{"text": "\n## recursive implementation\n\nfibonacci_rec := function( n )\n  \n  if n = 1 or n = 2 then\n      \n      return 1;\n      \n  fi;\n  \n  return fibonacci_rec( n - 1 ) + fibonacci_rec( n - 2 );\n  \nend;\n\n## iterative implementation\n\nfibonacci_iterative := function( n )\n  local prev, prev2, curr_fib; \n  \n  if n = 1 or n = 2 then\n      \n      return 1;\n      \n  fi;\n  \n  prev := 1;\n  \n  prev2 := 1;\n  \n  while n > 2 do\n      \n      curr_fib := prev + prev2;\n      \n      prev2 := prev;\n      \n      prev := curr_fib;\n      \n      n := n - 1;\n      \n  od;\n  \n  return curr_fib;\n  \nend;\n\n## using the internal function\n\nfibonacci_internal := i -> Fibonacci( i );\n\n## fibonacci iterator\n\nfibonacci_iterator := function( )\n  local previous_list;\n  \n  previous_list := [ 1, 1 ];\n  \n  return function( )\n    local ret_val, tmp_val;\n    \n    ret_val := previous_list[ 1 ];\n    \n    tmp_val := previous_list[ 1 ] + previous_list[ 2 ];\n    \n    previous_list[ 1 ] := previous_list[ 2 ];\n    \n    previous_list[ 2 ] := tmp_val;\n    \n    return ret_val;\n    \n  end;\n  \nend;\n\n", "meta": {"hexsha": "7c52bbed7c8b13c949baf6a8cb46c07ca2320e82", "size": 1055, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "Fibonacci_series/GAP/sebasguts/fibonacci.gi", "max_stars_repo_name": "Mynogs/Algorithm-Implementations", "max_stars_repo_head_hexsha": "13a74821fc1f0f7becaa9fb63b98e94134936bdb", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1184, "max_stars_repo_stars_event_min_datetime": "2015-01-01T14:11:29.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-21T19:40:47.000Z", "max_issues_repo_path": "Fibonacci_series/GAP/sebasguts/fibonacci.gi", "max_issues_repo_name": "Mynogs/Algorithm-Implementations", "max_issues_repo_head_hexsha": "13a74821fc1f0f7becaa9fb63b98e94134936bdb", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 89, "max_issues_repo_issues_event_min_datetime": "2015-01-01T15:49:17.000Z", "max_issues_repo_issues_event_max_datetime": "2021-12-05T19:11:38.000Z", "max_forks_repo_path": "Fibonacci_series/GAP/sebasguts/fibonacci.gi", "max_forks_repo_name": "Mynogs/Algorithm-Implementations", "max_forks_repo_head_hexsha": "13a74821fc1f0f7becaa9fb63b98e94134936bdb", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 388, "max_forks_repo_forks_event_min_datetime": "2015-01-02T03:26:17.000Z", "max_forks_repo_forks_event_max_datetime": "2022-03-24T14:36:10.000Z", "avg_line_length": 14.0666666667, "max_line_length": 57, "alphanum_fraction": 0.5355450237, "num_tokens": 305, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9674102571131692, "lm_q2_score": 0.9005297881200701, "lm_q1q2_score": 0.8711817538633048}}
{"text": "# GAP has built-in support for quaternions\n\nA := QuaternionAlgebra(Rationals);\n# <algebra-with-one of dimension 4 over Rationals>\n\nb := BasisVectors(Basis(A));\n# [ e, i, j, k ]\n\nq := [1, 2, 3, 4]*b;\n# e+(2)*i+(3)*j+(4)*k\n\n# Conjugate\nComplexConjugate(q);\n# e+(-2)*i+(-3)*j+(-4)*k\n\n# Division\n1/q;\n# (1/30)*e+(-1/15)*i+(-1/10)*j+(-2/15)*k\n\n# Computing norm may be difficult, since the result would be in a quadratic field.