b,i,j} + \\sum_{j \\in O} \\sum_{b \\in V} t_{b,j} u_{a,j,i,b} - \\sum_{j \\in O} \\sum_{b \\in V} f_{j,b} t_{a,j} t_{b,i} - \\sum_{j \\in O} f_{j,i} t_{a,j} + \\sum_{j \\in O} \\sum_{k \\in O} \\sum_{b \\in V} \\sum_{c \\in V} t_{c,k} t_{a,b,i,j} u_{j,k,b,c} + \\sum_{j \\in O} \\sum_{k \\in O} \\sum_{b \\in V} \\sum_{c \\in V} \\frac{1}{2} t_{a,k} t_{b,c,i,j} u_{j,k,b,c} + \\sum_{j \\in O} \\sum_{k \\in O} \\sum_{b \\in V} \\sum_{c \\in V} \\frac{1}{2} t_{c,i} t_{a,b,j,k} u_{j,k,b,c} - \\sum_{j \\in O} \\sum_{k \\in O} \\sum_{b \\in V} \\sum_{c \\in V} t_{a,j} t_{b,i} t_{c,k} u_{j,k,b,c} + \\sum_{b \\in V} f_{a,b} t_{b,i} + f_{a,i} - \\sum_{j \\in O} \\sum_{k \\in O} \\sum_{b \\in V} \\frac{1}{2} t_{a,b,j,k} u_{j,k,i,b} - \\sum_{j \\in O} \\sum_{k \\in O} \\sum_{b \\in V} t_{a,j} t_{b,k} u_{j,k,i,b} $$" ], "text/plain": [ "" @@ -331,8 +331,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "CPU times: user 81.8 ms, sys: 13 ms, total: 94.8 ms\n", - "Wall time: 8.5 s\n" + "CPU times: user 103 ms, sys: 13.6 ms, total: 116 ms\n", + "Wall time: 8.45 s\n" ] } ], @@ -358,7 +358,7 @@ { "data": { "text/latex": [ - "$$u_{a,b,i,j} + \\sum_{k \\in O} t_{a,k} u_{b,k,i,j} - \\sum_{k \\in O} f_{k,i} t_{a,b,k,j} - \\sum_{k \\in O} f_{k,j} t_{a,b,i,k} - \\sum_{k \\in O} t_{b,k} u_{a,k,i,j} + \\sum_{c \\in V} f_{b,c} t_{a,c,i,j} + \\sum_{c \\in V} t_{c,i} u_{a,b,c,j} + \\sum_{c \\in V} t_{c,j} u_{a,b,i,c} - \\sum_{c \\in V} f_{a,c} t_{b,c,i,j} + \\sum_{k \\in O} \\sum_{l \\in O} \\frac{1}{2} t_{a,b,k,l} u_{k,l,i,j} + \\sum_{k \\in O} \\sum_{l \\in O} t_{a,k} t_{b,l} u_{k,l,i,j} + \\sum_{k \\in O} \\sum_{c \\in V} t_{a,c,k,j} u_{b,k,i,c} + \\sum_{k \\in O} \\sum_{c \\in V} t_{b,c,i,k} u_{a,k,c,j} - \\sum_{k \\in O} \\sum_{c \\in V} t_{a,c,i,k} u_{b,k,c,j} - \\sum_{k \\in O} \\sum_{c \\in V} t_{b,c,k,j} u_{a,k,i,c} + \\sum_{k \\in O} \\sum_{c \\in V} f_{k,c} t_{a,k} t_{b,c,i,j} + \\sum_{k \\in O} \\sum_{c \\in V} t_{a,k} t_{c,i} u_{b,k,c,j} + \\sum_{k \\in O} \\sum_{c \\in V} t_{a,k} t_{c,j} u_{b,k,i,c} - \\sum_{k \\in O} \\sum_{c \\in V} f_{k,c} t_{b,k} t_{a,c,i,j} - \\sum_{k \\in O} \\sum_{c \\in V} f_{k,c} t_{c,i} t_{a,b,k,j} - \\sum_{k \\in O} \\sum_{c \\in V} f_{k,c} t_{c,j} t_{a,b,i,k} - \\sum_{k \\in O} \\sum_{c \\in V} t_{b,k} t_{c,i} u_{a,k,c,j} - \\sum_{k \\in O} \\sum_{c \\in V} t_{b,k} t_{c,j} u_{a,k,i,c} + \\sum_{c \\in V} \\sum_{d \\in V} \\frac{1}{2} t_{c,d,i,j} u_{a,b,c,d} + \\sum_{c \\in V} \\sum_{d \\in V} t_{c,i} t_{d,j} u_{a,b,c,d} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} t_{a,l} t_{b,c,i,k} u_{k,l,c,j} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} t_{b,l} t_{a,c,k,j} u_{k,l,i,c} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} t_{c,l} t_{a,b,i,k} u_{k,l,c,j} - \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} t_{a,l} t_{b,c,k,j} u_{k,l,i,c} - \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} t_{b,l} t_{a,c,i,k} u_{k,l,c,j} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\frac{1}{2} t_{c,i} t_{a,b,k,l} u_{k,l,c,j} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\frac{1}{2} t_{c,j} t_{a,b,k,l} u_{k,l,i,c} - \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} t_{c,l} t_{a,b,k,j} u_{k,l,i,c} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} t_{a,k} t_{b,l} t_{c,i} u_{k,l,c,j} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} t_{a,k} t_{b,l} t_{c,j} u_{k,l,i,c} + \\sum_{k \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{d,i} t_{b,c,k,j} u_{a,k,c,d} + \\sum_{k \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{d,j} t_{b,c,i,k} u_{a,k,c,d} + \\sum_{k \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{d,k} t_{a,c,i,j} u_{b,k,c,d} + \\sum_{k \\in O} \\sum_{c \\in V} \\sum_{d \\in V} \\frac{1}{2} t_{a,k} t_{c,d,i,j} u_{b,k,c,d} - \\sum_{k \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{d,i} t_{a,c,k,j} u_{b,k,c,d} - \\sum_{k \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{d,j} t_{a,c,i,k} u_{b,k,c,d} - \\sum_{k \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{d,k} t_{b,c,i,j} u_{a,k,c,d} + \\sum_{k \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{a,k} t_{c,i} t_{d,j} u_{b,k,c,d} - \\sum_{k \\in O} \\sum_{c \\in V} \\sum_{d \\in V} \\frac{1}{2} t_{b,k} t_{c,d,i,j} u_{a,k,c,d} - \\sum_{k \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{b,k} t_{c,i} t_{d,j} u_{a,k,c,d} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{a,c,k,j} t_{b,d,i,l} u_{k,l,c,d} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} \\frac{1}{4} t_{a,b,k,l} t_{c,d,i,j} u_{k,l,c,d} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} \\frac{1}{2} t_{a,b,l,j} t_{c,d,i,k} u_{k,l,c,d} - \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{a,c,i,k} t_{b,d,l,j} u_{k,l,c,d} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} \\frac{1}{2} t_{a,d,i,j} t_{b,c,k,l} u_{k,l,c,d} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{a,k} t_{d,l} t_{b,c,i,j} u_{k,l,c,d} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{a,l} t_{d,i} t_{b,c,k,j} u_{k,l,c,d} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{a,l} t_{d,j} t_{b,c,i,k} u_{k,l,c,d} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{c,l} t_{d,j} t_{a,b,i,k} u_{k,l,c,d} - \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} \\frac{1}{2} t_{a,b,i,l} t_{c,d,k,j} u_{k,l,c,d} - \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} \\frac{1}{2} t_{a,c,k,l} t_{b,d,i,j} u_{k,l,c,d} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} \\frac{1}{2} t_{a,k} t_{b,l} t_{c,d,i,j} u_{k,l,c,d} - \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{b,k} t_{d,l} t_{a,c,i,j} u_{k,l,c,d} - \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{b,l} t_{d,i} t_{a,c,k,j} u_{k,l,c,d} - \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{b,l} t_{d,j} t_{a,c,i,k} u_{k,l,c,d} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} \\frac{1}{2} t_{c,i} t_{d,j} t_{a,b,k,l} u_{k,l,c,d} - \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{c,i} t_{d,l} t_{a,b,k,j} u_{k,l,c,d} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{a,k} t_{b,l} t_{c,i} t_{d,j} u_{k,l,c,d} $$" + "$$u_{a,b,i,j} + \\sum_{k \\in O} t_{a,k} u_{b,k,i,j} - \\sum_{k \\in O} f_{k,i} t_{a,b,k,j} - \\sum_{k \\in O} f_{k,j} t_{a,b,i,k} - \\sum_{k \\in O} t_{b,k} u_{a,k,i,j} + \\sum_{c \\in V} f_{b,c} t_{a,c,i,j} + \\sum_{c \\in V} t_{c,i} u_{a,b,c,j} + \\sum_{c \\in