sage: mip.<x> = MixedIntegerLinearProgram('ppl') # base ring is QQ ## line 6 ## sage: lt = x[0] * vector([3,4]) + 1; lt ## line 7 ## (1, 1) + (3, 4)*x_0 sage: type(lt) ## line 9 ## <class 'sage.numerical.linear_tensor_element.LinearTensor'> sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 11 ## 0 sage: parent = MixedIntegerLinearProgram().linear_functions_parent().tensor(RDF^2) ## line 47 ## sage: parent({0: [1,2], 3: [-7,-8]}) ## line 48 ## (1.0, 2.0)*x_0 + (-7.0, -8.0)*x_3 sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 50 ## 0 sage: LT = MixedIntegerLinearProgram().linear_functions_parent().tensor(RDF^2) ## line 70 ## sage: LT({0: [1,2], 3: [-7,-8]}) ## line 71 ## (1.0, 2.0)*x_0 + (-7.0, -8.0)*x_3 sage: TestSuite(LT).run(skip=['_test_an_element', '_test_elements_eq_reflexive', '_test_elements_eq_symmetric', '_test_elements_eq_transitive', '_test_elements_neq', '_test_additive_associativity', '_test_elements', '_test_pickling', '_test_zero']) ## line 74 ## sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 78 ## 0 sage: p = MixedIntegerLinearProgram().linear_functions_parent().tensor(RDF^2) ## line 95 ## sage: lt = p({0:[1,2], 3:[4,5]}); lt ## line 96 ## (1.0, 2.0)*x_0 + (4.0, 5.0)*x_3 sage: lt[0] ## line 98 ## x_0 + 4*x_3 sage: lt[1] ## line 100 ## 2*x_0 + 5*x_3 sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 102 ## 0 sage: p = MixedIntegerLinearProgram().linear_functions_parent().tensor(RDF^2) ## line 120 ## sage: lt = p({0:[1,2], 3:[4,5]}) ## line 121 ## sage: lt.dict() ## line 122 ## {0: (1.0, 2.0), 3: (4.0, 5.0)} sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 124 ## 0 sage: mip.<b> = MixedIntegerLinearProgram() ## line 144 ## sage: lt = vector([1,2]) * b[3] + vector([4,5]) * b[0] - 5; lt ## line 145 ## (-5.0, -5.0) + (1.0, 2.0)*x_0 + (4.0, 5.0)*x_1 sage: lt.coefficient(b[3]) ## line 147 ## (1.0, 2.0) sage: lt.coefficient(0) # x_0 is b[3] ## line 149 ## (1.0, 2.0) sage: lt.coefficient(4) ## line 151 ## (0.0, 0.0) sage: lt.coefficient(-1) ## line 153 ## (-5.0, -5.0) sage: lt.coefficient(b[3] + b[4]) ## line 158 ## sage: lt.coefficient(2*b[3]) ## line 162 ## sage: mip.<q> = MixedIntegerLinearProgram(solver='ppl') ## line 166 ## sage: lt.coefficient(q[0]) ## line 167 ## sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 171 ## 0 sage: from sage.numerical.linear_functions import LinearFunctionsParent ## line 197 ## sage: R.<s,t> = RDF[] ## line 198 ## sage: LT = LinearFunctionsParent(RDF).tensor(R) ## line 199 ## sage: LT.an_element() # indirect doctest ## line 200 ## (s) + (5.0*s)*x_2 + (7.0*s)*x_5 sage: LT = LinearFunctionsParent(RDF).tensor(RDF^2) ## line 203 ## sage: LT.an_element() # indirect doctest ## line 204 ## (1.0, 0.0) + (5.0, 0.0)*x_2 + (7.0, 0.0)*x_5 sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 206 ## 0 sage: from sage.numerical.linear_functions import LinearFunctionsParent ## line 235 ## sage: LT = LinearFunctionsParent(RDF).tensor(RDF^(2,2)) ## line 236 ## sage: LT.an_element() # indirect doctest ## line 237 ## [1 + 5*x_2 + 7*x_5 1 + 5*x_2 + 7*x_5] [1 + 5*x_2 + 7*x_5 1 + 5*x_2 + 7*x_5] sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 240 ## 0 sage: from sage.numerical.linear_functions import LinearFunctionsParent ## line 278 ## sage: LT = LinearFunctionsParent(RDF).tensor(RDF^2) ## line 279 ## sage: LT({0: [1,2], 3: [-7,-8]}) + LT({2: [5,6], 3: [2,-2]}) + 16 ## line 280 ## (16.0, 16.0) + (1.0, 2.0)*x_0 + (5.0, 6.0)*x_2 + (-5.0, -10.0)*x_3 sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 282 ## 0 sage: from sage.numerical.linear_functions import LinearFunctionsParent ## line 298 ## sage: LT = LinearFunctionsParent(RDF).tensor(RDF^2) ## line 299 ## sage: -LT({0: [1,2], 3: [-7,-8]}) ## line 300 ## (-1.0, -2.0)*x_0 + (7.0, 8.0)*x_3 sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 302 ## 0 sage: from sage.numerical.linear_f