\n# Sqrt exists in GAP, but it is quite unusual: see ?E in GAP documentation, and the following example\nSqrt(5/3);\n# 1/3*E(60)^7+1/3*E(60)^11-1/3*E(60)^19-1/3*E(60)^23-1/3*E(60)^31+1/3*E(60)^43-1/3*E(60)^47+1/3*E(60)^59\n\n# However, the square of the norm is easy to compute\nq*ComplexConjugate(q);\n# (30)*e\n\nq1 := [2, 3, 4, 5]*b;\n# (2)*e+(3)*i+(4)*j+(5)*k\n\nq2 := [3, 4, 5, 6]*b;\n# (3)*e+(4)*i+(5)*j+(6)*k\n\nq1*q2 - q2*q1;\n# (-2)*i+(4)*j+(-2)*k\n\n# Can't add directly to a rational, one must make a quaternion of it\nr := 5/3*b[1];\n# (5/3)*e\nr + q;\n# (8/3)*e+(2)*i+(3)*j+(4)*k\n\n# For multiplication, no problem (we are in an algebra over rationals !)\nr*q;\n# (5/3)*e+(10/3)*i+(5)*j+(20/3)*k\n5/3*q;\n# (5/3)*e+(10/3)*i+(5)*j+(20/3)*k\n\n# Negative\n-q;\n(-1)*e+(-2)*i+(-3)*j+(-4)*k\n\n\n# While quaternions are built-in, you can define an algebra in GAP by specifying it's multiplication table.\n# See tutorial, p. 60, and reference of the functions used below.\n\n# A multiplication table of dimension 4.\n\nT := EmptySCTable(4, 0);\nSetEntrySCTable(T, 1, 1, [1, 1]);\nSetEntrySCTable(T, 1, 2, [1, 2]);\nSetEntrySCTable(T, 1, 3, [1, 3]);\nSetEntrySCTable(T, 1, 4, [1, 4]);\nSetEntrySCTable(T, 2, 1, [1, 2]);\nSetEntrySCTable(T, 2, 2, [-1, 1]);\nSetEntrySCTable(T, 2, 3, [1, 4]);\nSetEntrySCTable(T, 2, 4, [-1, 3]);\nSetEntrySCTable(T, 3, 1, [1, 3]);\nSetEntrySCTable(T, 3, 2, [-1, 4]);\nSetEntrySCTable(T, 3, 3, [-1, 1]);\nSetEntrySCTable(T, 3, 4, [1, 2]);\nSetEntrySCTable(T, 4, 1, [1, 4]);\nSetEntrySCTable(T, 4, 2, [1, 3]);\nSetEntrySCTable(T, 4, 3, [-1, 2]);\nSetEntrySCTable(T, 4, 4, [-1, 1]);\n\nA := AlgebraByStructureConstants(Rationals, T, [\"e\", \"i\", \"j\", \"k\"]);\nb := GeneratorsOfAlgebra(A);\n\nIsAssociative(A);\n# true\n\nIsCommutative(A);\n# false\n\n# Then, like above\n\nq := [1, 2, 3, 4]*b;\n# e+(2)*i+(3)*j+(4)*k\n\n# However, as is, GAP does not know division or conjugate on this algebra.\n# QuaternionAlgebra is useful as well for extensions of rationals,\n# and this one _has_ conjugate and division, as seen previously.\n\n# Try this on Q[z] where z is the square root of 5 (in GAP it's ER(5))\nF := FieldByGenerators([ER(5)]);\nA := QuaternionAlgebra(F);\nb := GeneratorsOfAlgebra(A);\n\nq := [1, 2, 3, 4]*b;\n# e+(2)*i+(3)*j+(4)*k\n\n# Conjugate and division\n\nComplexConjugate(q);\n# e+(-2)*i+(-3)*j+(-4)*k\n\n1/q;\n# (1/30)*e+(-1/15)*i+(-1/10)*j+(-2/15)*k\n", "meta": {"hexsha": "94fc6c25888be156933a17923323e4e3873faff7", "size": 2734, "ext": "gap", "lang": "GAP", "max_stars_repo_path": "Task/Quaternion-type/GAP/quaternion-type.gap", "max_stars_repo_name": "LaudateCorpus1/RosettaCodeData", "max_stars_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_stars_repo_licenses": ["Info-ZIP"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2018-11-09T22:08:38.000Z", "max_stars_repo_stars_event_max_datetime": "2018-11-09T22:08:38.000Z", "max_issues_repo_path": "Task/Quaternion-type/GAP/quaternion-type.gap", "max_issues_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_issues_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_issues_repo_licenses": ["Info-ZIP"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Task/Quaternion-type/GAP/quaternion-type.gap", "max_forks_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_forks_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_forks_repo_licenses": ["Info-ZIP"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2018-11-09T22:08:40.000Z", "max_forks_repo_forks_event_max_datetime": "2018-11-09T22:08:40.000Z", "avg_line_length": 24.6306306306, "max_line_length": 107, "alphanum_fraction": 0.6038771031, "num_tokens": 1204, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.959154282922475, "lm_q2_score": 0.8918110375304409, "lm_q1q2_score": 0.8553843762048584}}