V} t_{c,j} u_{a,b,i,c} - \\sum_{c \\in V} f_{a,c} t_{b,c,i,j} + \\sum_{k \\in O} \\sum_{l \\in O} \\frac{1}{2} t_{a,b,k,l} u_{k,l,i,j} + \\sum_{k \\in O} \\sum_{l \\in O} t_{a,k} t_{b,l} u_{k,l,i,j} + \\sum_{k \\in O} \\sum_{c \\in V} t_{a,c,k,j} u_{b,k,i,c} + \\sum_{k \\in O} \\sum_{c \\in V} t_{b,c,i,k} u_{a,k,c,j} - \\sum_{k \\in O} \\sum_{c \\in V} t_{a,c,i,k} u_{b,k,c,j} - \\sum_{k \\in O} \\sum_{c \\in V} t_{b,c,k,j} u_{a,k,i,c} + \\sum_{k \\in O} \\sum_{c \\in V} f_{k,c} t_{a,k} t_{b,c,i,j} + \\sum_{k \\in O} \\sum_{c \\in V} t_{a,k} t_{c,i} u_{b,k,c,j} + \\sum_{k \\in O} \\sum_{c \\in V} t_{a,k} t_{c,j} u_{b,k,i,c} - \\sum_{k \\in O} \\sum_{c \\in V} f_{k,c} t_{c,j} t_{a,b,i,k} - \\sum_{k \\in O} \\sum_{c \\in V} f_{k,c} t_{c,i} t_{a,b,k,j} - \\sum_{k \\in O} \\sum_{c \\in V} f_{k,c} t_{b,k} t_{a,c,i,j} - \\sum_{k \\in O} \\sum_{c \\in V} t_{b,k} t_{c,i} u_{a,k,c,j} - \\sum_{k \\in O} \\sum_{c \\in V} t_{b,k} t_{c,j} u_{a,k,i,c} + \\sum_{c \\in V} \\sum_{d \\in V} \\frac{1}{2} t_{c,d,i,j} u_{a,b,c,d} + \\sum_{c \\in V} \\sum_{d \\in V} t_{c,i} t_{d,j} u_{a,b,c,d} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} t_{c,l} t_{a,b,i,k} u_{k,l,c,j} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} t_{b,l} t_{a,c,k,j} u_{k,l,i,c} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} t_{a,l} t_{b,c,i,k} u_{k,l,c,j} - \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} t_{c,l} t_{a,b,k,j} u_{k,l,i,c} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\frac{1}{2} t_{c,i} t_{a,b,k,l} u_{k,l,c,j} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\frac{1}{2} t_{c,j} t_{a,b,k,l} u_{k,l,i,c} - \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} t_{b,l} t_{a,c,i,k} u_{k,l,c,j} - \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} t_{a,l} t_{b,c,k,j} u_{k,l,i,c} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} t_{a,k} t_{b,l} t_{c,i} u_{k,l,c,j} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} t_{a,k} t_{b,l} t_{c,j} u_{k,l,i,c} + \\sum_{k \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{d,k} t_{a,c,i,j} u_{b,k,c,d} + \\sum_{k \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{d,j} t_{b,c,i,k} u_{a,k,c,d} + \\sum_{k \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{d,i} t_{b,c,k,j} u_{a,k,c,d} - \\sum_{k \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{d,j} t_{a,c,i,k} u_{b,k,c,d} - \\sum_{k \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{d,i} t_{a,c,k,j} u_{b,k,c,d} + \\sum_{k \\in O} \\sum_{c \\in V} \\sum_{d \\in V} \\frac{1}{2} t_{a,k} t_{c,d,i,j} u_{b,k,c,d} - \\sum_{k \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{d,k} t_{b,c,i,j} u_{a,k,c,d} + \\sum_{k \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{a,k} t_{c,i} t_{d,j} u_{b,k,c,d} - \\sum_{k \\in O} \\sum_{c \\in V} \\sum_{d \\in V} \\frac{1}{2} t_{b,k} t_{c,d,i,j} u_{a,k,c,d} - \\sum_{k \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{b,k} t_{c,i} t_{d,j} u_{a,k,c,d} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{a,c,k,j} t_{b,d,i,l} u_{k,l,c,d} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} \\frac{1}{4} t_{a,b,k,l} t_{c,d,i,j} u_{k,l,c,d} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} \\frac{1}{2} t_{a,b,l,j} t_{c,d,i,k} u_{k,l,c,d} - \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{a,c,i,k} t_{b,d,l,j} u_{k,l,c,d} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} \\frac{1}{2} t_{a,d,i,j} t_{b,c,k,l} u_{k,l,c,d} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{c,l} t_{d,j} t_{a,b,i,k} u_{k,l,c,d} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{a,k} t_{d,l} t_{b,c,i,j} u_{k,l,c,d} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{a,l} t_{d,j} t_{b,c,i,k} u_{k,l,c,d} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{a,l} t_{d,i} t_{b,c,k,j} u_{k,l,c,d} - \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} \\frac{1}{2} t_{a,b,i,l} t_{c,d,k,j} u_{k,l,c,d} - \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} \\frac{1}{2} t_{a,c,k,l} t_{b,d,i,j} u_{k,l,c,d} - \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{c,i} t_{d,l} t_{a,b,k,j} u_{k,l,c,d} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} \\frac{1}{2} t_{c,i} t_{d,j} t_{a,b,k,l} u_{k,l,c,d} - \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{b,k} t_{d,l} t_{a,c,i,j} u_{k,l,c,d} - \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{b,l} t_{d,j} t_{a,c,i,k} u_{k,l,c,d} - \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{b,l} t_{d,i} t_{a,c,k,j} u_{k,l,c,d} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} \\frac{1}{2} t_{a,k} t_{b,l} t_{c,d,i,j} u_{k,l,c,d} + \\sum_{k \\in O} \\sum_{l \\in O} \\sum_{c \\in V} \\sum_{d \\in V} t_{a,k} t_{b,l} t_{c,i} t_{d,j} u_{k,l,c,d} $$" ], "text/plain": [ "" @@ -385,7 +385,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 16, "metadata": { "collapsed": true }, @@ -409,12 +409,12 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 17, "metadata": {}, "outputs": [ { "data": { - "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFQAAAAUBAMAAADhHQeeAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n", + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFQAAAAUBAMAAADhHQeeAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nkMqvoJBb0D48ZBbdoboBnN8CnRvR/wG34G94WYqMUwAAAABJRU5ErkJggg==\n", "text/latex": [ "$$66 no^{4} nv^{4}$$" ], @@ -423,7 +423,7 @@ "66⋅no ⋅nv " ] }, - "execution_count": 15, + "execution_count": 17, "metadata": {}, "output_type": "execute_result" } @@ -443,15 +443,15 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "CPU times: user 12.1 s, sys: 383 ms, total: 12.4 s\n", - "Wall time: 33.7 s\n" + "CPU times: user 7.31 s, sys: 239 ms, total: 7.54 s\n", + "Wall time: 21.2 s\n" ] } ], @@ -459,9 +459,8 @@ "%%time\n", "\n", "eval_seq = optimize(\n", - " working_eqn, substs={p.nv: p.no * 10}, \n", - " strategy=Strategy.ALL | Strategy.SUM | Strategy.COMMON,\n", - " drop_cutoff=2\n", + " working_eqn, substs={p.nv: 5000, p.no: 1000}, \n", + " contr_strat=ContrStrat.EXHAUST\n", ")" ] }, @@ -474,20 +473,20 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 19, "metadata": {}, "outputs": [ { "data": { - "image/png": "iVBORw0KGgoAAAANSUhEUgAAABQAAAAPBAMAAAAWtvJmAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAMpndu3bvImbNiRBU\nq0Qb3U6NAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAhklEQVQIHWNgYGAQYmAoUnEEMhgYTBi4LzCs\nfwBksaYw8G5gYEsAMiumMLAZMPB+BDIXTGHg/A1mchRMAfIZmH8zMGxlADPfLwDKQ5i2DAw8AmAm\nkwIDwy4GMDMIqPzs3bvfrjLwKDCUAzkMKWC7w0HMLwzsVqt0DYCsJf9vcP7//x/EhAEADcgg/vMy\n4xgAAAAASUVORK5CYII=\n", + "image/png": "iVBORw0KGgoAAAANSUhEUgAAABQAAAAOBAMAAADd6iHDAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIom7VJlmdt1E7xDN\nMqsI8sYEAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAkklEQVQIHWNgEFIyYWBgUCq6wMAYwOCfwLBn\nAusBBvYvDPwNDKYMzAYMnCsZ9h/g/AhUAwL+CcwLwAwG7iYG/rPqkUAOo0Y0w/5jDFwOIAmtCft/\nM7CuBjG5VgPNYPvJwCjAwPyF4wAD2zcG/t9AJt8CkCiXAQPHR16gWiAvgcG/gOERwy4HBoapoZYM\nDEyhbxkAA2IjsmKWDd8AAAAASUVORK5CYII=\n", "text/latex": [ - "$$42$$" + "$$36$$" ], "text/plain": [ - "42" + "36" ] }, - "execution_count": 17, + "execution_count": 19, "metadata": {}, "output_type": "execute_result" } @@ -498,21 +497,21 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 20, "metadata": {}, "outputs": [ { "data": { - "image/png": "iVBORw0KGgoAAAANSUhEUgAAARIAAAAWBAMAAAD+/w6yAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nn97+2tuT7Svoyv4JmtBdm4Xu/vbufoj/oT1QDxejilEAAAAASUVORK5CYII=\n", + "image/png": "iVBORw0KGgoAAAANSUhEUgAAARIAAAAWBAMAAAD+/w6yAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n3/M9+XeBtrJ5QovoaDhuR3sDczPEX0kLUPHMIF1MAAAAAElFTkSuQmCC\n", "text/latex": [ - "$$4 no^{4} nv^{2} + 6 no^{3} nv^{3} + 2 no^{2} nv^{4}$$" + "$$4 no^{4} nv^{2} + 8 no^{3} nv^{3} + 2 no^{2} nv^{4}$$" ], "text/plain": [ " 4 2 3 3 2 4\n", - "4⋅no ⋅nv + 6⋅no ⋅nv + 2⋅no ⋅nv " + "4⋅no ⋅nv + 8⋅no ⋅nv + 2⋅no ⋅nv " ] }, - "execution_count": 18, + "execution_count": 20, "metadata": {}, "output_type": "execute_result" } @@ -531,7 +530,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 21, "metadata": {}, "outputs": [ { @@ -540,7 +539,7 @@ "True" ] }, - "execution_count": 19, + "execution_count": 21, "metadata": {}, "output_type": "execute_result" } @@ -560,13 +559,13 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/latex": [ - "$$\\tau^{0}_{i,j,a,b} = t_{b,a,j,i} + 2 t_{a,i} t_{b,j} $$" + "$$\\tau^{0}_{i,j,a,b} = t_{b,a,j,i} + 2 t_{a,i} t_{b,j} $$" ], "text/plain": [ "" @@ -578,7 +577,7 @@ { "data": { "text/latex": [ - "$$\\tau^{1}_{i,j,k,a} = \\sum_{b \\in V} t_{b,i} u_{k,j,b,a} $$" + "$$\\tau^{1}_{i,j,k,a} = \\sum_{b \\in V} t_{b,i} u_{k,j,b,a} $$" ], "text/plain": [ "" @@ -602,31 +601,7 @@ { "data": { "text/latex": [ - "$$\\tau^{3}_{i,a} = \\sum_{j \\in O} \\sum_{b \\in V} t_{b,j} u_{j,i,b,a} + f_{i,a} $$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$$\\tau^{4}_{i,j} = \\sum_{a \\in V} f_{i,a} t_{a,j} $$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$$\\tau^{5}_{i,j} = - \\sum_{k \\in O} \\sum_{a \\in V} t_{a,k} u_{k,i,j,a} $$" + "$$\\tau^{3}_{i,a} = f_{i,a} + \\sum_{j \\in O} \\sum_{b \\in V} t_{b,j} u_{j,i,b,a} $$" ], "text/plain": [ "" @@ -638,7 +613,7 @@ { "data": { "text/latex": [ - "$$\\tau^{6}_{i,j} = \\sum_{k \\in O} \\sum_{a \\in V} \\sum_{b \\in V} \\tau^{0}_{k,j,a,b} u_{k,i,a,b} $$" + "$$\\tau^{4}_{i,j} = \\sum_{a \\in V} f_{i,a} t_{a,j} $$" ], "text/plain": [ "" @@ -650,7 +625,7 @@ { "data": { "text/latex": [ - "$$\\tau^{7}_{i,j} = 2 f_{i,j} + 2 \\tau^{4}_{i,j} + 2 \\tau^{5}_{i,j} + \\tau^{6}_{i,j} $$" + "$$\\tau^{5}_{i,j} = - \\sum_{k \\in O} \\sum_{a \\in V} t_{a,k} u_{k,i,j,a} $$" ], "text/plain": [ "" @@ -662,7 +637,7 @@ { "data": { "text/latex": [ - "$$\\tau^{8}_{i,j,a,b} = \\sum_{k \\in O} f_{k,i} t_{b,a,k,j} $$" + "$$\\tau^{6}_{i,j} = \\sum_{k \\in O} \\sum_{a \\in V} \\sum_{b \\in V} \\tau^{0}_{k,j,a,b} u_{k,i,a,b} $$" ], "text/plain": [ "" @@ -674,7 +649,7 @@ { "data": { "text/latex": [ - "$$\\tau^{9}_{i,j,a,b} = - \\sum_{c \\in V} t_{c,i} u_{b,a,j,c} $$" + "$$\\tau^{7}_{i,j} = 2 f_{i,j} + 2 \\tau^{4}_{i,j} + 2 \\tau^{5}_{i,j} + \\tau^{6}_{i,j} $$" ], "text/plain": [ "" @@ -686,7 +661,7 @@ { "data": { "text/latex": [ - "$$\\tau^{10}_{i,j} = 2 \\tau^{4}_{i,j} + 2 \\tau^{5}_{i,j} + \\tau^{6}_{i,j} $$" + "$$\\tau^{8}_{i,j,a,b} = - \\sum_{k \\in O} t_{a,k} u_{k,i,j,b} $$" ], "text/plain": [ "" @@ -698,7 +673,7 @@ { "data": { "text/latex": [ - "$$\\tau^{11}_{i,j,a,b} = \\sum_{k \\in O} \\tau^{10}_{k,i} t_{a,b,k,j} $$" + "$$\\tau^{9}_{i,j,a,b} = - \\sum_{c \\in V} t_{c,i} u_{j,a,c,b} $$" ], "text/plain": [ "" @@ -710,7 +685,7 @@ { "data": { "text/latex": [ - "$$\\tau^{12}_{i,j,a,b} = 2 \\tau^{8}_{i,j,b,a} - 2 \\tau^{9}_{i,j,b,a} + \\tau^{11}_{j,i,b,a} $$" + "$$\\tau^{10}_{i,j,a,b} = t_{b,a,j,i} - t_{a,j} t_{b,i} $$" ], "text/plain": [ "" @@ -722,7 +697,7 @@ { "data": { "text/latex": [ - "$$\\tau^{13}_{i,j,a,b} = - \\sum_{k \\in O} t_{a,k} u_{k,b,j,i} $$" + "$$\\tau^{11}_{i,j,a,b} = \\sum_{k \\in O} \\sum_{c \\in V} \\tau^{10}_{k,i,c,a} u_{k,j,c,b} $$" ], "text/plain": [ "" @@ -734,7 +709,7 @@ { "data": { "text/latex": [ - "$$\\tau^{14}_{i,j,a,b} = \\sum_{k \\in O} \\sum_{c \\in V} t_{c,a,k,i} u_{k,j,c,b} $$" + "$$\\tau^{12}_{i,j,a,b} = - u_{j,a,i,b} + \\tau^{8}_{j,i,a,b} + \\tau^{9}_{i,j,a,b} + \\tau^{11}_{i,j,a,b} $$" ], "text/plain": [ "" @@ -746,7 +721,7 @@ { "data": { "text/latex": [ - "$$\\tau^{15}_{i,j,a,b} = \\sum_{k \\in O} \\sum_{c \\in V} t_{c,a,k,i} \\tau^{14}_{j,k,b,c} $$" + "$$\\tau^{13}_{i,j,a,b} = \\sum_{k \\in O} \\sum_{c \\in V} t_{c,b,k,j} \\tau^{12}_{i,k,a,c} $$" ], "text/plain": [ "" @@ -758,7 +733,7 @@ { "data": { "text/latex": [ - "$$\\tau^{16}_{i,j,a,b} = \\sum_{c \\in V} f_{a,c} t_{c,b,j,i} $$" + "$$\\tau^{14}_{i,a,b,c} = - u_{i,a,c,b} + \\sum_{j \\in O} t_{a,j} u_{j,i,b,c} $$" ], "text/plain": [ "" @@ -770,7 +745,7 @@ { "data": { "text/latex": [ - "$$\\tau^{17}_{a,b} = \\sum_{i \\in O} f_{i,a} t_{b,i} $$" + "$$\\tau^{15}_{a,b,c,d} = u_{b,a,d,c} - \\sum_{i \\in O} t_{a,i} u_{i,b,c,d} - \\sum_{i \\in O} t_{b,i} \\tau^{14}_{i,a,d,c} $$" ], "text/plain": [ "" @@ -782,7 +757,7 @@ { "data": { "text/latex": [ - "$$\\tau^{18}_{a,b} = - \\sum_{i \\in O} \\sum_{c \\in V} t_{c,i} u_{i,a,c,b} $$" + "$$\\tau^{16}_{i,j,a,b} = \\sum_{k \\in O} t_{a,k} \\tau^{2}_{i,k,j,b} $$" ], "text/plain": [ "" @@ -794,7 +769,7 @@ { "data": { "text/latex": [ - "$$\\tau^{19}_{a,b} = \\sum_{i \\in O} \\sum_{j \\in O} \\sum_{c \\in V} \\tau^{0}_{i,j,c,b} u_{i,j,c,a} $$" + "$$\\tau^{17}_{i,j,a,b} = u_{j,a,i,b} - \\tau^{9}_{i,j,a,b} - \\tau^{16}_{i,j,a,b} $$" ], "text/plain": [ "" @@ -806,7 +781,7 @@ { "data": { "text/latex": [ - "$$\\tau^{20}_{a,b} = 2 \\tau^{17}_{b,a} + 2 \\tau^{18}_{a,b} + \\tau^{19}_{b,a} $$" + "$$\\tau^{18}_{i,j,k,l} = - \\sum_{a \\in V} t_{a,i} u_{k,j,l,a} $$" ], "text/plain": [ "" @@ -818,7 +793,7 @@ { "data": { "text/latex": [ - "$$\\tau^{21}_{i,j,a,b} = \\sum_{c \\in V} \\tau^{20}_{a,c} t_{c,b,i,j} $$" + "$$\\tau^{19}_{i,j,a,b} = - t_{b,a,j,i} + 2 t_{a,j} t_{b,i} $$" ], "text/plain": [ "" @@ -830,7 +805,7 @@ { "data": { "text/latex": [ - "$$\\tau^{22}_{i,j,a,b} = - 2 \\tau^{13}_{j,i,a,b} + 2 \\tau^{15}_{j,i,a,b} - 2 \\tau^{16}_{j,i,a,b} + \\tau^{21}_{j,i,b,a} $$" + "$$\\tau^{20}_{i,j,k,l} = 2 u_{j,i,l,k} + 2 \\tau^{18}_{k,j,i,l} - 2 \\tau^{18}_{l,j,i,k} - \\sum_{a \\in V} \\sum_{b \\in V} \\tau^{19}_{l,k,a,b} u_{j,i,a,b} $$" ], "text/plain": [ "" @@ -842,7 +817,7 @@ { "data": { "text/latex": [ - "$$\\tau^{23}_{i,j,k,a} = \\sum_{b \\in V} t_{b,i} u_{j,a,k,b} $$" + "$$\\tau^{21}_{a,b} = \\sum_{i \\in O} f_{i,a} t_{b,i} $$" ], "text/plain": [ "" @@ -854,7 +829,7 @@ { "data": { "text/latex": [ - "$$\\tau^{24}_{i,j,a,b} = \\sum_{k \\in O} t_{a,k} \\tau^{23}_{i,k,j,b} $$" + "$$\\tau^{22}_{a,b} = - \\sum_{i \\in O} \\sum_{c \\in V} t_{c,i} u_{i,a,c,b} $$" ], "text/plain": [ "" @@ -866,7 +841,7 @@ { "data": { "text/latex": [ - "$$\\tau^{25}_{i,j,a,b} = - \\sum_{c \\in V} t_{c,i} u_{j,a,c,b} $$" + "$$\\tau^{23}_{a,b} = \\sum_{i \\in O} \\sum_{j \\in O} \\sum_{c \\in V} \\tau^{0}_{i,j,c,b} u_{i,j,c,a} $$" ], "text/plain": [ "" @@ -878,7 +853,7 @@ { "data": { "text/latex": [ - "$$\\tau^{26}_{i,j,a,b} = \\sum_{k \\in O} t_{a,k} \\tau^{2}_{i,k,j,b} $$" + "$$\\tau^{24}_{a,b} = - 2 f_{a,b} + 2 \\tau^{21}_{b,a} + 2 \\tau^{22}_{a,b} + \\tau^{23}_{b,a} $$" ], "text/plain": [ "" @@ -890,7 +865,7 @@ { "data": { "text/latex": [ - "$$\\tau^{27}_{i,j,a,b} = - u_{j,a,i,b} + \\tau^{25}_{i,j,a,b} + \\tau^{26}_{i,j,a,b} $$" + "$$\\tau^{25}_{i,j,a,b} = \\sum_{c \\in V} \\tau^{24}_{a,c} t_{c,b,i,j} $$" ], "text/plain": [ "" @@ -902,7 +877,7 @@ { "data": { "text/latex": [ - "$$\\tau^{28}_{i,j,a,b} = \\sum_{k \\in O} \\sum_{c \\in V} t_{c,b,k,j} \\tau^{27}_{i,k,a,c} $$" + "$$\\tau^{26}_{i,j,k,a} = \\sum_{b \\in V} t_{b,i} u_{j,a,k,b} $$" ], "text/plain": [ "" @@ -914,7 +889,7 @@ { "data": { "text/latex": [ - "$$\\tau^{29}_{i,j,a,b} = \\tau^{24}_{i,j,a,b} + \\tau^{28}_{j,i,b,a} $$" + "$$\\tau^{27}_{i,j,a,b} = u_{i,a,j,b} - \\tau^{9}_{j,i,a,b} $$" ], "text/plain": [ "" @@ -926,7 +901,7 @@ { "data": { "text/latex": [ - "$$\\tau^{30}_{i,j,a,b} = - t_{b,a,j,i} + 2 t_{a,j} t_{b,i} $$" + "$$\\tau^{28}_{i,j,k,l} = u_{j,i,l,k} - \\tau^{18}_{l,j,i,k} $$" ], "text/plain": [ "" @@ -938,7 +913,7 @@ { "data": { "text/latex": [ - "$$\\tau^{31}_{i,j,k,l} = - \\sum_{a \\in V} t_{a,i} u_{k,j,l,a} $$" + "$$\\tau^{29}_{i,j,k,a} = - u_{i,a,k,j} - \\tau^{26}_{j,i,k,a} + \\sum_{b \\in V} t_{b,k} \\tau^{27}_{i,j,a,b} - \\sum_{l \\in O} t_{a,l} \\tau^{28}_{l,i,k,j} $$" ], "text/plain": [ "" @@ -950,7 +925,7 @@ { "data": { "text/latex": [ - "$$\\tau^{32}_{i,j,k,l} = 2 u_{j,i,l,k} + 2 \\tau^{31}_{k,j,i,l} - 2 \\tau^{31}_{l,j,i,k} - \\sum_{a \\in V} \\sum_{b \\in V} \\tau^{30}_{l,k,a,b} u_{j,i,a,b} $$" + "$$\\tau^{30}_{i,a,b,c} = - u_{b,a,i,c} + \\sum_{d \\in V} t_{d,i} u_{a,b,d,c} $$" ], "text/plain": [ "" @@ -962,7 +937,7 @@ { "data": { "text/latex": [ - "$$\\tau^{33}_{a,b,c,d} = - \\sum_{i \\in O} t_{a,i} u_{i,b,d,c} $$" + "$$\\tau^{31}_{i,j,a,b} = \\sum_{k \\in O} \\tau^{7}_{k,j} t_{a,b,k,i} $$" ], "text/plain": [ "" @@ -974,7 +949,7 @@ { "data": { "text/latex": [ - "$$\\tau^{34}_{a,b,c,d} = u_{b,a,d,c} + \\tau^{33}_{a,b,d,c} - \\tau^{33}_{b,a,d,c} $$" + "$$\\tau^{32}_{i,j,k,a} = u_{j,a,k,i} + \\tau^{26}_{i,j,k,a} $$" ], "text/plain": [ "" @@ -986,7 +961,7 @@ { "data": { "text/latex": [ - "$$e = \\sum_{i \\in O} \\sum_{a \\in V} f_{i,a} t_{a,i} + \\sum_{i \\in O} \\sum_{j \\in O} \\sum_{a \\in V} \\sum_{b \\in V} \\frac{1}{4} \\tau^{0}_{i,j,a,b} u_{i,j,a,b} $$" + "$$e = \\sum_{i \\in O} \\sum_{a \\in V} f_{i,a} t_{a,i} + \\sum_{i \\in O} \\sum_{j \\in O} \\sum_{a \\in V} \\sum_{b \\in V} \\frac{1}{4} \\tau^{0}_{i,j,a,b} u_{i,j,a,b} $$" ], "text/plain": [ "" @@ -998,7 +973,7 @@ { "data": { "text/latex": [ - "$$t_{a,i} = \\sum_{b \\in V} f_{a,b} t_{b,i} - \\sum_{j \\in O} \\sum_{b \\in V} t_{b,j} u_{j,a,i,b} + f_{a,i} - \\sum_{j \\in O} \\sum_{k \\in O} \\sum_{b \\in V} \\frac{1}{2} t_{b,a,j,k} \\tau^{2}_{i,j,k,b} + \\sum_{j \\in O} \\sum_{b \\in V} \\tau^{3}_{j,b} t_{b,a,j,i} + \\sum_{j \\in O} \\sum_{b \\in V} \\sum_{c \\in V} \\frac{1}{2} \\tau^{0}_{j,i,b,c} u_{j,a,b,c} - \\sum_{j \\in O} \\frac{1}{2} t_{a,j} \\tau^{7}_{j,i} $$" + "$$t_{a,i} = - \\sum_{j \\in O} \\sum_{b \\in V} t_{b,j} u_{j,a,i,b} + \\sum_{b \\in V} f_{a,b} t_{b,i} + f_{a,i} - \\sum_{j \\in O} \\sum_{k \\in O} \\sum_{b \\in V} \\frac{1}{2} t_{b,a,j,k} \\tau^{2}_{i,j,k,b} + \\sum_{j \\in O} \\sum_{b \\in V} \\sum_{c \\in V} \\frac{1}{2} \\tau^{0}_{j,i,b,c} u_{j,a,b,c} + \\sum_{j \\in O} \\sum_{b \\in V} \\tau^{3}_{j,b} t_{b,a,j,i} - \\sum_{j \\in O} \\frac{1}{2} t_{a,j} \\tau^{7}_{j,i} $$" ], "text/plain": [ "" @@ -1010,7 +985,7 @@ { "data": { "text/latex": [ - "$$t_{a,b,i,j} = u_{b,a,j,i} - \\frac{1}{2} \\tau^{12}_{i,j,a,b} + \\frac{1}{2} \\tau^{12}_{j,i,a,b} - \\frac{1}{2} \\tau^{22}_{i,j,a,b} + \\frac{1}{2} \\tau^{22}_{i,j,b,a} + \\tau^{29}_{i,j,a,b} - \\tau^{29}_{i,j,b,a} - \\tau^{29}_{j,i,a,b} + \\tau^{29}_{j,i,b,a} - \\sum_{k \\in O} \\sum_{l \\in O} \\frac{1}{4} \\tau^{30}_{k,l,b,a} \\tau^{32}_{k,l,j,i} - \\sum_{c \\in V} \\sum_{d \\in V} \\frac{1}{2} \\tau^{30}_{j,i,c,d} \\tau^{34}_{b,a,c,d} $$" + "$$t_{a,b,i,j} = u_{b,a,j,i} - \\sum_{c \\in V} t_{c,i} u_{a,b,j,c} + \\tau^{13}_{i,j,a,b} - \\tau^{13}_{j,i,a,b} + \\sum_{c \\in V} \\sum_{d \\in V} \\frac{1}{2} t_{c,d,j,i} \\tau^{15}_{b,a,c,d} - \\sum_{k \\in O} \\sum_{c \\in V} \\tau^{10}_{k,i,c,a} \\tau^{17}_{j,k,b,c} + \\sum_{k \\in O} \\sum_{c \\in V} t_{c,a,k,j} \\tau^{17}_{i,k,b,c} + \\sum_{k \\in O} \\sum_{l \\in O} \\frac{1}{4} t_{b,a,k,l} \\tau^{20}_{k,l,j,i} - \\frac{1}{2} \\tau^{25}_{j,i,b,a} + \\frac{1}{2} \\tau^{25}_{j,i,a,b} - \\sum_{k \\in O} t_{b,k} \\tau^{29}_{k,j,i,a} - \\sum_{c \\in V} t_{c,j} \\tau^{30}_{i,b,a,c} + \\frac{1}{2} \\tau^{31}_{j,i,b,a} - \\frac{1}{2} \\tau^{31}_{i,j,b,a} - \\sum_{k \\in O} t_{a,k} \\tau^{32}_{j,k,i,b} $$" ], "text/plain": [ "" @@ -1024,15 +999,6 @@ "for eqn in eval_seq:\n", " eqn.display(False)" ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [] } ], "metadata": { @@ -1051,7 +1017,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.5.3" + "version": "3.6.2" } }, "nbformat": 4,